Kaskade Namespace Reference

Namespaces
namespace	AdaptationStrategy_Detail
namespace	Adaptivity
namespace	AmiraMeshReader
	Reader for Amira meshes.
namespace	Assembler
namespace	AssemblyDetail
namespace	BDDC
namespace	BoundaryInterpolationDetail
namespace	BoundaryLocatorDetail
namespace	BoundarySpace_Detail
namespace	Bridge
	Namespace of Classes that implement the abstract interface classes via the bridge-pattern.
namespace	CellLocatorDetail
namespace	CG_Detail
namespace	CoarseningDetail
namespace	Crsutil_Detail
namespace	DerivativeCheck
namespace	DirectSolver_Detail
namespace	DomainDecompositionPreconditionerDetail
namespace	DynamicMatrixDetail
namespace	Elastomechanics
namespace	ErrorestDetail
namespace	ErrorEstimator_Detail
namespace	Functional_Aux_Detail
namespace	FunctionSpace_Detail
namespace	FunctionViews
	Namespace of views on a FunctionSpaceElement Views on Function SpaceElements can be used in a restricted sense like FunctionSpaceElements. The idea is to transform a given function to another function while evaluating it at a certain point. Such a view has provide certain functionality:
namespace	GridIterateDetail
namespace	HierarchicErrorEstimator_Detail
namespace	ifff
	Creates a (linear) model to a linearization of a functional.
namespace	IOTools
namespace	JacobiPreconditionerDetail
namespace	LinAlg
namespace	LinearSpace_Detail
namespace	MultiGridSolver_Detail
namespace	OPT_MODEL_FUNCTIONS_Detail
namespace	PartitionedSpaceDetail
namespace	ScalarSpaceDetail
namespace	SchurPreconditionerDetail
namespace	SemiEulerDetail
namespace	Simplex
namespace	TaylorHoodPreconditionerDetail
namespace	TensorAccess
namespace	ThreadedMatrixDetail
namespace	WeakFunctionViews
	Namespace of classes that mimick a FunctionSpaceElement in a very weak sense.
namespace	XMLHelper
	Some helper's for a correct indentation of XML-code.

Classes
class	AbstractAdaptiveGrid
	Representation of an adaptive grid and a simple set of operations thereon. More...
class	AbstractChart
class	AbstractCompositeStepErrorEstimator
	Representation of an error estimator. More...
class	AbstractConnectedLinearization
class	AbstractErrorEstimate
	Representation of an error estimate, i.e. the output of an error estimator. More...
class	AbstractErrorEstimator
	Representation of an error estimator. More...
class	AbstractFlushConnection
	Abstract connection. More...
class	AbstractFunctional
	Representation of a nonlinear functional. More...
class	AbstractFunctionSpaceElement
	Abstract Vector for function space algorithms. More...
class	AbstractHierarchicalErrorEstimator
class	AbstractLinearization
	Abstract linearization. More...
class	AbstractNewtonDirection
	Class that models the functionality of a (possibly inexact) linear solver. More...
class	AbstractNorm
class	AbstractNormalDirection
class	AbstractParameterFunctional
	Creates a functional from a homotopy of functionals by inserting a parameter. More...
class	AbstractParameters
	Representation of parameters. More...
class	AbstractPreconditioner
class	AbstractScalarProduct
class	AbstractTangentialSpace
	Class that models the functionality of a (possibly inexact) linear solver. More...
struct	ActiveStressModelBase
	Convenience base class for active stress generation models providing numerical differentiation. More...
struct	AdaptationCoarseningPolicy
	policy class for LocalTransfer These two structures are used for determining whether to perform a "normal" grid transfer (default, AdaptionCoarseningPolicy), or to calculate prolongation matrices for a FE function space based on a HierarchicIndexSet (see mgtools.hh). More...
class	AdaptiveParameters
	Parameters that are used by SimpleAdaptiveRefinement. More...
class	AdditiveMultiGrid
	An additive multigrid preconditioner for P1 elements. More...
class	AdditiveSchwarzPreconditioner
struct	AddToFunctionSpaceElement
struct	AddToFunctionSpaceElement< FSE, CoeffVector, rbegin, rbegin >
class	AdjointEquationHBErrorEstimator
class	AdjointEquationLinearPropagationHBErrorEstimator
class	Adjugate
class	Adjugate< 2, Source >
class	Adjugate< 3, Source >
class	AdvectedFunctionView
	A weak function view that defines an advected function. More...
class	AgglomerationPreconditioner
	An agglomeration-based preconditioner for elliptic problems discretized with higher-order Lagrange finite elements. More...
class	AgglomerationPreconditioner< AssembledGalerkinOperator< Assembler, firstRow, firstRow+1, firstCol, firstCol+1, IstlInterfaceDetail::RangeBlockSelector< firstRow, firstRow+1, firstCol, firstCol+1 >, true > >
class	Algorithm
	Base class for algorithms. Provides a unified interface and some simple wrapper routines, which perform optional timing, etc. More...
struct	AlievPanfilov
	Phenomenological model by Aliev and Panfilov. More...
struct	AlwaysRegularizeWithThetaGuess
class	AngleFeatureDetector
	Specifying geometric features in terms of angles between face normals and edge tangents. More...
class	AnotherHBErrorEstimator
class	AnsysMeshReader
	Reader for Ansys *.inp grid files. More...
class	ApproximateSchurComplement
	Approximation of the schur complement according to Pearson/Wathen '10. More...
class	ApproximateSchurComplement2
	Approximation of the schur complement. More...
class	ARMSPreconditioner
class	AssembledGalerkinOperator
	An adaptor presenting a Dune::LinearOperator <domain_type,range_type> interface to a contiguous sub-blockmatrix of an assembled heterogeneous Galerkin operator. More...
class	BabuskaRheinboldtCriterion
	Babuska-Rheinboldt refinement criterion. Determines the refinement thresholds such that all cells with an error contribution exceeding the expected error contribution of the worst cell after refinement will be marked. This tends to equilibrate the error contributions quite fast. More...
struct	Barrier
	Barrier<q,p> = sum_{i=p}^{q} Barrier<i,i> More...
struct	Barrier< 0, 0 >
	Logarithmic Barrier functions. More...
struct	Barrier< q, q >
	Rational Barrier functions of order q/2+1 (gradient has rational order q/2+1) More...
class	BasicGridElement
class	BezierMortar
	Defines a constraint formulation where samples are weighted by Bezier test functions. More...
class	BlockDiagonalSchurPreconditioner
class	BlockLUFactorization
struct	BlockSchurParameters
class	BoomerAMG
class	BoundaryDisplacementByInterpolation
class	BoundaryEdge
	A class storing a boundary edge consisting of two vertex indices and associated boundary curve tangents. More...
class	BoundaryFace
	A class for representing displaced/deformed boundary faces. More...
class	BoundaryInterpolationDisplacement
	The BoundaryInterpolationDisplacement class provides a Kaskade WeakFunctionView on the displacement from grid to actual domain boundary (which is computed by boundary interpolation). More...
struct	BoundaryJumpsTimesTestFunction
class	BoundaryLocator
class	BoundaryMapper
	A local to global mapper implementation for boundary spaces, with functions defined on the domain boundary (or parts of it) only. More...
struct	BoundaryStar
	A class storing all the corners (vertex-boundaryface incidences) at a boundary vertex. More...
class	BoundaryTangents
	A class providing information about domain boundary tangent vectors. More...
class	BulkCriterion
	Bulk refinement criterion. Determines the refinement thresholds such that approximately the specified fraction of the total error is removed by the refinement (under the unrealistically optimistic assumption that refinement eliminates the error completely in that cell - in reality, it's only reduced by a certain factor, so the total error is reduced somewhat less). More...
class	BWErrorFunction
	Obtain an error function by solving local Neumann problems in the flavour of Bank/Weiser. More...
class	CacheBase
	Provides implementations of d1 and d2 for (possibly mixed) use of scalar and power spaces. More...
class	CachingBoundaryDetector
struct	CardioD2
class	CellData
	Class that stores information for each cell of a grid. More...
class	CellLocator
class	CellRanges
	A class storing cell ranges of roughly equal size for multithreaded mesh traversal. More...
class	CGBase
	regularized preconditioned conjugate gradient method More...
struct	CGFminModel
class	ChebyshevPreconditioner
	Preconditioner based on the Chebyshev semi-iteration. In order to provide a linear preconditioner the termination criterion based on relative descent in the energy-norm induced by the preconditioner is disabled here. Instead the preconditioner performs a fixed number of iterations thus yielding a linear preconditioner. More...
class	ChebyshevSemiIteration
	Preconditioned chebyshev semi iteration. More...
struct	CheckPoint
struct	ChooseProjectionPolicy
struct	ChooseProjectionPolicy< InexactTangentSpacePreconditioner< Functional, Assembler, components > >
class	Circle
class	Cofactor
struct	Components
	Helper class for specifying the number of components of a variable. More...
class	CompositeStep
class	ConcurrentQueue
	A concurrent fifo queue. More...
class	ConstantMapper
struct	ConstraintD1LipschitzConstant
struct	ConstructCoefficientVector
	A boost::fusion functor for generating coefficient vectors for given variables. More...
struct	ConstructElement
	A boost::fusion functor for generating function space elements for given variables. More...
class	ContinuousHierarchicExtensionMapper
	A degrees of freedom manager for globally continuous FEFunctionSpace s of piecewise polynomials. More...
class	ContinuousHierarchicExtensionMapperImplementation
class	ContinuousHierarchicMapper
	A degrees of freedom manager for globally continuous FEFunctionSpace s of piecewise polynomials. More...
class	ContinuousHierarchicMapperImplementation
class	ContinuousLagrangeBoundaryMapper
class	ContinuousLagrangeMapper
	A degrees of freedom manager for globally continuous FEFunctionSpace s of piecewise polynomials. More...
class	ContinuousLagrangeMapperImplementation
class	ContinuousLagrangeMapperSubdomain
	A local-to-global mapper for continuous finite elements on a subdomain. More...
class	ContinuousLagrangeMapperSubdomainImplementation
class	ContinuousScalarFunction
class	ContractionModelFunction
struct	ConvertTo
	Reports the converted type. More...
struct	ConvertTo< Dune::FieldMatrix< T, n, m >, Real >
struct	CopyFromFunctionSpaceElement
struct	CopyFromFunctionSpaceElement< FSE, CoeffVector, rbegin, rbegin >
struct	Corner
	A class storing algebraic and geometric information about a vertex-boundaryface incidence in simplicial grids. More...
struct	Creator
	Abstract base class of creators that can be registered at the pluggable factory. More...
struct	Creator< Factorization< Scalar > >
	Abstract base class for factorization creators to be plugged into a factorization factory. More...
class	CSCubicRegularization
struct	csr_matrix
class	Cube
class	CubicModel1dForFmin
class	CubicModelFunction
class	CUBThetaModelFunction
	For optimization with cubic upper bounds method. More...
class	DampedCovariantNewtonMethod
	Damped Newton's method that measures the Newton contraction via a simplified Newton step. More...
class	DampedCovariantNewtonParameters
	Paramters that are used and Logged by GuardedCovariantNewtonMethod. More...
class	DefaultDualPairing
	Default implementation of dual pairing (relies on scalar product operator * being defined) More...
struct	DefaultProjectionPolicy
class	DeformingGridManager
	A grid manager for asymptotically \( G^1 \)-continuous domains. More...
class	DenseCholeskyLocalMatrixStorage
	An inverse local matrix representation that simply stores a dense Cholesky factor. More...
class	DenseCholeskyStorageTag
	A parametrized tag type for selecting storage of inverses by dense Cholesky factors with floating point representation of type Scalar. More...
class	DenseInverseLocalMatrixStorage
	An inverse local matrix representation that simply stores the dense inverse. More...
class	DenseInverseStorageTag
	A parametrized tag type for selecting dense storage of inverses with floating point representation of type Scalar. More...
class	Deprecated
	Convenience class for marking deprecated functions. A static object of this class can be created inside deprecated functions. It will output a warning message to stderr if the deprecated function is called, but only once. More...
class	DerivativeChecker
	Class that checks the derivatives of a functional at a linearization point. More...
class	DetailedException
	A wrapper class for conveniently providing exceptions with context information. More...
class	Determinant
	A class for computing determinants and their derivatives. More...
class	Determinant< 2, Source >
class	Determinant< 3, Source >
	Determinant. More...
class	DiagonalCombiner
	A base class for implementing combiners with diagonal structure. More...
class	DifferentiableScalarFunction
struct	Dim
	Get dimension as nested integral static constexpr. More...
class	DiracMortar
	Defines a constraint formulation where each sample is taken as a single constraint of its own. More...
class	DirectBlockSchurSolver
class	DirectLinearSolver
	Direct solver.Implements Direct Solver Interface of Algorithms. More...
class	DirectNormalSolver
class	DirectPreconditioner
class	DirectPreconditionerFloatWrapper
class	DirectSolver
class	DirectSolver< Dune::FieldVector< S, n >, Dune::FieldVector< S, n > >
class	DirectSolverException
	To be raised if a direct solver fails. More...
class	DirichletNitscheBoundary
	Dirichlet boundary conditions by Nitsche's method. More...
class	DirichletPenaltyBoundary
	Dirichlet boundary conditions by the penalty approach. More...
class	DiscontinuousHierarchicExtensionMapper
	A degrees of freedom manager for FEFunctionSpace s of piecewise polynomials of given order. More...
class	DiscontinuousHierarchicExtensionMapperImplementation
class	DiscontinuousHierarchicMapper
	A degrees of freedom manager for FEFunctionSpace s of piecewise polynomials of order Order. More...
class	DiscontinuousHierarchicMapperImplementation
class	DiscontinuousLagrangeMapper
	A degrees of freedom manager for FEFunctionSpace s of piecewise polynomials of order Order. More...
class	DiscontinuousLagrangeMapperImplementation
class	DiscontinuousLagrangeMapperSubdomain
struct	DiscreteBlockTraits
struct	DoNotAlwaysRegularize
struct	DoNotMeasureTime
struct	DoRegularization
class	DualPairing
	Abstract base class for dual pairing of \( X \) and its dual space \( X^* \). More...
struct	Dummy
class	DynamicMatrix
	A LAPACK-compatible dense matrix class with shape specified at runtime. More...
class	EdgeScanner
	Class to scan functions along the edges of a computational grid. More...
class	EmbeddedErrorEstimator
	Embedded error estimation and mesh refinement. More...
class	EmptyShapeFunctionSet
struct	EnergyScalarProduct
class	EntityNumbering
struct	EntryTraits
struct	EntryTraits< Dune::FieldMatrix< Entry, n, m > >
struct	EntryTraits< Dune::FieldVector< Entry, n > >
struct	EntryTraits< Tensor< Entry, Sizes... > >
class	EquidistantLagrange
	Lagrange shape functions on an equidistant grid over the simplex. These are polynomial basis functions \( p_i \) over the unit simplex, together with interpolation nodes \( \xi_j \), such that \( p_i(\xi_j) = \delta_{ij} \) holds. More...
class	ErrorDistribution
struct	ErrorEstimationTraits
class	ErrorEstimatorBase
struct	EstimatorDescription
class	EtaModel
class	Euclid
class	EulerSDC
	Base class to perform SDC iterations based on forward Euler method. Total iterations performed depends on the value set for variable maxSDCiterations. More...
class	Exp
	Exponential function of the form a*exp(b*x) More...
class	ExtrapolationTableau
	Polynomial extrapolation following Aitken-Neville. More...
class	Factorization
	Abstract base class for matrix factorizations. More...
struct	FactorizationOptions
	The Options struct allows to specify several options of factorization. More...
class	Factory
	A pluggable factory. More...
class	FEFunctionSpace
	A representation of a finite element function space defined over a domain covered by a grid. More...
class	FentonKarma
	The 3-variable Fenton-Karma membrane model. More...
class	FileIOException
	An exception class for file IO errors. More...
class	FinalAdaptiveRefinement
	Performs error estimation and creates error indicators, but does not refine. Good for testing error estimators. More...
struct	FirstGreater
	A comparator functor that supports sorting std::pair by their first component. More...
struct	FirstLess
	A comparator functor that supports sorting std::pair by their first component. More...
class	FixedFractionCriterion
	Fixed fraction refinement criterion. Determines the refinement thresholds such that at least the specified fraction of the cells are marked for refinement. This ensures that not too few cells are marked, which could lead to very many refinement iterations, but may lead to erratic refinement if there are indeed only very local refinements necessary. More...
class	FixedSolverWithErrorEstimate
	Performs error estimation and creates error indicators, but does not refine. Good for testing error estimators. More...
class	ForwardingBoundaryDetector
class	FunctionalBase
	Convenience base class for the easy definition of variational functionals and weak formulations. More...
class	FunctionSpaceElement
	A class for representing finite element functions. More...
class	FunctionViewAdaptor
	An adaptor that allows to turn lambda functions into function views. More...
class	GaussSeidelPreconditioner
	A simple single-level symmetric Gauss-Seidel preconditioner. More...
class	GaussTimeGrid
	spectral time grid for defect correction methods with Gauss points More...
class	Gbit
	Iterative solution of a large linear system using an error based termination-criterium. Includes some special termination-criterium options which are used by the giantGbit code. More...
class	GeometricFeatureDetector
	The interface for specifying feature edges and feature vertices. More...
struct	Get
	Get object from reference or functor. Is itself a functor. More...
struct	Get< Type, Type >
class	GetEvaluators
	A boost::fusion functor for creating an evaluator from the space, using a shape function cache that is given on construction of the functor. More...
class	GetEvaluatorTypes
	A boost::fusion functor for extracting the evaluator type from a pointer to a FE space. This is more or less redundant to GetEvaluators, but no shape function cache type needs to be provided. More...
struct	GetScalar
	Get scalar type from Dune (-> field_type) or Kaskade (-> Scalar) member. More...
struct	GetSubType
struct	GetSubType< Scalar, dim, Dune::FieldMatrix< Scalar, dim, dim > >
class	GetVarArgs
	A boost::fusion functor for creating a variational arg from the space, using a shape function cache that is given on construction of the functor. More...
class	Giant
	Solution of a nonlinear system of equations by a damped Newton-method with adaptive precision control of the used iterative linear solver Gbit. More...
class	GlobalBarycentricPermutation
	A class for computing permutations of local vertex numbers of simplex subentities to a globally unique ordering. More...
class	GlobalLocalIndexRelationship
	The GlobalLocalIndexRelationship class provides relationships between local indices of (e.g. matrix) blocks and global indices (of the corresponding block matrix) More...
class	GoalOrientedErrorEstimator
struct	GradientAverage
struct	GradientAverageFull
struct	GradientJumpsTimesTestFunction
class	GridException
	An exception class for grid related errors. More...
struct	GridLocking
	Grid locking information based on grid type. More...
struct	GridLocking< Dune::GeometryGrid< HostGrid, Deformation, Allocator > >
class	GridManager
	Class that takes care of the transfer of data (of each FunctionSpaceElement) after modification of the grid. More...
class	GridManagerBase
	Basic functionality for managing grids and their refinement. More...
struct	GridSignals
	A class that provides access to signals that are emitted from the grid manager on various occasions. More...
class	GuardedCovariantNewtonParameters
	Paramters that are used and Logged by GuardedCovariantNewtonMethod. More...
struct	H1Norm
	H1-norms. More...
struct	H1SemiNorm
	H1-semi-norms. More...
struct	HalfGradientJump
class	HcurlConverter
	A class mapping local vectorial shape function values and gradients to global shape function values and gradients in \( H(\text{curl}) \) conforming FE spaces. More...
class	HdivConverter
	A class mapping local vectorial shape function values and gradients to global shape function values and gradients in \( H(\text{div}) \) conforming FE spaces. More...
class	HdivMapper
	Degrees of freedom manager for H(div) conforming elements. More...
class	HdivShapeFunctionSetContainer
class	HdivSimplexShapeFunction
	Vectorial \( H(\text{div}) \) conforming shape functions on the unit simplex. More...
class	HdivSimplexShapeFunctionSet
	A shape function set of \( H(\text{div}) \) conforming functions. More...
class	HierarchicalBasisErrorEstimator
class	HierarchicalBasisErrorEstimator2
class	HierarchicalBasisErrorEstimator3
class	HierarchicalBasisPreconditioner
	A hierarchical basis preconditioner. More...
class	HierarchicErrorEstimator
	Defines assembly of hierarchically extended problems for defining DLY style error estimators. More...
class	HierarchicExtensionMapperImplementation
class	HierarchicExtensionShapeFunctionSetContainer
class	HierarchicExtensionSimplexShapeFunctionSet
	A container of hierarchic shape functions of nominal order Ord on the unit simplex of grid dimension. For Ord<0, this set is empty. More...
class	HierarchicMapperImplementation
class	HierarchicMapperImplementationBase
	A local to global mapper implementation for scalar hierarchic bases. More...
class	HierarchicShapeFunctionSetContainer
class	HierarchicSimplexShapeFunction
	Scalar hierarchic shape functions on the unit simplex. More...
class	HierarchicSimplexShapeFunctionSet
	A container of hierarchic shape functions (see HierarchicSimplexShapeFunction) up to a given nominal order on the unit simplex of grid dimension. More...
class	HigherOrderRecovery
	Construct a higher order estimate for the finite element solution from gradient information. More...
class	HomogeneousNeumannBoundary
	A simple boundary cache implementing homogeneous Neumann boundary conditions. More...
class	HomotopyBase
	Base class for homotopy methods. Here, the main algorithm is programmed. More...
class	HypIP
class	HypIPParameters
class	ICC_0Preconditioner
	Incomplete Cholesky factorization by algorithm from book "Matrix Computations" by Gene Golub & Charles van Loan. More...
class	IdentityChart
class	IdentityPreconditioner
	The trivial (identity) preconditioner. More...
struct	IdentityScaling
	A trivial Scaling. More...
class	ILUKPreconditioner
class	ILUTPreconditioner
struct	InDomainTraits
class	InexactTangentSpacePreconditioner
class	InexactTangentSpacePreconditionerILU
class	InfeasibleProblemException
	To be raised if an iterative solver detects the problem to be infeasible (has no valid solution). More...
class	Integral
	Evaluation class for integrals. More...
struct	IntegralF
	Integral. More...
class	Integrator
class	InteriorPointParameters
class	InteriorPointParametersSqrt
class	InteriorPointSimple
	Very simple implementation of homotopy method: fixed stepsize. More...
class	InteriorPointSlopeEstimate
class	InteriorPointSqrtModel
	InteriorPointMethod with a sqrt-model of the path: eta ~ mu^{-1/2}, omega ~mu^{-1/2}. More...
class	InteriorPointTangentialPredictor
class	InverseLinearOperator
	Dune::LinearOperator interface for inverse operators. More...
class	InverseLocalMatrixStorageBase
	A base class providing common functionality for storage of inverse local matrices. More...
struct	InverseVolume
	A Weighing that associates to each cell its inverse volume. More...
class	IOException
	An exception class for IO errors. More...
struct	IoOptions
	options for VTK/AMIRA output More...
class	IPFunctional
	Functional that adds barrier terms to VarFu. More...
struct	IsFunction
	Checks if type is a function or member function. More...
class	IsotropicCubicRegularization
class	IterationParameters
	Base class for algorithmic parameters. More...
class	IterativeSolverException
	To be raised if an iterative solver fails. More...
class	JacobiPreconditioner
class	JacobiPreconditioner< AssembledGalerkinOperator< Assembler, firstRow, lastRow, firstCol, lastCol, BlockFilter, symmetric > >
	A recursive Jacobi preconditioner for heterogeneous square block matrices from a variational assembler. More...
class	JacobiPreconditioner< NumaBCRSMatrix< Entry, Index > >
	A simple single-level Jacobi preconditioner working on sparse matrices. More...
class	JacobiPreconditionerForTriplets
class	JacobiSolver
class	JacobiSolverForTriplets
class	JModel
class	JModelLin
class	Kalloc
	A simple memory manager for NUMA systems. More...
class	KallocUnlocked
	A class for local memory management. More...
struct	L2Norm
	L_2-norms. More...
class	LagrangeBase
class	LagrangeCubeShapeFunction
	Scalar Lagrange shape functions on the unit cube. More...
class	LagrangeCubeShapeFunctionSet
class	LagrangeLinearization
class	LagrangeMapperImplementation
	A local to global mapper for scalar Lagrange bases. More...
class	LagrangeOperator
class	LagrangeShapeFunctionSetContainer
class	LagrangeSimplexShapeFunction
	Scalar Lagrange shape functions on the unit simplex. More...
class	LagrangeSimplexShapeFunctionSet
	A container of Lagrange shape functions of order Ord on the unit simplex of grid dimension. For Ord<0, this set is empty. More...
struct	LagrangianD2LipschitzConstant
class	Laplace
	Convenience class for handling diffusion terms in elliptic/parabolic equations. More...
struct	LeaveRHS
class	Limex
	Extrapolated linearly implicit Euler method. More...
class	LinearAlgebraException
	A base class for linear algebra exceptions. More...
class	LinearizationAt
	Proxy class for the linearization of a nonlinear functional. More...
class	LinearizationDifferenceAt
	Proxy class for evaluating differences of linearizations of a nonlinear functional. More...
class	LinearProductSpace
class	LinesearchException
	To be raised if a linesearch fails. More...
class	LN
	Natural logarithm of the form a*\ln(x) More...
class	LobattoGridLagrange
class	LobattoTimeGrid
	spectral time grid for defect correction methods with Lobatto points on \( [a,b]\) More...
class	LocalGeometryInCoarseGridAncestor
class	LocalIntegral
	Create a CellData by computing local integrals over each Cell. More...
class	LocalMatrices
	A structure for holding a sequence of several local matrices to be filled sequentially and to be scattered jointly. More...
class	LocalMatrix
	Providing a matrix or array interface to LAPACK-ordered entries. More...
struct	LocalNormalMatrixBlock
struct	LocalNormalMatrixRow
class	LocalTransfer
	Class that stores for a cell ("this entity" or "father") a local projection matrix. More...
class	LocalVector
	Providing a vector interface for contiguously stored entries. More...
class	LocalVectors
	A structure for holding a sequence of several local vectors to be filled sequentially and to be scattered jointly. More...
class	LoggedQuantity
	Class that represents a quantity that can be logged during the course of an algortihm. More...
class	Logger
	Simple logging facility. More...
class	LogLogModel
	Polynomial model in a loglog scale. More...
class	LookupException
	An exception that can be thrown whenever a key lookup fails. More...
class	MakeAdditiveSchwarzSmoother
	Functor for creating overlapping Schwarz smoothers. More...
class	MakeJacobiSmoother
	Functor for creating Jacobi smoothers. More...
class	MartinsErrorEstimator
class	MaterialAmiraMeshWriter
struct	Matrix_to_Triplet
	A class template that supports converting certain Dune matrices into the coordinate (triplet) format. More...
struct	Matrix_to_Triplet< Dune::BCRSMatrix< Dune::FieldMatrix< K, N, M >, Allocator > >
struct	Matrix_to_Triplet< Dune::FieldMatrix< K, n, m > >
struct	Matrix_to_Triplet< NumaBCRSMatrix< Dune::FieldMatrix< K, N, M >, Index > >
class	MatrixAsTriplet
class	MatrixRepresentedOperator
	Operator with matrix-representation and coordinate mappings. More...
class	MatrixRepresentedOperator< Dune::BCRSMatrix< MatrixBlock, Allocator >, Domain_, Range_ >
class	MatrixRepresentedOperator< MatrixAsTriplet< Scalar_, SparseInt >, Domain_, Range_ >
struct	MatrixTraits
	Defines domain and range types for matrix classes. More...
struct	MatrixTraits< Dune::FieldMatrix< Scalar, n, m > >
struct	MatrixTraits< NumaBCRSMatrix< Entry, Index > >
class	MaxValueCriterion
	Max value refinement criterion. Determines the refinement thresholds such that all cells with an error contribution exceeding a certain fraction of the maximum error contribution are refined. More...
struct	MeasureTime
struct	MembraneModelBase
	Convenience base class for membrane models providing numerical differentiation. More...
class	MGProjectionOnTangentSpace
class	MGProlongation
	A prolongation operator for P1 finite elements from a coarser grid level to the next finer level. More...
class	MGSolverStatistics
	An interface for gathering multigrid solver statistics. More...
class	ModifiedCovariantNewtonParameters
class	Monomial
	Monomial a*x^k of order k. More...
class	MorleyMapper
	Degrees of freedom manager for Morley nonconforming elements. More...
class	Mortar
	Abstract base class for computation of constraints from constraint samples. More...
struct	MortarB
	Defines the sample-based contact constraint formulation. More...
class	MultiGridPreconditioner
class	MultigridSolver
class	MultiGridStack
	Class for multigrid stacks. More...
struct	MultilevelCoarseningPolicy
	policy class for LocalTransfer These two structures are used for determining whether to perform a "normal" grid transfer (default, AdaptionCoarseningPolicy), or to calculate prolongation matrices for a FE function space based on a HierarchicIndexSet (see mgtools.hh). More...
class	MultiLevelLocalGeometry
	Transformation of coordinates between ancestor and child. More...
class	MultiplicativeMultiGrid
	A general multiplicative multigrid preconditioner. More...
class	MUMPSFactorization
	Factorization of sparse linear systems with mumps. More...
class	Mutex
	A utility class implementing appropriate copy semantics for boost mutexes. More...
class	NedelecMapper
	Degrees of freedom manager for Nedelec edge elements. More...
class	NedelecShapeFunctionSetContainer
class	NedelecSimplexShapeFunction
	Vectorial Nedelec shape functions on the unit simplex. More...
class	NedelecSimplexShapeFunctionSet
class	NestedDissection
	a nested dissection factorization for symmetric positive definite sparse matrices More...
class	NestedDissectionCholeskyLocalMatrixStorage
	An inverse local matrix representation that stores a sparse Cholesky factor using nested dissection. More...
class	NestedDissectionStorageTag
	A parametrized tag type for selecting storage of inverses by nested dissection with floating point representation of type Scalar. More...
class	NewtonCotesRule3
class	NewtonParameters
class	NewtonsMethod
	Base class for Newton's method. Defines the main algorithm, potentially using damping. More...
class	NleqSolver
	Solution of a nonlinear system of equations by a damped Newton-method. More...
class	NMIIIAPCGSolver
	conjugate gradient method More...
class	NMIIICGSolver
	conjugate gradient method More...
class	NMIIIPCGSolver
	conjugate gradient method More...
class	NonpositiveMatrixException
	To be raised if the matrix is not positive definite. More...
class	NonsquareMatrixException
	To be raised if the matrix is nonsquare. More...
struct	NoRegularization
class	NormalStep
class	NormalStepNewton
class	NormalStepPreconditioner
class	NormalStepPreconditioner2
class	NormalStepPreconditioner3
struct	NormModelCreator
class	NumaAllocator
	An STL allocator that uses memory of a specific NUMA node only. More...
class	NumaBCRSMatrix
	A NUMA-aware compressed row storage matrix adhering mostly to the Dune ISTL interface (to complete...) More...
class	NumaCRSPattern
	A NUMA-aware compressed row storage sparsity pattern. More...
class	NumaCRSPatternCreator
	A NUMA-aware creator for matrix sparsity patterns. More...
class	NumaDenseMatrix
	A dense matrix class tailored towards NUMA architectures. More...
class	NumaThreadPool
	Implementation of thread pools suitable for parallelization of (more or less) memory-bound algorithms (not only) on NUMA machines. More...
class	NumaVector
	A vector class tailored towards NUMA architectures. This vector distributes its entries in blocks of approximately equal size to the different nodes of NUMA machines in order to exploit the larger accumulated memory bandwidth for fast vector operations. This is most beneficial for large vectors exceeding the cache of the CPUs. Modern processors (2015-01-01) have up to 6MB 3rd level cache, so this is intended for vectors of more than 50,000 doubles, say. More...
class	OmegaModel
class	Optimization
class	OptimizationParameters
class	Options
class	Parameters
	...for parameter dependent functionals, implements AbstractParameters More...
class	PardisoFactorization
	Factorization with DirectType::PARDISO. More...
class	PartialDirectPreconditioner
	DEPRECATED A partial direct preconditioner applicable to assembled operators. More...
class	PatchDomainDecompositionPreconditioner
	An additive overlapping domain decomposition type preconditioner for higher order finite elements applied to elliptic equations. More...
struct	PatchDomainDecompositionPreconditionerTraits
	Provides the actual type of local matrix storage based on a tag and the number of components. More...
struct	PatchDomainDecompositionPreconditionerTraits< DenseCholeskyStorageTag< Scalar >, components >
struct	PatchDomainDecompositionPreconditionerTraits< DenseInverseStorageTag< Scalar >, components >
struct	PatchDomainDecompositionPreconditionerTraits< NestedDissectionStorageTag< StorageScalar, FactorizationScalar >, components >
class	Pcg
	preconditioned conjugate gradient method More...
class	PCGCountingTerminationCriterion
	PCG termination after a given number of iterations. More...
class	PCGEnergyErrorTerminationCriterion
	TerminationCriterion based on an absolute energy error estimate. More...
class	PCGTerminationCriterion
	Interface for IterateType::PCG termination criterion policy classes. More...
class	PenaltyFunction
	Sets a function to std::numeric_limits<double>::max() for negative arguments. More...
struct	PhysiologicalAlievPanfilov
	Phenomenological model based on Aliev and Panfilov, scaled to physiological values. More...
class	PiecewiseContinuousLagrangeMapper
	A degrees of freedom manager for piecewise continuous FEFunctionSpace s of local polynomials. More...
struct	PlainAverage
	A Weighing that associates to each cell a constant weight of 1. More...
class	Polynomial
class	PolynomialModel
class	PPCGAsNormalSolver
class	PreconditionerAsNormalSolver
class	PreconditionerFactory
class	PrimalChart
class	ProjectedAPCGSolver
class	ProjectionOnTangentSpace
class	QPALSolver
	An augmented Lagrangian solver for small instances of a particular class of quadratic programs. More...
class	QPBoundSolver
	An iterative solver for small instances of bound constrained quadratic programs. More...
class	QPBoundSolverBase
	An iterative solver for small instances of bound constrained quadratic programs. More...
class	QPDirectSparse
	A solver for sparse, medium-sized instances of bound constrained quadratic programs. More...
class	QPMultiGrid
	A multigrid solver for convex QPs. More...
class	QPMultiGridBase
	A base class for multigrid solver for QPs. More...
class	QPMultiGridStrict
class	QPPenalizedSolver
	An iterative solver for small instances of a particular class of quadratic programs. More...
class	QPPenaltySmoother
class	QPSlackSolver
	An iterative solver for particular instances of bound constrained quadratic programs. More...
class	QPSmoother
class	QPSolver
	An iterative solver for small instances of a particular class of quadratic programs. More...
class	QuadraticAndLogBase
class	QuadraticFunction
	TODO !!!!! Entscheidung über Vektortyp !!!!!! More...
class	QuadraticModel
	Creates a (linear) model to a linearization of a functional. More...
struct	QuadraticModelCreator
struct	QuadratureTraits
	A cache that stores suitable quadrature rules for quick retrieval. More...
struct	QuadratureTraits< Dune::QuadratureRule< ctype, dim > >
	A cache that stores suitable quadrature rules for quick retrieval. More...
class	RadauTimeGrid
	spectral time grid for defect correction methods with Radau points on \( [a,b]\). More...
class	RangeView
	DEPRECATED. Use boost::iterator_range instead. More...
class	RefinedTrapezoidal
class	RefinementCriterion
	Base class for refinement criteria. More...
class	RegularizedQuadraticFunction
class	RestrictedShapeFunctionSet
	Restricted shape function set. Introduces a new local ordering for the shape functions. To retrieve the original shape function id use getId(int newLocalId) More...
class	ScalarConverter
	A Converter for scalar shape functions that do not change their value under transformation from reference to actual element geometry. More...
class	ScalarLaplace
	Convenience class for handling diffusion terms in elliptic/parabolic equations. More...
class	ScalarModelFunction
	Interface for a scalar model function on a scalar domain that may fit data. More...
class	ScalarProductView
	(Scalar) product of two functions. More...
class	ScalarTraits
	Helper class for working with (real or complex) scalar field types. More...
class	ScalarTraits< std::complex< T > >
class	Scaledl2ScalarProduct
class	ScaledTwoNorm2Collector
	A functor for computing scaled \(L^2\)-norms of a set of (possibly vector-valued) functions. More...
struct	ScatterFullLocalSolution
struct	ScatterLocalSolution
class	ScopedTimingSection
	A scope guard object that automatically closes a timing section on destruction. More...
class	Sdc
	Encapsulates the state of an SDC fixed point iteration and provides stepping. More...
class	SDCGridImplementationBase
	A convenience class simplifying the implementation of different SDCTimeGrid derived classes. More...
class	SDCTimeGrid
	Abstract base class of time grids for (block) spectral defect correction methods. More...
class	SearchSpaceCreator
class	SemiImplicitEulerStep
	Linearly implicit Euler method. More...
class	SemiLinearizationAt
	Proxy class for the linearization of semi-linear time stepping schemes. More...
class	SemiLinearizationAtInner
class	ShapeFunction
	Shape functions. More...
class	ShapeFunctionCache
	This class caches values and derivatives of shape functions at quadrature points. More...
class	ShapeFunctionSet
	A set of shape functions. More...
class	ShapeFunctionSetContainer
	Base class for sets of shape function containers. More...
class	SimpleAdaptiveRefinement
	Adaptive refinement algorithm. More...
class	SimpleSparseLinearSystem
	Simple Implementation for SparseLinearSystem. More...
class	SingularMatrixException
	To be raised if the matrix is singular. More...
class	SLAPMatrix
	Very simple dense matrix class for interfacing with LAPACK routines and the optimization tool uncmin. More...
struct	SolveLocalSystem
struct	SpaceIndex
	Helper class for specifying the FE space index of a variable. More...
struct	SpaceType
	Extracts the type of FE space with given index from set of spaces. More...
class	SparseLinearSystem
	Abstract base class for a sparse linear system. More...
class	Sqrt
class	Square
class	StateConstraintsNewtonMethod
	A Newton method that uses a pointwise damping strategy to cope with bounds. More...
class	StateEquationHBErrorEstimator
struct	StaticIndexRange
	A compile-time index range. More...
class	StepPolicyProjectedRHS
class	StrakosTichyEnergyErrorTerminationCriterion
	Relative energy error termination criterion according to Strakos, Tichy: Error estimation in preconditioned conjugate gradients. Requires that IterateType::CG starts at \( x = 0 \). More general starting values might be used, but must be chosen such that the estimate for the energy norm of the solution stays positive (see the above mentioned paper for details). More...
class	StrakosTichyPTerminationCriterion
	Relative error termination criterion based on the norm induced by the preconditioner, according to Strakos, Tichy: Error estimation in preconditioned conjugate gradients. Requires that IterateType::CG starts at \( x = 0 \). More general starting values might be used, but must be chosen such that the estimate for the energy norm of the solution stays positive (see the above mentioned paper for details). More...
struct	StrongBoundaryValues
struct	StrongResidualsTimesTestFunction
class	StupidHBErrorEstimator
struct	SubstractCorrection
class	SumCache
class	SumFunctional
struct	SummationCollector
	A Collector that sums up the weighted contributions. More...
struct	SumUp
class	SUPERLUFactorization
	Factorization of sparse linear systems with mumps. More...
class	SymmetricLinearOperator
	Interface for symmetric linear operators. More...
class	SymmetricLinearOperatorWrapper
	Wrapper class to present (hopefully) symmetric linear operators in the SymmetricLinearOperator interface. More...
class	SymmetricMatrixOperator
	A symmetric operator represented by a matrix. More...
class	SymmetricPreconditioner
	Interface for symmetric preconditioners. More...
class	SymmetricPreconditionerWrapper
	Wrapper class presenting a symmetric preconditioner interface for any preconditioner. More...
class	SymmetricTaylorHoodPreconditioner
	Symmetric Taylor-Hood constraint preconditioner. More...
struct	SystDim
struct	SystDimFull
class	TangentialStep
class	TangentialStepArmijo
class	TangentialStepNewton
class	TangentSpacePreconditioner
class	TangentSpacePreconditioner2
class	TaskTiming
	A class that gathers data on task timing and provides gnuplot visualization. More...
class	TaylorHoodPreconditioner
	Constraint preconditioner for Taylor-Hood discretizations of incompressibility problems. More...
class	TCG
	preconditioned conjugate gradient method More...
class	Tensor
	A class for representing tensors of arbitrary static rank and extents. More...
class	Tensor< Entry, Size0 >
struct	TenTusscher16
	Physiologcial model by tenTusscher et al. More...
struct	TenTusscher18
	Physiologcial model by tenTusscher et al. (2006) More...
class	TestErrorEstimator
class	TimeSeriesVTKWriter
class	Timings
	Supports gathering and reporting execution times information for nested program parts. More...
class	TransferData
	A class storing data collected before grid adaptation that is necessary to transfer FE functions. This includes global indices of shape functions on leaf cells and restriction matrices to coarser cells in case some leaf cells might be removed during grid adaptation. More...
class	TransformedPolynomialModel
class	TransposedOperator
class	TrapezoidalRule
class	TrivialBoundaryDetector
class	TrivialCacheBase
	Base class simplifying the definition of domain and boundary caches. More...
class	TrivialPreconditioner
	The trivial preconditioner: this is simply the identity that does exactly nothing. More...
class	UMFFactorization
	Factorization of sparse linear systems with UMFPack. More...
struct	UnaryTrue
class	UnboundedProblemException
	To be raised if an iterative solver detects the optimization problem to be unbounded (has no valid solution). More...
class	UNCMINVector
	Very simple vector wrapper for the use of the optimization tool uncmin, which is not capable of using std::vector :(. More...
class	UniformPartitionedMapper
	Base class for piecewise continuous mappers. More...
class	UniformSampler
	Class that can sample a Function(View) on a uniform rectangular grid. More...
class	UniformScalarMapper
	Base class for uniform scalar local to global mappers. More...
class	UzawaSolver
	An inexact Uzawa type solver for solving symmetric saddle point systems. More...
struct	Variable
	A class defining elementary information about a single variable. More...
struct	VariableDescription
	A class storing elementary information about a single variable.This includes the number of components, the id and name of the variable, and the index of the associated FEFunctionSpace from which the variable comes. More...
struct	VariableId
	DEPRECATED. More...
class	VariableSet
	A class for storing a heterogeneous collection of FunctionSpaceElement s. More...
class	VariableSetDescription
	A class that stores information about a set of variables. More...
struct	VariationalArg
	A class that stores values, gradients, and Hessians of evaluated shape functions. More...
class	VariationalEquationHBErrorEstimator
class	VariationalFunctionalAssembler
	A class for assembling Galerkin representation matrices and right hand sides for variational functionals depending on multiple variables. More...
struct	vec
class	VectorialConverterBase
	A class mapping local vectorial shape function values and gradients to global shape function values and gradients. More...
struct	Volume
	A Weighing that associates to each cell its volume. More...
class	VTKReader
	A class to create a grid and load coefficients from a VTK file. More...
struct	WeakBoundaryValues
struct	WeakBoundaryValuesFull
class	WeakFunctionViewAdaptor
	An adaptor that turns callables (e.g., lambdas) into weak function views. More...
struct	WeakResiduum
struct	WeakResiduumFull
struct	WeakResiduumMainPart
class	XXstress
	Active stress generation from XX. More...
class	YetAnotherHBErrorEstimator
class	YetAnotherHBErrorEstimator_Elasticity
class	ZeroDualPairing
	Zero dual pairing implementation (mainly useful whenever a dual pairing is needed for formal language reasons, but never used) More...

Typedefs
template<class GridView >
using	GridAngleFeatureDetector = AngleFeatureDetector< typename GridView::IndexSet::IndexType, typename GridView::ctype, GridView::dimension >
template<class TestVars , int row>
using	D1Result = Dune::FieldVector< typename TestVars::Scalar, TestVars::template Components< row >::m >
	The return type of the d1() method of DomainCache and BoundaryCache. More...
template<class TestVars , int row, class AnsatzVars , int col>
using	D2Result = Dune::FieldMatrix< typename TestVars::Scalar, TestVars::template Components< row >::m, AnsatzVars::template Components< col >::m >
	The return type of the d1() method of DomainCache and BoundaryCache. More...
template<class Spaces >
using	Evaluators = typename boost::fusion::result_of::as_vector< typename boost::fusion::result_of::transform< Spaces, GetEvaluatorTypes >::type >::type
	the heterogeneous sequence type of Evaluators for the given spaces More...
template<class GridView >
using	Cell = typename GridView::template Codim< 0 >::Entity
	The type of cells (entities of codimension 0) in the grid view. More...
template<class GridView >
using	Face = typename GridView::Intersection
	The type of faces in the grid view. More...
template<class GridView >
using	GlobalPosition = Dune::FieldVector< typename GridView::ctype, GridView::dimensionworld >
	The type of global positions within the grid view. More...
template<class GridView >
using	LocalPosition = Dune::FieldVector< typename GridView::ctype, GridView::dimension >
	The type of local positions within cells of the grid view. More...
template<class GridView >
using	FaceLocalPosition = Dune::FieldVector< typename GridView::ctype, GridView::dimension-1 >
	The type of local positions within faces of the grid view. More...
template<class SFData >
using	UniformPartitionedMapperCombinerArgument = RangeView< typename std::vector< boost::compressed_pair< size_t, SFData > >::const_iterator >
	The sequence type that is provided as first argument to the call of the Combiner constructor. More...
template<class SFData >
using	UniformScalarMapperCombinerArgument = RangeView< typename std::vector< boost::compressed_pair< size_t, SFData > >::const_iterator >
	The sequence type that is provided as first argument to the call of the Combiner constructor. More...
template<class Grid , class Scalar = double>
using	ConstantSpace = FEFunctionSpace< ConstantMapper< Scalar, typename Grid::LeafGridView > >
	A finite element space of globally constant functions on the leaf grid view. More...
template<class Grid , class Scalar = double>
using	H1Space = FEFunctionSpace< ContinuousLagrangeMapper< Scalar, typename Grid::LeafGridView > >
	An \( H^1 \) conforming finite element space on the leaf grid view with Lagrange basis. More...
template<class Grid , class Scalar = double>
using	H1HierarchicSpace = FEFunctionSpace< ContinuousHierarchicMapper< Scalar, typename Grid::LeafGridView > >
	An \( H^1 \) conforming finite element space on the leaf grid view with hierarchic basis. More...
template<class Grid , class Scalar = double>
using	H1HierarchicExtensionSpace = FEFunctionSpace< ContinuousHierarchicExtensionMapper< Scalar, typename Grid::LeafGridView > >
	An \( H^1 \) conforming finite element extension space on the leaf grid view with hierarchic basis. More...
template<class Grid , class Scalar = double>
using	L2Space = FEFunctionSpace< DiscontinuousLagrangeMapper< Scalar, typename Grid::LeafGridView > >
	An \( L^2 \) conforming finite element space on the leaf grid view with Lagrange basis. More...
template<class Grid , class Scalar = double>
using	L2HierarchicSpace = FEFunctionSpace< DiscontinuousHierarchicMapper< Scalar, typename Grid::LeafGridView > >
	An \( L^2 \) conforming finite element space on the leaf grid view with hierarchic basis. More...
template<class Grid , class Scalar = double>
using	L2HierarchicExtensionSpace = FEFunctionSpace< DiscontinuousHierarchicExtensionMapper< Scalar, typename Grid::LeafGridView > >
	An \( L^2 \) conforming finite element extension space on the leaf grid view with hierarchic basis. More...
using	ValueMethod = decltype(valueMethod)
	The type of the valueMethod helper functor. More...
using	DerivativeMethod = decltype(derivativeMethod)
	The type of the derivativeMethod helper functor. More...
template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>
using	CG = CGBase< X, Xstar, CGImplementationType::STANDARD, TimerPolicy >
template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>
using	TCG = CGBase< X, Xstar, CGImplementationType::TRUNCATED, TimerPolicy >
template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>
using	RCG = CGBase< X, Xstar, CGImplementationType::REGULARIZED, TimerPolicy >
template<class X , class Xstar , class Regularization = NoRegularization>
using	TPCG = TCG< X, Xstar, Regularization >
using	Prolongation = NumaBCRSMatrix< Dune::FieldMatrix< double, 1, 1 > >
template<class Grid , int nComponents = 1>
using	MultiGridSolver = MultigridSolver< Grid, nComponents >
template<class Type >
using	ScalarType = typename GetScalar< Type >::type
	Extracts the scalar field type from linear algebra data types. More...
template<int k>
using	PenaltyMonomial = PenaltyFunction< Monomial< k > >
typedef PenaltyFunction< LN >	PenaltyLN
typedef PenaltyFunction< Polynomial< 5,-5 > >	Hartmann03
typedef PenaltyFunction< Polynomial< 2,-2 > >	QuadQuad
typedef PenaltyFunction< QuadraticAndLogBase >	QuadraticAndLog
template<int k>
using	QuadraticAndPolynomial = PenaltyFunction< Polynomial< 2, k > >
typedef std::packaged_task< void()>	Task
	Abstract interface for tasks to be scheduled for concurrent execution. More...
typedef std::future< void >	Ticket
	Abstract waitable job ticket for submitted tasks. More...

Enumerations
enum class	RegularityTest { Failed , Passed }
enum class	AcceptanceTest {   InitialGuess , FailedRecompute , Failed , NormalStepFailed ,   TangentialStepFailed , Passed , LeftAdmissibleDomain }
enum class	Convergence { Missed , Achieved }
enum class	ErrorNorm { Energy , L2 , H1 , H1_half }
enum	ProblemType { VariationalFunctional , WeakFormulation }
	A type for describing the nature of a PDE problem. More...
enum class	Endian {   Unknown , Big , Little , BigWord ,   LittleWord }
enum	schwarzType { DIAGONAL , COMPLETE }
enum class	CGImplementationType { STANDARD , TRUNCATED , REGULARIZED , HYBRID }
enum class	GaussSeidelPreconditionerMode { FORWARD =0x1 , BACKWARD =0x2 , SYMMETRIC =0x3 }
enum class	QPConvexificationStrategy { DONOTHING , INCREMENTALADDITION , EIGENVALUEADDITION }
enum class	QPStructure { DENSE , SPARSE }
	A flag that determines whether the QP solver shall work with dense or sparse linear algebra. More...
enum class	TaylorHoodPreconditionerFlavour { TaylorHoodPreconditionerFlavour::SYMMETRIC , TaylorHoodPreconditionerFlavour::PRESMOOTH , TaylorHoodPreconditionerFlavour::POSTSMOOTH }
	tag for controlling the TaylorHoodPreconditioner flavour More...

Functions
template<class ParameterType >
Parameters< ParameterType >	makePars (ParameterType const &p)
template<int rbegin, int rend, class FSE , class CoeffVector >
void	copyFromFunctionSpaceElement (FSE const &fse, CoeffVector &coeffVector)
template<int rbegin, int rend, class FSE , class CoeffVector >
void	addToFunctionSpaceElement (CoeffVector const &coeffVector, FSE &fse)
template<class Assembler , class Lin , int rbegin, int rend, int cbegin, int cend>
void	ddxpy_template (Lin &lin, AbstractFunctionSpaceElement &y, AbstractFunctionSpaceElement const &x)
template<typename Scalar >
std::ostream &	operator<< (std::ostream &s, std::vector< Scalar > const &vec)
template<class OriginalEvaluators , class ExtensionEvaluators , class Functional , class ArgYH , class ArgYE , class ArgUH , class ArgUE , class ArgPH , class ArgPE >
void	evaluateData (OriginalEvaluators &originalEvaluators, ExtensionEvaluators &extendedEvaluators, Functional const &f, ArgYH &yl, ArgYE &yh, ArgUH &ul, ArgUE &uh, ArgPH &pl, ArgPE &ph, double w)
template<class ArgYL , class ArgYH , class ArgUL , class ArgUH , class ArgPL , class ArgPH >
void	clearVarArgs (ArgYL &yl, ArgYH &yh, ArgUL &ul, ArgUH &uh, ArgPL &pl, ArgPH &ph)
template<class ArgU , class ArgY , class ArgP >
double	computeL2Error (ArgU const &u, ArgY const &y, ArgP const &p)
template<class ArgU , class ArgY , class ArgP >
double	computeH1HalfError (ArgU const &u, ArgY const &y, ArgP const &p)
bool	biggerThanAbs (const std::pair< double, int > &x1, const std::pair< double, int > &x2)
double	add (const double &x1, const std::pair< double, int > &x2)
template<class Equation >
double	bisection (double a, double b, Equation const &f, double accuracy, int &iterations)
	Performs bisection algorithm to find a zero of a. More...
template<class Value >
void	assignIfNegative (Value &val, Value newVal)
template<class Function >
CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector	gradientAveraging (Function const &f)
	Perform gradient averaging in order to construct an error estimator. More...
template<class GradientError , class Function >
void	gradientAveraging (GradientError &dx, Function const &x)
	Perform gradient averaging in order to construct a representation of the gradient error. More...
template<class Function >
CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector	lowOrderInterpolation (Function const &f)
	Perform lower order interpolation in order to construct an error estimator. More...
template<class LocalMatrix , class Evaluators , class RT , class Cache >
void	localNormalMatrix (LocalMatrix &localmatrix, RT intEl, Evaluators const &evaluators, Cache const &cache)
template<class LocalVector , class Evaluators , class RT >
void	rank1KernelVector (LocalVector &localvector, RT intEl, Evaluators const &evaluators)
template<class VariableDescriptions , int sysdim, class Result , class F , class Spaces , class ExtendedSpaces >
void	edgeAveraging (Result &result, F const &f, Spaces const &spaces, ExtendedSpaces const &extendedSpaces)
	Computes an error representation function, which is useful for goal oriented adaptivity. More...
template<class LocalVector , class LocalMatrix >
void	solveLocalFullSystem (LocalVector &c, LocalMatrix &A, LocalVector &b)
template<class VariableDescriptions , int sysdim, class Result , class F , class FS , class Spaces , class ExtendedSpaces >
void	edgeAveragingFull (Result &result, F const &f, FS const &fs, Spaces const &spaces, ExtendedSpaces const &extendedSpaces)
	Computes an error representation function, which is useful for goal oriented adaptivity. More...
template<class Description , class Function , class Functional >
CellData< typenameFunction::Grid >::CellDataVector	BWErrorIndicator (Function const &f, Functional const &vf)
	Construct an error indicator in the flavour of Bank/Weiser. More...
template<class CoordType , int dim>
Dune::FieldVector< CoordType, dim+1 >	barycentric (Dune::FieldVector< CoordType, dim > const &x)
	Computes the barycentric coordinates of a point in the unit simplex. More...
template<class CoordType , int dim, std::enable_if_t< std::is_floating_point_v< CoordType >, int > = 0>
Dune::FieldVector< CoordType, dim >	projectToUnitSimplex (Dune::FieldVector< CoordType, dim > x)
	Projects a vector onto the unit simplex. More...
template<class CoordType , int dim>
Dune::FieldVector< CoordType, dim+1 >	barycentric2 (Dune::FieldVector< CoordType, dim > const &x)
	Computes barycentric coordinates of a point in the unit simplex. More...
template<class CoordType , int dim>
Dune::FieldMatrix< CoordType, dim+1, dim >	barycentric2Derivative (Dune::FieldVector< CoordType, dim > const &x)
	Computes the derivative of the barycentric coordinates of a point in the unit simplex. More...
template<size_t dim>
std::array< int, dim+1 >	barycentric (std::array< int, dim > const &x, int bsum)
	Converts integer coordinate index to barycentric indices. More...
template<class GridView >
std::map< typename GridView::IndexSet::IndexType, BoundaryStar< typename GridView::IndexSet::IndexType, typename GridView::ctype, GridView::dimension > >	computeBoundaryStars (GridView const &gv)
	Computes the boundary stars (i.e. corners around a vertex) for all boundary vertices of the grid view. More...
template<class Index , class ctype >
void	adjustEdgeTangents (BoundaryStar< Index, ctype, 3 > &star, std::map< std::array< Index, 2 >, Dune::FieldVector< ctype, 3 > > &orientedEdges, GeometricFeatureDetector< Index, ctype, 3 > const &features)
	Detects feature edges and adjusts the edge tangent vectors accordingly. More...
template<class Index , class ctype >
void	adjustEdgeTangents (BoundaryStar< Index, ctype, 2 > &star, std::map< std::array< Index, 2 >, Dune::FieldVector< ctype, 2 > > &orientedEdges, GeometricFeatureDetector< Index, ctype, 2 > const &features)
template<class GridView >
std::vector< Dune::FieldVector< typename GridView::ctype, GridView::dimension > >	interpolateVertexPositions (GridView const &gv, GridBoundaryTangents< GridView > const &tangents, bool computeDisplacements=false)
	Computes a new position for each grid vertex based on boundary interpolation. More...
template<class Grid , class T >
CellData< Grid, int >::CellDataVector	markByBulkCriterion (CellData< Grid, T > &ic, double Theta)
	Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "bulk criterion". More...
template<class Grid , class T >
void	deleteAllAboveLevel (CellData< Grid, T > &ic, int maxlevel)
	Delete all error entries of entities which are above a certain level. More...
template<class Grid , class T >
CellData< Grid, int >::CellDataVector	markByMaxCriterion (CellData< Grid, T > &ic, double Ratio)
	Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion". More...
template<class Grid , class T >
CellData< Grid, int >::CellDataVector	markWithinInterval (CellData< Grid, T > &ic, double lower, double upper, int times)
	Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion". More...
template<class Grid >
CellData< Grid, int >::CellDataVector	unmarkOutOf (CellData< Grid, int > const &ic, Dune::FieldVector< typename Grid::ctype, Grid::dimension > center, double radius)
	Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion". More...
template<class Indicator >
Indicator	errorL2 (Indicator const &indi)
	Scale error indicators for H^1, such that L_2 indicators are the result. More...
template<typename FSElement >
void	extendMarks (FSElement &fse, FSElement const &fu, int neighboursForMarking)
template<class VariableSetDescription , class Scaling >
void	coarsening (VariableSetDescription const &varDesc, typename VariableSetDescription::VariableSet const &sol, Scaling const &scaling, std::vector< std::pair< double, double > > const &tol, GridManager< typename VariableSetDescription::Grid > &gridManager, int verbosity=1, int minRefLevel=0)
template<class VariableSetDescription , class Scaling >
void	coarsening (VariableSetDescription const &varDesc, typename VariableSetDescription::VariableSet const &sol, Scaling const &scaling, std::vector< std::pair< double, double > > const &tol, GridManager< typename VariableSetDescription::Grid > &gridManager, std::vector< bool > &coarsenedCells, int verbosity=1, int minRefLevel=0)
	coarsening routine More...
template<class ScalarA , class ScalarB , int r, int c>
Dune::FieldMatrix< ScalarA, r, c >	castMatrixEntries (Dune::FieldMatrix< ScalarB, r, c > const &m)
	Copies matrix into another matrix with possibly different entry type (e.g. from double to float). More...
template<class Space , class DisplacedFace , class Displacement >
auto	getContactConstraint (Space const &space, BoundaryLocator< typename Space::GridView, Displacement > const &boundaryLocator, DisplacedFace const &face, Dune::FieldVector< typename Space::GridView::ctype, Space::GridView::Grid::dimension-1 > const &xi, double overlap)
	Computes a single multibody contact point constraint. More...
template<class Space1 , class DisplacedFace1 , class Displacement1 , int dimw1 = Space1::GridView::Grid::dimension, class Space2 , class Displacement2 , int dimw2 = Space2::GridView::Grid::dimension>
auto	getContactConstraint (Space1 const &space1, BoundaryLocator< typename Space1::GridView, Displacement1, Space1::GridView::Grid::dimension > const &boundaryLocator1, Space2 const &space2, BoundaryLocator< typename Space2::GridView, Displacement2, Space2::GridView::Grid::dimension > const &boundaryLocator2, DisplacedFace1 const &face, Dune::FieldVector< typename Space1::GridView::ctype, Space1::GridView::Grid::dimension-1 > const &xi, double overlap, int which=0)
	Computes a single multibody contact point constraint. More...
template<int dim>
std::vector< Dune::QuadraturePoint< double, dim > >	constraintPositions (Dune::GeometryType gt, int nodesPerEdge)
	Computes contact sample points on faces. More...
template<class Space , class Displacement >
auto	getContactConstraints (Space const &space, BoundaryLocator< typename Space::GridView, Displacement > const &boundaryLocator, int pointsPerEdge, double overlap=std::numeric_limits< double >::lowest(), Mortar< typename Space::Grid::ctype, Space::Grid::dimension > const &mortar=ContactConstraintsDetail::defaultMortar< typename Space::Grid::ctype, Space::Grid::dimension >())
	Computes a complete set of pointwise multibody contact constraints. More...
template<class Space1 , class Displacement1 , class Space2 , class Displacement2 , bool flattened = false>
auto	getContactConstraints (Space1 const &space1, BoundaryLocator< typename Space1::GridView, Displacement1, Space1::GridView::Grid::dimension > const &boundaryLocator1, Space2 const &space2, BoundaryLocator< typename Space2::GridView, Displacement2, Space1::GridView::Grid::dimension > const &boundaryLocator2, int order, double overlap=std::numeric_limits< double >::lowest(), bool symmetric=true)
	Computes a complete pointwise twobody contact constraint. More...
template<class GridView , class Displacement >
double	getContactArea (BoundaryLocator< GridView, Displacement > const &boundaryLocator1, BoundaryLocator< GridView, Displacement > const &boundaryLocator2, int order, double overlap=std::numeric_limits< double >::lowest(), double maxGap=1e-4)
	Computes the contact area for the first body. More...
template<class Displacement , class BoundaryDisplacement >
double	contactLinesearch (Displacement const &u, BoundaryLocator< typename Displacement::GridView, BoundaryDisplacement > &boundaryLocator, Displacement const &direction, int pointsPerEdge, double trialStepSize=0.2, double overlap=std::numeric_limits< double >::lowest(), double targetOverlap=0, Mortar< typename Displacement::ctype, Displacement::GridView::dimension > const &mortar=ContactConstraintsDetail::defaultMortar< typename Displacement::ctype, Displacement::GridView::dimension >())
	Computes a feasible step size for contact constraints. More...
template<class Displacement1 , class BoundaryDisplacement1 , class Displacement2 , class BoundaryDisplacement2 >
double	contactLinesearch (Displacement1 const &u1, BoundaryLocator< typename Displacement1::GridView, BoundaryDisplacement1 > &boundaryLocator1, Displacement1 const &direction1, Displacement2 const &u2, BoundaryLocator< typename Displacement2::GridView, BoundaryDisplacement2 > &boundaryLocator2, Displacement2 const &direction2, int order, double trialStepSize=0.2, double overlap=std::numeric_limits< double >::lowest(), double targetOverlap=0)
	Computes a feasible step size for contact constraints. More...
double	massDensity (std::string const &name)
	Mass density of several materials in kg/m^3. More...
std::map< std::string, double > const &	massDensities ()
	A map from known material names to their mass densities. More...
double	thermalExpansion (std::string const &name, double pressure=101300)
	Volumetric thermal expansion coefficient of materials. More...
double	heatConductivity (std::string const &name)
	Heat conductivity [W/m/K]. More...
std::map< std::string, double > const &	heatConductivities ()
	A map from known material names to their heat conductivities. More...
double	specificHeatCapacity (std::string const &name)
	Specific heat capaciity [J/kg/K]. More...
std::map< std::string, double > const &	specificHeatCapacities ()
	A map from known material names to their specific heat capaciities. More...
double	dynamicViscosity (std::string const &name)
	Dynamic viscosity of several materials in kg/m/s. More...
std::map< std::string, double > const &	dynamicViscosities ()
	A map from known material names to their dynamic viscosities. More...
template<class VariableSetDescription >
void	projectHierarchically (VariableSet< VariableSetDescription > &f)
	Projects the given FE function onto the the polynomial ansatz subspace of one order lower. This relies on the hierarchic projection defined by the shape function sets on each cell. More...
template<class VariableSet , class GridManager >
std::array< size_t, 3 >	uniformEmbeddedErrorEstimation (VariableSet const &u, Dune::FieldVector< double, VariableSet::Descriptions::noOfVariables > const &tol, GridManager &gridManager, double rhoMin=0.1, double rhoMax=0.9)
	Embedded error estimation and simultaneous mesh refinement/coarsening. More...
template<class VariableSetDescription , class Scaling >
bool	embeddedErrorEstimator (VariableSetDescription const &varDesc, typename VariableSetDescription::VariableSet const &err, typename VariableSetDescription::VariableSet const &sol, Scaling const &scaling, std::vector< std::pair< double, double > > const &tol, GridManager< typename VariableSetDescription::Grid > &gridManager, int verbosity=1)
	Embedded error estimation and mesh refinement. More...
template<class GridManager , class GridView >
void	markAndRefine (GridManager &gridManager, GridView const &gridView, boost::multi_array< double, 2 > const &normalizedErrors, std::vector< double > const &threshold)
	Refines the grid according to the normalized errors and the given thresholds. More...
template<class Space , class ShapeFunctionSet >
void	evaluateGlobalShapeFunctions (Space const &space, Cell< typename Space::GridView > const &cell, std::vector< LocalPosition< typename Space::GridView > > const &xi, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &sfValues, ShapeFunctionSet const &shapeFunctionSet)
	Computes the values of global shape functions at the given points (which are supposed to be local coordinates inside the cell to which the evaluator is currently moved). More...
template<class Space >
void	evaluateGlobalShapeFunctions (Space const &space, Cell< typename Space::GridView > const &cell, std::vector< LocalPosition< typename Space::GridView > > const &x, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &sfValues)
template<class Space , class ShapeFunctionSet >
void	approximateGlobalValues (Space const &space, typename Space::Grid::template Codim< 0 >::Entity const &cell, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &globalValues, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, 1, 1 > > &coeff, ShapeFunctionSet const &sfs)
	Computes global shape function coefficients such that the given set of global function values at the interpolation nodes of the shape function set are approximated by the resulting linear combinations of global shape functions. More...
template<class Space >
void	approximateGlobalValues (Space const &space, typename Space::Grid::template Codim< 0 >::Entity const &cell, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &globalValues, DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, 1, 1 > > &coeff)
template<class ChildSpace , class FatherSpace >
void	localProlongationMatrix (ChildSpace const &childSpace, Cell< typename ChildSpace::Grid > const &child, FatherSpace const &fatherSpace, Cell< typename FatherSpace::Grid > const &father, DynamicMatrix< Dune::FieldMatrix< typename ChildSpace::Scalar, 1, 1 > > &prolongation, typename ChildSpace::Mapper::ShapeFunctionSet const &childSfs, typename FatherSpace::Mapper::ShapeFunctionSet const &fatherSfs)
	Computes a local prolongation matrix for global shape functions from father cell to child cell. More...
template<class ChildSpace , class FatherSpace >
void	localProlongationMatrix (ChildSpace const &childSpace, Cell< typename ChildSpace::GridView > const &child, FatherSpace const &fatherSpace, Cell< typename FatherSpace::GridView > const &father, DynamicMatrix< Dune::FieldMatrix< typename ChildSpace::Scalar, 1, 1 > > &prolongation)
	Computes a local prolongation matrix from father cell to child cell. More...
template<typename Weighing = PlainAverage, typename FSElement , typename Function >
void	interpolateGlobally (FSElement &fse, Function const &fu)
	Interpolates FunctionSpaceElement to FunctionSpaceElement. More...
template<typename Weighing = PlainAverage, typename Target , typename Source >
void	interpolateGloballyWeak (Target &target, Source const &fu)
	Interpolates WeakFunctionViews to FunctionSpaceElement. More...
template<class Fu1 , class Fu2 >
void	spaceTransfer (Fu1 &f1, Fu2 const &f2)
	DEPRECATED. Use interpolateGlobally instead. More...
template<class Scalar , int n>
auto	horzcat (Dune::FieldVector< Scalar, n > const &c1)
template<class Scalar , int n, class ... Rest>
auto	horzcat (Dune::FieldVector< Scalar, n > const &a, Rest ... rest)
	Concatenates an arbitrary number of column vectors and matrices with coinciding number of rows to a larger matrix. More...
template<class Scalar , int n, int m>
auto	horzcat (Dune::FieldMatrix< Scalar, n, m > const &a)
template<class Scalar , int n, int m, class ... Rest>
auto	horzcat (Dune::FieldMatrix< Scalar, n, m > const &a, Rest ... rest)
template<class Scalar , int n>
Dune::FieldMatrix< Scalar, n, 3 >	horzcat (Dune::FieldVector< Scalar, n > const &col1, Dune::FieldVector< Scalar, n > const &col2, Dune::FieldVector< Scalar, n > const &col3)
template<class Scalar , int n, int m>
Dune::FieldVector< Scalar, n >	column (Dune::FieldMatrix< Scalar, n, m > const &A, int j)
	Extracts the j-th column of the given matrix A. More...
template<class Scalar , int n>
Dune::FieldVector< Scalar, n *n >	vectorize (Dune::FieldMatrix< Scalar, n, n > const &A)
	matrix entries as vector, concatenating columns More...
template<int n, class Scalar >
Dune::FieldMatrix< Scalar, n, n >	unvectorize (Dune::FieldVector< Scalar, n *n > const &v)
	forming quadratic matrix columns of vector segments More...
template<class T , int n, int m>
T	contraction (Dune::FieldMatrix< T, n, m > const &A, Dune::FieldMatrix< T, n, m > const &B)
	Matrix contraction (Frobenius product) \( (A,B) \mapsto A:B = \sum_{i,j} A_{ij} B_{ij} \). More...
template<class GridView , class Functor >
void	forEachCell (GridView const &gridView, Functor functor)
	DEPRECATED: use range based for loops and Dune::elements() directly. iterates over each cell and applies functor to cell. Each cell is visited exactly once. More...
template<class GridView , class Functor >
void	forEachVertex (GridView const &gridView, Functor functor)
	DEPRECATED: use range based for loops and Dune::vertices() directly. iterates over each vertex and applies functor to vertex. Each vertex is visited exactly once. More...
template<class GridView , class Functor >
void	forEachFace (GridView const &gridView, Functor functor)
template<class GridView , class Functor >
void	forEachFaceOfCell (GridView const &gridView, Functor functor)
	same as forEachFace, but the functor is applied to the face and the cell from which the face is visited More...
template<class GridView , class Functor >
void	forEachBoundaryFace (GridView const &gridView, Functor functor)
	iterates over each boundary face and applies functor to face. Each boundary face is visited exactly once. More...
template<class GridView , class Functor >
void	forEachInnerFace (GridView const &gridView, Functor functor)
	iterates over each inner face and applies functor to face. Each inner face is visited exactly twice (and so functor is applied twice). More...
template<class GridView , class Functor >
void	forEachCellAndEachFace (GridView const &gridView, Functor functor)
	iterates over each cell and applies functor to cell and then iterates over each face of cell and applies functor to face More...
template<class GridManager , class Functor >
void	markCells (GridManager &gridManager, Functor functor)
template<class Functional >
LinearizationDifferenceAt< Functional >	linearizationDifference (Functional const &f, typename Functional::OriginVars::VariableSet const &u1, typename Functional::OriginVars::VariableSet const &u2)
	Convenience routine: construct linearization without having to know the type of the functional. More...
template<class Cell , class ctype >
std::pair< Cell, Dune::FieldVector< ctype, Cell::dimension > >	findCellOnLevel (Cell cell, Dune::FieldVector< ctype, Cell::dimension > xi, int level=std::numeric_limits< int >::max())
	Returns a descendant or ancestor cell of the given cell containing the specified local coordinate. More...
template<class GridView >
Cell< GridView >	findCell (GridView const &gv, GlobalPosition< GridView > global)
	Returns a cell of the given grid containing the specified global coordinate. More...
template<class Space , int m, class InIter >
InIter	vectorFromSequence (FunctionSpaceElement< Space, m > &v, InIter in)
template<class Evaluators , class Cell >
void	moveEvaluatorsToCell (Evaluators &evals, Cell const &cell)
	Moves all provided evaluators to the given cell. More...
template<class Evaluators , class Cell , class Index >
void	moveEvaluatorsToCell (Evaluators &evals, Cell const &cell, Index idx)
	Moves all provided evaluators to the given cell with provided index. More...
template<class Evaluator , class QuadratureRule >
void	useQuadratureRuleInEvaluators (Evaluator &evals, QuadratureRule const &qr, int subId)
	Tells all evaluators to use the given quadrature rule on the given subentity. More...
template<class Evaluators , class CoordType , int dim, int subDim>
void	moveEvaluatorsToIntegrationPoint (Evaluators &evals, Dune::FieldVector< CoordType, dim > const &x, Dune::QuadratureRule< CoordType, subDim > const &qr, int ip, int subId)
	Moves all provided evaluators to the given integration point, evaluating the shape functions there. More...
template<class Evaluators , class CoordType , int dim>
void	moveEvaluatorsToIntegrationPoint (Evaluators &evals, Dune::FieldVector< CoordType, dim > const &x)
	Moves all provided evaluators to the given integration point, evaluating the shape functions there. More...
template<class Evaluators >
int	maxOrder (Evaluators const &evals)
	Computes the maximum ansatz order used in a collection of evaluators. More...
template<template< class Fct1, class Fct2 > class View, class Fct1 , class Fct2 >
View< Fct1, Fct2 >	makeView (Fct1 const &f1, Fct2 const &f2)
	Construct a View on two Functions without having to state the type of these explicitely. More...
template<template< typename Function > class View, typename Function >
View< Function >	makeView (Function const &f1)
	Construct a View on a Function without having to state the type of it explicitely. More...
template<class View , class Space >
CellData< typenameSpace::Grid, Dune::FieldVector< double, 1 > >::CellDataVector	evalCellProperties (Space const &space)
	Evaluate WeakFunctionViews and construct CellData. More...
template<class Map , class IndexSet , class LocalDofs >
size_t	computeDofStartIndices (int dim, Map &map, IndexSet const &is, LocalDofs &localDof)
	For each codimension (i.e., type of subentity) computes the number of global ansatz functions as well as an accumulated index into an array of all ansatz functions. More...
void	vertexids (int d, int c, int k, int *idx)
	Computes the d-c+1 local vertex indices of the vertices incident to the k-th subentity of codimension c in the reference simplex of dimension d. More...
template<class GridView >
std::pair< Dune::FieldVector< typename GridView::ctype, GridView::dimensionworld >, Dune::FieldVector< typename GridView::ctype, GridView::dimensionworld > >	boundingBox (GridView const &gv)
	Computes a the bounding box of the given grid view. More...
template<class GridView >
std::unique_ptr< typename GridView::Grid >	createCoverGrid (GridView const &gv, double volumeRatio=10)
	Creates a cartesian structured grid occupying the bounding box of the given grid view. More...
template<class Grid >
void	refineAtBoundary (GridManagerBase< Grid > &gridManager)
	A convenience routine that refines all cells incident to a boundary face. More...
template<class ExtensionVariables , class LinearFunctional >
HierarchicErrorEstimator< LinearFunctional, ExtensionVariables >	hierarchicErrorEstimator (LinearFunctional const &lf, typename LinearFunctional::AnsatzVars::VariableSet const &u)
template<class ctype , int dimension, class Scalar >
HierarchicShapeFunctionSetContainer< ctype, dimension, Scalar >::value_type const &	hierarchicShapeFunctionSet (Dune::GeometryType type, int order)
	Returns a Hierarchic shape function set for given reference element type and given polynomial order. Singleton function. More...
template<class ctype , int dimension, class Scalar >
HierarchicExtensionShapeFunctionSetContainer< ctype, dimension, Scalar >::value_type const &	hierarchicExtensionShapeFunctionSet (Dune::GeometryType type, int order)
template<class Function , class Functor >
void	forEachQuadPoint (Function const &f, Functor &accumulator)
	Loops over the whole domain occupied by the grid and calls an accumulator for each integration point with the value of the function f. This version of forEach requires the function f to be evaluatable by an Evaluator of the associated space of f. More...
template<class Functor , class Space >
void	forEachQP (Functor &g, Space const &space)
	Loops over the whole domain occupied by the grid and calls the functor g for each integration point with an evaluator of the associated space. More...
template<class Functor , class Function , class Space >
void	forEachQuadPoint (Function const &f, Functor &g, Space &space)
	Loops over the whole domain occupied by the grid and calls the functor g for each integration point with the value of the function f. More...
template<class FEFunction >
FEFunction::ValueType	integrateOverIntersection (FEFunction const &function, typename FEFunction::Space::GridView::Intersection const &intersection, typename FEFunction::Space::Evaluator &evaluator)
	integrateOverIntersection computes the integral of an FE function over a grid intersection (face). More...
template<class FEFunction >
FEFunction::ValueType	integrateOverBoundary (FEFunction const &function)
	integrateOverBoundary computes the integral of an FE function over the whole boundary of the underlying grid. More...
template<template< class, class > class DomainMapper, typename Scalar , typename GridView , int m>
FunctionSpaceElement< FEFunctionSpace< BoundaryMapper< DomainMapper, Scalar, GridView > >, m >::ValueType	integrateOverBoundary (FunctionSpaceElement< FEFunctionSpace< BoundaryMapper< DomainMapper, Scalar, GridView > >, m > const &function)
	integrateOverBoundary computes the integral of an FE function which is restricted to (parts of) the boundary over the boundary of the underlying grid. More...
template<typename Function , class = typename Function::Space>
Function::ValueType	integral (Function const &f)
	Evaluate integrals of finite element functions. More...
template<class WeakFunctionView , class Space >
auto	integral (WeakFunctionView const &f, Space const &space)
template<class VariableList , class Collector , class Functions , class Spaces >
void	gridIterate (VariableList const &vars, Functions const &functions, Spaces const &spaces, Collector &f)
	A function that supports general iterations over a spatial domain and supports efficient evaluation of FE functions at the iterated quadrature points. This is a low-level function working directly on variable lists and function lists. There's a convenience overload working on VariableSets. More...
template<class VariableSet , class Collector >
void	gridIterate (VariableSet const &functions, Collector &f)
	A function that supports general iterations over a spatial domain and supports efficient evaluation of FE functions at the iterated quadrature points. More...
template<class Variables , class Functions , class Spaces , class Scaling , class Collector >
void	scaledTwoNormSquared (Variables const &varDesc, Functions const &f, Spaces const &spaces, Scaling const &scaling, Collector &sum)
	Evaluates the square of the scaled \(L^2\)-norms of a set of functions. More...
template<class Variables , class OutIter , class Functions , class Spaces , class Scaling >
void	relativeError (Variables const &varDesc, Functions const &f1, Functions const &f2, Functions const &f3, Spaces const &spaces, Scaling const &scaling, OutIter out)
template<class ctype , int dimension, class Scalar = double, bool restricted = false>
LagrangeShapeFunctionSetContainer< ctype, dimension, Scalar, restricted >::value_type const &	lagrangeShapeFunctionSet (Dune::GeometryType type, int order)
	Returns a Lagrange shape function set for given reference element type and given polynomial order. Singleton function. More...
template<int m, class Scalar , class Sequence >
auto &	component (LinearProductSpace< Scalar, Sequence > &x)
template<class Space , class Density , int m = 1, class Scalar = double>
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, m, m > >	massMatrix (Space const &space, Density const &rho)
	Creates a mass matrix for the given FE space. More...
template<class Space , class Conductivity , int m = 1, class Scalar = double>
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, m, m > >	stiffnessMatrix (Space const &space, Conductivity const &kappa)
	Creates a stiffness matrix for the given FE space. More...
template<class ctype , int dimension, class T >
NedelecShapeFunctionSetContainer< ctype, dimension, T >::value_type const &	nedelecShapeFunctionSet (Dune::GeometryType type, int order)
template<class ctype , int dimension, class T = double>
HdivShapeFunctionSetContainer< ctype, dimension, T >::value_type const &	hdivShapeFunctionSet (Dune::GeometryType type, int order)
	Returns a Hdiv shape function set for given reference element type and given polynomial order. Singleton function. More...
template<class Function >
CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector	localH1SemiNorm (Function const &f)
	local (cellwise) H1-semi-norms More...
template<class Function >
CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector	localL2Norm (Function const &f)
	local (cellwise) L2-norms More...
template<class FEFunction >
auto	boundaryL2Norm (FEFunction const &function)
	boundaryL2Norm computes the L2-norm of an FE function on the whole boundary of the underlying grid. More...
template<class ShapeFunctionSet >
void	computeSimplexSfPermutation (ShapeFunctionSet const &sfs, int const *vPermutation, int *sfPermutation, int *sign)
template<class ErrorDescriptions , class F , class FS , class TestFunctions , class Spaces , class TestSpaces >
void	residualTimesTestFunction (std::vector< Dune::FieldVector< typename SpaceType< Spaces, 0 >::type::RT, boost::fusion::result_of::size< ErrorDescriptions >::type::value > > &ind, ErrorDescriptions const &varDesc, F const &f, FS const &fs, TestFunctions const &tf, Spaces const &spaces, TestSpaces const &testSpaces)
	Evaluates strong residual, applied to some test-function <f(x), tf> More...
template<class Space , class Range >
std::vector< size_t >	algebraicPatch (Space const &space, Range const &cells)
	Computes the global indices of all ansatz functions whose support is a subset of the union of given cells. More...
template<class Space , class Range >
std::vector< size_t >	algebraicPatch (Space const &space, Range const &cells, size_t vertexIdx, std::vector< std::vector< size_t > > const &indicesOnFacets)
	Computes the global indices of all ansatz functions whose support is a subset of the union of given cells. More...
template<class GridView >
auto	computePatches (GridView const &gridview)
	Computes the patches around vertices of the grid view. More...
template<class Variables , class Functions , class Evaluators , class Method >
auto	evaluateFunctions (Functions const &fs, Evaluators const &eval, Method const &method=Method())
	A function evaulating all functions in a variable set using the provided method. More...
template<class VariableSet , class Method >
auto	evaluateVariables (VariableSet const &vars, typename VariableSet::Descriptions::Evaluators const &eval, Method const &method=Method())
	A function evaulating all functions in a variable set using the provided method. More...
template<class It >
RangeView< It >	rangeView (It first, It last)
	Convenience function for constructing range views on the fly. More...
template<class GridView >
void	copyHeader (GridView const &gridView, std::string const &file_in, std::string const &file_out)
template<class GridView , class VariableSet >
void	writeAMIRAFile (GridView const &gridView, VariableSet const &vars, std::string file_out, IoOptions options=ioOptions_default, Dune::BlockVector< Dune::FieldVector< double, 1 > > materialData=Dune::BlockVector< Dune::FieldVector< double, 1 > >(), std::string file_in="")
Endian	endianness ()
	Return endianness. More...
bool	bigEndian ()
	Return true if byte order is big endian. More...
bool	littleEndian ()
	Return true if byte order is little endian. More...
std::string	paddedString (int n, int places=3)
	creates a zero-padded string representation of the given number More...
template<class GridView , class Writer , class VariableSet , class Filter , class Options >
void	writePartialFile (GridView const &gridView, Writer &writer, VariableSet const &vars, std::string const &filename, Filter const &filter, Options const &options)
template<class Material >
void	writeMarc (Material const &material, std::string const &filename, double const scale=1.0, IoOptions options=IoOptions())
	Writes grid and material IDs given as FE function to a Marc input file. More...
template<class Entry , class Index , class VEntry >
void	writeToMatlabBinary (NumaBCRSMatrix< Entry, Index > const &A, Dune::BlockVector< VEntry > const &b, std::string const &basename, std::string const &path, int precision=16)
	Writes the given matrix and vector to an binary file based zero. More...
template<class Entry , class Index >
void	writeToMatlab (NumaBCRSMatrix< Entry, Index > const &A, std::string const &basename, std::string const &outPath, int precision=16)
	Writes the given matrix to an executable matlab file. More...
template<class Entry , class Index , class VEntry >
void	writeToMatlab (NumaBCRSMatrix< Entry, Index > const &A, Dune::BlockVector< VEntry > const &b, std::string const &basename, int precision=16)
	Writes the given matrix and vector to an executable matlab file. More...
template<class Assembler >
void	writeToMatlab (Assembler const &assembler, std::string const &basename, int precision=16)
template<class Assembler >
void	writeToMatlab (Assembler const &assembler, std::string const &path, std::string const &basename, int precision=16)
template<class Function >
void	writeVTK (Function const &f, std::string const &filename, IoOptions options, std::string fname)
	Writes a single finite element function to a VTK file. More...
std::ostream &	operator<< (std::ostream &stream, VTKReader::FunctionInfo const &info)
template<class VariableSet >
void	writeVTK (VariableSet const &vars, IoOptions options, std::ostream &s)
	Writes a set of finite element functions in VTK XML format to a stream. More...
template<class VariableSet >
void	writeVTK (VariableSet const &vars, std::string fname, IoOptions const &options)
	Writes a set of finite element functions in VTK XML format to a file. More...
void	dgetrf_ (int *m, int *n, double *a, int *lda, int *ipiv, int *info)
void	dgetrs_ (char *trans, int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info)
template<class Domain , class Range >
bool	requiresInitializedInput (Dune::Preconditioner< Domain, Range > const *p)
	Whether a preconditioner needs zero initialized result vector or not. More...
template<class Scalar , class Entry >
std::unique_ptr< Dune::MatrixIndexSet >	conjugationPattern (Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 > > const &P, Dune::BCRSMatrix< Entry > const &A, bool onlyLowerTriangle=false)
	Creates the sparsity pattern of \( P^T A P\). More...
template<class Scalar , class Entry >
void	conjugation (Dune::BCRSMatrix< Entry > &C, Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 > > const &P, Dune::BCRSMatrix< Entry > const &A, bool onlyLowerTriangle=false)
	Computes the triple sparse matrix product \( C = C + P^T A P \). More...
template<class OutIter >
OutIter	vectorToSequence (double x, OutIter iter)
template<class OutIter >
OutIter	vectorToSequence (float x, OutIter iter)
template<class K , int size, class OutIter >
OutIter	vectorToSequence (Dune::FieldVector< K, size > const &v, OutIter iter)
template<class B , class A , class OutIter >
OutIter	vectorToSequence (Dune::BlockVector< B, A > const &v, OutIter iter)
	copies the entries of a vector sequentially to the output iterator. More...
template<class K , class OutIter >
OutIter	vectorToSequence (std::vector< K > const &v, OutIter iter)
template<class InIter >
InIter	vectorFromSequence (double &x, InIter iter)
template<class InIter >
InIter	vectorFromSequence (float &x, InIter iter)
template<class K , int size, class InIter >
InIter	vectorFromSequence (Dune::FieldVector< K, size > &v, InIter iter)
template<class B , class A , class InIter >
InIter	vectorFromSequence (Dune::BlockVector< B, A > &v, InIter in)
	copies the elements obtained from the input iterator sequentially to the entries of the vector. More...
template<class K , class InIter >
InIter	vectorFromSequence (std::vector< K > &v, InIter iter)
template<class Matrix , class OutIteratorI , class OutIteratorD >
void	matrix_to_triplet (Matrix const &a, OutIteratorI i, OutIteratorI j, OutIteratorD z)
	converts a matrix to the coordinate (triplet) format. More...
template<class SparseInt >
std::vector< std::vector< SparseInt > >	getBCRSIndicesFromTriplet (SparseInt nrows, std::vector< SparseInt > const &ridx, std::vector< SparseInt > const &cidx, int nr=1, int nc=1)
	Sorts the sparse matrix nonzero positions into row buckets. More...
template<class B , class A >
std::ostream &	operator<< (std::ostream &out, Dune::BCRSMatrix< B, A > const &a)
template<class GOP , int firstRow, int lastRow, int firstCol, int lastCol>
InverseLinearOperator< DirectSolver< typename AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol >::Domain, typename AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol >::Range > >	directInverseOperator (AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol > const &A, DirectType directType, MatrixProperties properties)
template<class Matrix , class Domain , class Range >
InverseLinearOperator< DirectSolver< Domain, Range > >	directInverseOperator (MatrixRepresentedOperator< Matrix, Domain, Range > const &A, DirectType directType=DirectType::UMFPACK, MatrixProperties properties=MatrixProperties::GENERAL)
std::array< std::vector< size_t >, 3 >	nestedDissection (std::vector< std::pair< size_t, size_t > > const &edges, std::vector< size_t > const &edgeStart)
	Computes a nested dissection of the given graph. More...
template<class T , typename = std::enable_if_t<std::is_arithmetic<T>::value>>
T	transpose (T x)
template<class Scalar , int d>
Dune::FieldVector< Scalar, d >	eigenvalues (Dune::FieldMatrix< Scalar, d, d > A)
	Computes the eigenvalues of a symmetric matrix \( A \). More...
template<class Scalar , int d>
Dune::FieldVector< Scalar, d >	eig (Dune::FieldMatrix< Scalar, d, d > &A, bool computeEigenvectors=true)
	Computes the eigenvalues and eigenvectors of a symmetric matrix \( A \). More...
template<int dimIn, int dimOut>
Dune::BlockVector< Dune::FieldVector< double, dimOut > >	reshapeBlocks (Dune::BlockVector< Dune::FieldVector< double, dimIn > > const &b)
	reshapes a Dune::BlockVector block structure More...
template<class Entry , int n>
Dune::FieldMatrix< Entry, n, n >	diag (Dune::FieldVector< Entry, n > const &d)
	Creates a fixed-size diagonal matrix from the given diagonal vector. More...
template<class Scalar , class Index >
void	tripletToCompressedColumn (Index nRows, Index nCols, size_t nNonZeros, std::vector< Index > const &ridx, std::vector< Index > const &cidx, std::vector< Scalar > const &values, std::vector< Index > &Ap, std::vector< Index > &Ai, std::vector< Scalar > &Az)
	Converts a matrix in triplet format to a compressed column format. More...
template<class Scalar , class Index >
std::unique_ptr< Factorization< Scalar > >	getFactorization (DirectType directType, MatrixAsTriplet< Scalar, Index > const &A, FactorizationOptions options)
	Creates a factorization of the given triplet matrix. More...
template<class Scalar >
std::unique_ptr< Factorization< Scalar > >	getFactorization (DirectType directType, Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 > > const &A, FactorizationOptions options)
	Creates a factorization of the given BCRSmatrix. More...
template<class Scalar , int n, int m, class Index >
std::unique_ptr< Factorization< Scalar > >	getFactorization (DirectType directType, NumaBCRSMatrix< Dune::FieldMatrix< Scalar, n, m >, Index > const &A, FactorizationOptions options)
	Creates a factorization of the given NumaBCRS matrix. More...
template<class Entry , bool diagonal, class SortedRowIdx , class SortedColIdx >
std::ostream &	operator<< (std::ostream &out, LocalMatrix< Entry, diagonal, SortedRowIdx, SortedColIdx > const &A)
template<class Entry , class Index >
void	insertMatrixBlockIndices (NumaCRSPatternCreator< Index > &globalCreator, NumaBCRSMatrix< Entry, Index > const &matrixBlock, typename NumaBCRSMatrix< Entry, Index >::size_type startRow, typename NumaBCRSMatrix< Entry, Index >::size_type startCol)
template<class Entry >
void	insertMatrixBlockIndices (Dune::MatrixIndexSet &globalIndexSet, Dune::BCRSMatrix< Entry > const &matrixBlock, Dune::MatrixIndexSet::size_type startRow, Dune::MatrixIndexSet::size_type startCol)
template<class BMatrix >
void	insertMatrixBlockEntries (BMatrix &globalMatrix, BMatrix const &matrixBlock, typename BMatrix::size_type startRow, typename BMatrix::size_type startCol)
template<class BVector >
void	insertVectorBlock (BVector &globalVector, BVector const &vectorBlock, typename BVector::size_type startIdx)
template<class MatrixA , class MatrixB , class VectorX , class VectorB >
std::array< typename ScalarTraits< typename MatrixA::field_type >::Real, 4 >	checkKKT (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x, VectorB const &lambda)
	Computes the KKT residual for approximate solutions of certain QPs. More...
template<class MatrixA , class MatrixB , class VectorX , class VectorB , class Real >
Real	qpLinesearch (MatrixA const &A, MatrixB const &B, Real gamma, VectorX const &c, VectorB const &b, VectorX const &dx)
	Performs linesearch for penalized QPs. More...
template<class MatrixA , class MatrixB , class VectorX , class VectorB , class Real >
Real	qpLinesearch (MatrixA const &A, MatrixB const &B, Real gamma, VectorX const &c, VectorB const &b, VectorX const &x, VectorX const &dx)
	Performs linesearch for penalized QPs. More...
template<int n, class Entry , int m, class A >
Dune::BlockVector< Dune::FieldVector< Entry, n >, A >	reshapeBlocks (Dune::BlockVector< Dune::FieldVector< Entry, m >, A > const &x)
	Reshapes a nested block vector to differen entry sizes. More...
template<class Kb , int nb, int mb, class Ka , int na, int ma>
DynamicMatrix< Dune::FieldMatrix< Kb, nb, mb > >	reshapeBlocks (DynamicMatrix< Dune::FieldMatrix< Ka, na, ma > > const &A)
void	printVec (std::vector< double > const &v, int vend=1000000)
	Adapter class for DUNE::IterativeSolver. More...
void	LeastSquares (SLAPMatrix< double > a, std::vector< double > const &b, std::vector< double > &x)
	Solve linear least squares problem, given by a*x=b. More...
void	SymmetricEigenvalues (SLAPMatrix< double > a, std::vector< double > &eig)
template<class Scalar >
void	pseudoinverse (SLAPMatrix< Scalar > A, SLAPMatrix< Scalar > &Ainv)
void	MatrixMultiply (SLAPMatrix< double > A, std::vector< double > &in, std::vector< double > &out)
	Matrix multiplication. More...
void	TransposedMatrixMultiply (SLAPMatrix< double > A, std::vector< double > &in, std::vector< double > &out)
void	MatrixKT_A_K (SLAPMatrix< double > A, SLAPMatrix< double > &K, SLAPMatrix< double > &out)
void	MatrixMultiplication (SLAPMatrix< double > A, SLAPMatrix< double > &B, SLAPMatrix< double > &AB)
template<class Entry , int ... Sizes>
std::ostream &	operator<< (std::ostream &out, Tensor< Entry, Sizes... > const &t)
template<class Target , class Source , class RowIndices , class ColIndices >
Target	submatrix (Source const &A, RowIndices const &ri, ColIndices const &ci)
template<class Index , class Index2 >
NumaCRSPattern< Index >	operator+ (NumaCRSPattern< Index > const &pa, NumaCRSPattern< Index2 > const &pb)
template<class Scalar , int n, class Index = size_t>
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, n, n >, Index >	sparseUnitMatrix (Index N)
	creates a unit matrix in NUMA block compressed row storage format More...
template<class Scalar , int n, int m, class Index = size_t>
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, n, m >, Index >	sparseZeroMatrix (Index N, Index M)
	creates a zero matrix in NUMA block compressed row storage format More...
template<class Scalar >
void	deleteLowerTriangle (std::vector< int > &ridx, std::vector< int > &cidx, std::vector< Scalar > &data)
	removes subdiagonal entries from the matrix entries stored in elementary triplet format More...
template<typename Scalar , typename SparseIndexInt >
std::ostream &	operator<< (std::ostream &s, MatrixAsTriplet< Scalar, SparseIndexInt > const &mat)
void	umfpack_solve (std::vector< int > const &ridx, std::vector< int > const &cidx, std::vector< double > const &values, std::vector< double > const &b, std::vector< double > &x)
template<class X , class Y >
void	applyPreconditioner (Dune::Preconditioner< X, Y > &p, X &x, Y &y)
	Convenience function for simple application of preconditioners. Calls pre(), apply(), and post() sequentially. More...
template<class MatA , class SolA , class MatB , class MatBt , class PrecS >
auto	uzawa (MatA &A, SolA &invA, MatB &B, MatBt &Bt, PrecS &precS, double reduction=1e-3, int maxit=1000, int verbose=0)
	Convenience function for constructing an UzawaSolver. \tparem MatA derived from Dune::LinearOperator<X,X> More...
template<class Scalar , class Sequence >
auto	nestUzawa (LinearProductSpace< Scalar, Sequence > const &z)
	Convenience function for creating Uzawa domain/range arguments. More...
template<class Scalar , class Sequence >
auto	unnestUzawa (LinearProductSpace< Scalar, Sequence > const &z)
	Convenience function for unpacking Uzawa domain/range results. More...
template<class Entry , class A >
Dune::BlockVector< Entry, A >	vertcat (Dune::BlockVector< Entry, A > const &x, Dune::BlockVector< Entry, A > const &y)
template<class Entry , class Index , class Prolongation , class MakeSmoother , class MakeCoarsePreconditioner >
auto	makeAdditiveMultiGrid (NumaBCRSMatrix< Entry, Index > const &A, std::vector< Prolongation > const &prolongations, MakeSmoother const &makeSmoother, MakeCoarsePreconditioner const &makeCoarsePreconditioner, bool onlyLowerTriangle=false)
	Convenience function creating additive multigrid preconditioners for P1 elements. More...
template<class Entry , class Index , class GridMan >
auto	makeBPX (NumaBCRSMatrix< Entry, Index > const &A, GridMan const &gridman, bool onlyLowerTriangle=false)
	Convenience function creating a BPX preconditioner for P1 elements. More...
template<class Entry , class Index , class FineSpace , class MakeSmoother , class MakeCoarseSmoother >
auto	makeAdditivePMultiGrid (NumaBCRSMatrix< Entry, Index > A, FineSpace const &space, H1Space< typename FineSpace::Grid > const &p1Space, MakeSmoother const &makeSmoother, MakeCoarseSmoother const &makeCoarseSmoother, int coarseLevel=0, bool onlyLowerTriangle=false)
	Convenience function creating additive multigrid preconditioner of V-cycle type for higher order elements. More...
template<class StorageTag , class Entry , class Index , class FineSpace >
auto	makePBPX (NumaBCRSMatrix< Entry, Index > A, FineSpace const &space, H1Space< typename FineSpace::Grid > const &p1Space, StorageTag storageTag, int coarseLevel=0, bool onlyLowerTriangle=false)
	Convenience function creating additive multigrid preconditioner of V-cycle type with domain decomposition and Jacobi smoother for higher order elements. More...
template<class FromSpace , class ToSpace >
Prolongation	twoGridProlongation (FromSpace const &from, ToSpace const &to)
	Computes an interpolation matrix for transfer between P1 finite element spaces on two different grids. More...
template<class FromSpace , class ToSpace >
Prolongation	nonNestedProlongation (FromSpace const &from, ToSpace const &to, double tolTrunc=0.1)
	Computes an interpolation matrix for transfer between P1 finite element spaces on two different (possibly non-nested) grids. More...
std::vector< Prolongation >	nonNestedProlognationStack (std::vector< Prolongation > ps)
	Computes a full column rank prolongation stack from a colum rank deficient prolongation stack. More...
template<class Space >
std::vector< Prolongation >	makeNonNestedPstack (std::initializer_list< Space > spacelist, double tolTrunc=0.1)
	Computes an interpolation matrix for transfer between P1 finite element spaces on two different (possibly non-nested) grids. More...
template<class Space1 , class Space2 >
std::vector< Prolongation >	makeJointPstack (Space1 space1, Space2 space2, int coarseLevel=0)
	Computes a (joint) prolongation stack for a geometry defined by two grids. More...
template<class Space , class Entry , class Index >
MultiGridStack< Prolongation, Entry, Index >	makeAuxiliarySpaceMultigridStack (Space const &space, NumaBCRSMatrix< Entry, Index > const &A, double volumeRatio=100)
	creates a semi-geometric multigrid preconditioner based on an auxiliary space More...
template<class Entry , class Index , class Space >
auto	makeMultigrid (NumaBCRSMatrix< Entry, Index > const &A, Space const &space, bool onlyLowerTriangle=false, DirectType directType=DirectType::MUMPS)
	Convenience function for creating a (multiplicative) multigrid preconditioner for elliptic equations. More...
template<typename Matrix >
auto	makeDirectPreconditioner (Matrix &&A, DirectType directType=DirectType::MUMPS)
	Creates a direct solver for the given matrix. More...
template<int domainBlockSize, int rangeBlockSize, class Index >
auto	makeDirectPreconditioner (NumaBCRSMatrix< Dune::FieldMatrix< float, rangeBlockSize, domainBlockSize >, Index > &&A, DirectType directType=DirectType::MUMPS)
	Creates a direct solver for the given matrix. This specialization is for matrices containing floats (single precision) as scalar entries. Since the Kaskade interface for direct solvers only works for doubles, the matrix is copied into a new matrix with double as scalar entries. Since the coarse grid matrix often is much smaller, this hopefully means neglectable overhead. More...
template<class SparseIndex = size_t, class CoarseSpace , class FineSpace >
NumaBCRSMatrix< Dune::FieldMatrix< typename FineSpace::Scalar, 1, 1 >, SparseIndex >	prolongation (CoarseSpace const &coarseSpace, FineSpace const &fineSpace)
	Computes an interpolation-based prolongation matrix from a (supposedly) coarser space to a finer space. More...
template<class SparseIndex , class Mapper >
std::vector< NumaBCRSMatrix< Dune::FieldMatrix< typename Mapper::Scalar, 1, 1 >, SparseIndex > >	prolongationStack (FEFunctionSpace< Mapper > const &space)
	Computes a stack of prolongation matrices for higher order finite element spaces. More...
std::ostream &	operator<< (std::ostream &out, MGProlongation const &p)
template<class Entry , class Index >
auto	conjugation (MGProlongation const &p, NumaBCRSMatrix< Entry, Index > const &a, bool onlyLowerTriangle=false)
	Creates a Galerkin projected Matrix \( P^T A P \) from a prolongation \( P \) and a symmetric matrix \( A \). More...
template<class GridMan >
std::vector< MGProlongation >	prolongationStack (GridMan const &gridman, int coarseLevel=0, size_t minNodes=0)
	Computes a sequence of prolongation matrices for P1 finite elements in hierarchical grids. More...
template<class GridMan >
std::vector< NumaBCRSMatrix< Dune::FieldMatrix< double, 1, 1 > > >	deformedProlongationStack (GridMan const &gridman, int coarseLevel=0, size_t minNodes=0, bool interpolateAtShiftedPosition=true)
	Computes a sequence of prolongation matrices for P1 finite elements in hierarchical grids. More...
template<typename Prolongations , typename Entry , typename Index >
std::ostream &	operator<< (std::ostream &out, MultiGridStack< Prolongations, Entry, Index > const &mgStack)
template<class GridMan , class Entry , class Index >
MultiGridStack< MGProlongation, Entry, Index >	makeGeometricMultiGridStack (GridMan const &gridManager, NumaBCRSMatrix< Entry, Index > &&A, size_t minNodes=10000, bool onlyLowerTriangle=false)
	convenience routine for creating multigrid stacks based on geometric coarsening for P1 elements More...
template<class Entry , class Index >
MultiGridStack< MGProlongation, Entry, Index >	makeAlgebraicMultigridStack (NumaBCRSMatrix< Entry, Index > &&A, Index n=0, bool onlyLowerTriangle=false)
	Creates stack of prolongations and projected Galerkin matrices. More...
template<typename FineSpace >
auto	makeDeepProlongationStack (FineSpace const &space, int coarseLevel=0, int minNodes=0)
	Convenience routine for creating a deep prolongation stack from coarse to fine grid and on from P1 to higher order. More...
template<typename FineSpace , typename Matrix >
auto	makePMultiGridStack (FineSpace const &space, Matrix &&A, bool onlyLowerTriangle)
	convenience routine for creating multigrid stacks based on coarsening by reducing the ansatz order from P to P1 More...
template<typename FineSpace , typename CoarseSpace , typename Matrix >
auto	makePMultiGridStack (FineSpace const &fineSpace, Matrix &&fA, CoarseSpace const &coarseSpace)
	convenience routine for creating multigrid stacks between two spaces. More...
template<typename FineSpace , typename CoarseSpace , typename Matrix >
auto	makePMultiGridStack (FineSpace const &fineSpace, Matrix &&fA, CoarseSpace const &coarseSpace, Matrix &&cA)
	convenience routine for creating multigrid stacks between two spaces. More...
template<class Scalar >
void	bsplineDifferentiationMatrix (Dune::DynamicVector< Scalar > const &t, Dune::DynamicVector< Scalar > const &s, int p, Dune::DynamicMatrix< Scalar > &d)
	computes the differentiation matrix for bspline interpolation of order p on t More...
template<class Scalar >
void	bsplineEvaluationMatrix (Dune::DynamicVector< Scalar > const &t, Dune::DynamicVector< Scalar > const &s, int p, Dune::DynamicMatrix< Scalar > &e)
	computes the evaluation on s matrix for bspline interpolation of order p on t More...
template<class Matrix , class Vectors , class ReactionDerivatives , class Solver >
Matrix::field_type	sdcIterationStep (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &r, ReactionDerivatives const &f_u, Vectors const &u, Vectors &du)
	A single spectral defect correction iteration sweep. More...
template<class Matrix , class Vectors , class Solver >
Matrix::field_type	sdcIMEXStep (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &r, Vectors const &u, Vectors &du)
	A single IMEX SDIRK spectral deferred correction sweep. More...
template<class Matrix , class Vectors , class ReactionDerivatives , class Solver >
Matrix::field_type	sdcIterationStep2 (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix const &Shat, Solver const &solve, Matrix const &M, Matrix const &A, Vectors const &rUi, ReactionDerivatives const &f_u, Vectors const &Mdu, Vectors &du)
	A single spectral defect correction iteration sweep. More...
template<class Matrix , class Vectors , class ReactionDerivatives >
double	waveformRelaxationStep2 (SDCTimeGrid const &grid, Matrix const &M, Matrix const &A, Vectors const &rUi, ReactionDerivatives const &f_u, Vectors &du)
	A single waveform relaxation iteration. More...
template<class Vector >
Vector::field_type	maxNorm (std::vector< Vector > const &values)
	A function to compute the partial \(\max-\)norm or \(L^{\infty}-\)norm of a vector of vectors. If \(\mathbf{x}\) denotes a vector of vectors, where \(\mathbf{x} = \{ \mathbf{x_1},\ldots , \mathbf{x_n}\}^{T}\), then \(\| \mathbf{x} \|_{\infty} = \max_{1 \leq i \leq N} \|\mathbf{x_i}\|$\f. Here the norm \)|.| \( is some arbitrary norm and in the current template function it is implemented as a \)\max- \(norm. \tparam Vector, a vector type, usually Dune::DenseVector \param[in]values a vector of vectors. \return the \)\infty-. More...
template<class Vector >
Vector::field_type	sdcExEulerIterationStep (Kaskade::SDCTimeGrid const &grid, std::vector< Vector > &yi, std::vector< Vector > &dyi, std::function< Vector(typename Vector::field_type, Vector const &)> rhsFunc, std::function< typename Vector::field_type(std::vector< Vector > const &)> normFunc, bool verbose=false)
	A single spectral defect correction iteration sweep based on explicit Euler method. More...
template<int d, class Real >
Real	bezier (int p, int i, Dune::FieldVector< Real, d > const &x)
	Computes the i-th Bezier function of order p at the given point in the unit simplex. More...
constexpr int	binomial (int n, int k)
	Computes the binomial coefficient \( \binom{n}{k} \). More...
template<size_t m>
size_t	multinomial (std::array< size_t, m > const &ks)
	Computes the multinomial coefficient \( \binom{n}{k_1,\dots,k_m}\), where \( n = \sum_{i=1}^m k_i \). More...
constexpr int	numberOfMultiindices (int d, int m)
	Computes the number of multiindices of order m and dimension d. More...
template<int d>
std::array< size_t, d >	multiIndex (size_t m, size_t n)
	Random access to multiindices. More...
template<class It >
void	next_multiindex (It first, It last, int const m)
	Computes the next nonnegative multiindex of order m. More...
std::string	getDateAndTime ()
std::string	getDate ()
std::string &	appendDateAndTime (std::string &str)
	append current time and date to string str More...
std::string &	appendDate (std::string &str)
	append current date to string str More...
std::vector< double >	lobattoNodes (int n)
	Computes the n Lobatto nodes on [-1,1] including the interval end points. More...
std::vector< double >	radauNodes (int n)
	Computes the n Radau nodes on [-1,1] including the right end point. More...
std::vector< double >	gaussNodes (int n)
	Computes the n Gauß nodes on [-1,1] excluding the interval end points. More...
template<class Grid , class Type >
std::unique_ptr< Grid >	createGrid (std::vector< Type > const &cubes)
	Extract simplicial grid from list of cubes. More...
template<class Grid , class Scalar , int dim, class EdgeLength >
std::unique_ptr< Grid >	createCuboid (Dune::FieldVector< Scalar, dim > const &x0, Dune::FieldVector< Scalar, dim > const &dx, EdgeLength const &dh, bool symmetric=true)
	Creates a uniform simplicial grid on a rectangular or cuboid domain. More...
template<class Grid >
std::unique_ptr< Grid >	createUnitSquare (double dh=1., bool symmetric=true)
	Creates a unit square, filled regularly. More...
template<class Grid >
std::unique_ptr< Grid >	createUnitCube (double dh=1., bool symmetric=true)
	Creates a unit cube. More...
template<class Grid , class Scalar >
std::unique_ptr< Grid >	createRectangle (Dune::FieldVector< Scalar, 2 > const &x0, Dune::FieldVector< Scalar, 2 > const &dx, Scalar dh, bool symmetric=true)
	Fill rectangle with squares. More...
template<class Grid , class Scalar , int dim>
std::unique_ptr< Grid >	createLShape (Dune::FieldVector< Scalar, dim > const &x0, Scalar dx, Scalar dy, Dune::FieldVector< Scalar, dim > const &thickness, Scalar dh, bool symmetric=true)
	Fill L-shaped domain with cubes. More...
template<class Grid , class Scalar , int dim>
std::unique_ptr< Grid >	createTShape (Dune::FieldVector< Scalar, dim > const &x0, Scalar dx, Scalar dy, Dune::FieldVector< Scalar, dim > const &thickness, Scalar dh, bool symmetric=true)
	Fill L-shaped domain with cubes. More...
template<class Grid , class Scalar , int dim>
std::unique_ptr< Grid >	createTwoLayerCuboid (Dune::FieldVector< Scalar, dim > const &x0, Dune::FieldVector< Scalar, dim > const &dx1, Dune::FieldVector< Scalar, dim > const &dx2, Dune::FieldVector< Scalar, dim > const &dh1, Scalar dh2, bool symmetric=true)
template<class Grid , class Scalar , int dim>
std::unique_ptr< Grid >	createTwoLayerCuboid (Dune::FieldVector< Scalar, dim > const &x0, Dune::FieldVector< Scalar, dim > const &dx1, Dune::FieldVector< Scalar, dim > const &dx2, Dune::FieldVector< Scalar, dim > const &dh1, Dune::FieldVector< Scalar, dim > const &dh2, bool symmetric=true)
template<class Grid >
std::unique_ptr< Grid >	createHexahedron ()
	Creates a hexahedron consisting of five tetrahedra. More...
template<class Grid >
std::unique_ptr< Grid >	createOctahedron (Dune::FieldVector< typename Grid::ctype, 3 > extent=Dune::FieldVector< typename Grid::ctype, 3 >(1.0))
	Creates an octahedron consisting of eight tetrahedra. More...
template<class Grid >
std::unique_ptr< Grid >	createIcosahedron ()
	Creates an icosahedron consisting of 20 tetrahedra. More...
template<class Grid >
std::unique_ptr< Grid >	createCylinder (double radius, double height, int layers, int circumEdges=6)
	Creates a cylinder. More...
template<class Grid , class Deformation >
std::unique_ptr< Grid >	createCylinder (double radius, double height, int layers, int circumEdges, Deformation const &deformation)
	Creates a deformed cylinder. More...
template<class Grid >
std::unique_ptr< Grid >	createPentagon (double radius=1)
	Creates an regular pentagon consisting of five triangles, centered at the origin and with radius r. More...
template<class Grid >
std::unique_ptr< Grid >	createUshape (double l, double d, double eps)
	Creates an U-shaped domain. More...
bool	getKaskadeOptions (int argc, char **argv, Options const &options)
	Supports the extraction of program option values from command line arguments. More...
template<class A >
auto	moveUnique (A &&a)
	Creates a dynamically allocated object from an r-value reference. More...
template<class A >
A	duplicate (A const &a)
	Creates a copy of a given object. More...
template<class R >
R	power (R base, int exp)
	Computes integral powers of values in a multiplicative half-group. More...
template<class R >
R	square (R x)
	returns the square of its argument. More...
template<class R >
R	faculty (int n)
	Computes faculties. Is this somewhere in the standard? no. More...
constexpr int	sqrti (int n)
	Computes floor(sqrt(n)) for integers n at compile time. More...
std::string	createFileName (std::string const &desiredName, std::string const &ending=std::string(), bool useEnding=true, int length=3)
	create file name More...
bool	createFolder (std::string folder_name)
std::string	createFileNameInFolder (std::string folderName, std::string const &desiredName, std::string const &ending=std::string(), bool const useEnding=true, int const length=3)
template<class Entry >
EntryTraits< Entry >::real_type	frobenius_norm2 (Entry const &x)
void	equalWeightRanges (std::vector< size_t > &x, size_t n)
	Computes partitioning points such that the sum of weights in each partition is roughly the same. More...
template<class BlockIndex , class Index >
Index	uniformWeightRangeStart (BlockIndex i, BlockIndex n, Index m)
	Computes partitioning points of ranges for uniform weight distributions. More...
template<class Index >
Index	uniformWeightRange (Index j, Index n, Index m)
	Computes the range in which an index is to be found when partitioned for uniform weights. More...
template<class Func >
void	parallelFor (Func const &f, int maxTasks=std::numeric_limits< int >::max())
	A parallel for loop that executes the given functor in parallel on different CPUs. More...
template<class Func >
void	parallelFor (size_t first, size_t last, Func const &f, size_t nTasks=std::numeric_limits< size_t >::max())
	A parallel for loop that executes the given functor in parallel on different CPUs. More...
template<class Func >
void	parallelForNodes (Func const &f, int maxTasks=std::numeric_limits< int >::max())
	A parallel for loop that executes the given functor in parallel on different NUMA nodes. More...
void	runInBackground (std::function< void()> &f)
	Executes a function in a child process. More...
template<class T >
T &	removeConst (T const &t)
	A convenience template for removing the const qualifier from references and pointers. More...
template<class T >
T *	removeConst (T const *t)
Approximate integration matrices
The convergence properties of SDC are essentially defined by the selection of an approximate integration matrix \( \hat S \) acting as a lower triangular preconditioner for the spectral integration matrix \( S \). We provide several choices.
void	eulerIntegrationMatrix (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix &Shat)
	Triangular approximate integration matrix \( \hat S \) corresponding to the implicit Euler integrator. More...
SDCTimeGrid::RealMatrix	eulerIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to the implicit Euler integrator. More...
void	luIntegrationMatrix (SDCTimeGrid const &grid, SDCTimeGrid::RealMatrix &Shat)
	Triangular approximate integration matrix \( \hat S \) corresponding to a specialized DIRK sweep. More...
SDCTimeGrid::RealMatrix	luIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to a specialized DIRK sweep. More...
SDCTimeGrid::RealMatrix	singleEulerIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to an Euler sweep with constant "step size". More...
SDCTimeGrid::RealMatrix	SDIRKIntegrationMatrix (SDCTimeGrid const &grid)
	Triangular approximate integration matrix \( \hat S \) corresponding to an SDIRK sweep (i.e. with constant "step size"). More...

Variables
template<class Functional , int n>
constexpr bool	symmetryCheck = Functional_Aux_Detail::checkSymmetry<Functional,n>::pass
template<class Functional >
constexpr bool	hasInnerBoundaryCache
	Checks whether InnerBoundaryCache is declared in Functional. More...
IoOptions	ioOptions_default
template<class Vec >
constexpr bool	contiguousStorage = Crsutil_Detail::VectorTraits<Vec>::contiguous
template<class T >
constexpr int	rank = ScalarDetail::Rank<T>::value
	Reports the rank of vector, matrix, and tensor types of static size. More...
std::mutex	DuneQuadratureRulesMutex
	A global lock for the Dune::QuadratureRules factory, which is not thread-safe as of 2015-01-01. More...
boost::mutex	refElementMutex
	A global lock for the Dune::GenericReferenceElement singletons, which are not thread-safe. More...

Detailed Description

Typedef Documentation

CG

template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>

using Kaskade::CG = typedef CGBase<X,Xstar,CGImplementationType::STANDARD,TimerPolicy>

Standard preconditioned conjugate gradient method.

Template Parameters

X	type of domain space element
Xstar	type of image space element
TimerPolicy	enable timers for dual pairings, axpy-operations, matrix-vector products and preconditioners with struct MeasureTime

Definition at line 16 of file linalg/cg.hh.

D1Result

template<class TestVars , int row>

using Kaskade::D1Result = typedef Dune::FieldVector<typename TestVars::Scalar, TestVars::template Components<row>::m>

The return type of the d1() method of DomainCache and BoundaryCache.

This is a vector type with length given by the number of components of the test variable with index row.

Definition at line 212 of file functional_aux.hh.

D2Result

template<class TestVars , int row, class AnsatzVars , int col>

using Kaskade::D2Result = typedef Dune::FieldMatrix<typename TestVars::Scalar, TestVars::template Components<row>::m, AnsatzVars::template Components<col>::m>

The return type of the d1() method of DomainCache and BoundaryCache.

This is a matrix type with rows given by the number of components of test variable with index row, and columns given by the number of components of the ansatz variable with index col.

Definition at line 224 of file functional_aux.hh.

GridAngleFeatureDetector

template<class GridView >

using Kaskade::GridAngleFeatureDetector = typedef AngleFeatureDetector<typename GridView::IndexSet::IndexType, typename GridView::ctype,GridView::dimension>

Definition at line 480 of file boundaryInterpolation.hh.

Hartmann03

typedef PenaltyFunction<Polynomial<5,-5> > Kaskade::Hartmann03

Definition at line 66 of file penaltyFunctions.hh.

MultiGridSolver

template<class Grid , int nComponents = 1>

using Kaskade::MultiGridSolver = typedef MultigridSolver<Grid,nComponents>

Definition at line 490 of file multiGridSolver.hh.

PenaltyLN

typedef PenaltyFunction<LN> Kaskade::PenaltyLN

Definition at line 167 of file elementary_functions.hh.

PenaltyMonomial

template<int k>

using Kaskade::PenaltyMonomial = typedef PenaltyFunction<Monomial<k> >

Definition at line 105 of file elementary_functions.hh.

Prolongation

using Kaskade::Prolongation = typedef NumaBCRSMatrix<Dune::FieldMatrix<double,1,1> >

Definition at line 28 of file amg.hh.

QuadQuad

typedef PenaltyFunction<Polynomial<2,-2> > Kaskade::QuadQuad

Definition at line 67 of file penaltyFunctions.hh.

QuadraticAndLog

typedef PenaltyFunction<QuadraticAndLogBase> Kaskade::QuadraticAndLog

Definition at line 68 of file penaltyFunctions.hh.

QuadraticAndPolynomial

template<int k>

using Kaskade::QuadraticAndPolynomial = typedef PenaltyFunction<Polynomial<2,k> >

Definition at line 70 of file penaltyFunctions.hh.

RCG

template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>

using Kaskade::RCG = typedef CGBase<X,Xstar,CGImplementationType::REGULARIZED,TimerPolicy>

Regularized preconditioned conjugate gradient method for nonconvex problems. Denote the used operator by \(A\) and the preconditioner by \(P\). Then if a direction of negative curvature is encountered \(A\) is implicitly replaced by the regularization $ \(A+\thetaP\). Then the IterateType::CG method is restarted for the regularized problem. The necessary quantities are available during the standard cg implementation, thus the costs for computing the regularization are neglishible.

Template Parameters

X	type of domain space element
Xstar	type of image space element
TimerPolicy	enable timers for dual pairings, axpy-operations, matrix-vector products and preconditioners with struct MeasureTime

Definition at line 39 of file linalg/cg.hh.

ScalarType

template<class Type >

using Kaskade::ScalarType = typedef typename GetScalar<Type>::type

Extracts the scalar field type from linear algebra data types.

Different conventions for specifying the scalar field type as member type alias are in use in Dune (field_type) and Kaskade (Scalar). This type alias extracts the scalar type from any of those.

Definition at line 110 of file duneInterface.hh.

TCG

template<class X , class Xstar , class TimerPolicy = DoNotMeasureTime>

using Kaskade::TCG = typedef CGBase<X,Xstar,CGImplementationType::TRUNCATED,TimerPolicy>

Truncated preconditioned conjugate gradient method for nonconvex problems. Stops iteration if a direction of negative curvature is encountered.

Template Parameters

X	type of domain space element
Xstar	type of image space element
TimerPolicy	enable timers for dual pairings, axpy-operations, matrix-vector products and preconditioners with struct MeasureTime

Definition at line 26 of file linalg/cg.hh.

TPCG

template<class X , class Xstar , class Regularization = NoRegularization>

using Kaskade::TPCG = typedef TCG<X,Xstar,Regularization>

Definition at line 291 of file tcg.hh.

UniformPartitionedMapperCombinerArgument

template<class SFData >

using Kaskade::UniformPartitionedMapperCombinerArgument = typedef RangeView<typename std::vector<boost::compressed_pair<size_t,SFData> >::const_iterator>

The sequence type that is provided as first argument to the call of the Combiner constructor.

This is a lightweight view type and should be kept by value, not by reference.

Definition at line 194 of file partitionedspace.hh.

UniformScalarMapperCombinerArgument

template<class SFData >

using Kaskade::UniformScalarMapperCombinerArgument = typedef RangeView<typename std::vector<boost::compressed_pair<size_t,SFData> >::const_iterator>

The sequence type that is provided as first argument to the call of the Combiner constructor.

This is a lightweight view type and should be kept by value, not by reference.

Definition at line 175 of file scalarspace.hh.

Enumeration Type Documentation

AcceptanceTest

enum class Kaskade::AcceptanceTest

strong

Enumerator
InitialGuess
FailedRecompute
Failed
NormalStepFailed
TangentialStepFailed
Passed
LeftAdmissibleDomain

Definition at line 19 of file algorithm_base.hh.

CGImplementationType

enum class Kaskade::CGImplementationType

strong

Enumerator
STANDARD
TRUNCATED
REGULARIZED
HYBRID

Definition at line 27 of file cgImplementation.hh.

Convergence

enum class Kaskade::Convergence

strong

Enumerator
Missed
Achieved

Definition at line 20 of file algorithm_base.hh.

Endian

enum class Kaskade::Endian

strong

Enumerator
Unknown
Big
Little
BigWord
LittleWord

Definition at line 19 of file check_endianness.hh.

ErrorNorm

enum class Kaskade::ErrorNorm

strong

Enumerator
Energy
L2
H1
H1_half

Definition at line 39 of file errorDistribution.hh.

GaussSeidelPreconditionerMode

enum class Kaskade::GaussSeidelPreconditionerMode

strong

Enumerator
FORWARD
BACKWARD
SYMMETRIC

Definition at line 34 of file GaussSeidelPreconditioner.hh.

QPConvexificationStrategy

enum class Kaskade::QPConvexificationStrategy

strong

Enumerator
DONOTHING
INCREMENTALADDITION
EIGENVALUEADDITION

Definition at line 59 of file qp.hh.

QPStructure

enum class Kaskade::QPStructure

strong

A flag that determines whether the QP solver shall work with dense or sparse linear algebra.

Enumerator
DENSE
SPARSE

Definition at line 64 of file qp.hh.

RegularityTest

enum class Kaskade::RegularityTest

strong

Enumerator
Failed
Passed

Definition at line 18 of file algorithm_base.hh.

schwarzType

enum Kaskade::schwarzType

Enumerator
DIAGONAL
COMPLETE

Definition at line 25 of file additiveschwarz.hh.

Function Documentation

add()

double Kaskade::add	(	const double &	x1,
		const std::pair< double, int > &	x2
	)

Definition at line 39 of file goalOrientedErrorEstimator.hh.

Referenced by Kaskade::GoalOrientedErrorEstimator< TemplateFunctional, OriginalVariableSetDescription, ExtensionVariableSetDescription, ExtensionSpace >::operator()().

addToFunctionSpaceElement()

template<int rbegin, int rend, class FSE , class CoeffVector >

void Kaskade::addToFunctionSpaceElement	(	CoeffVector const &	coeffVector,
		FSE &	fse
	)

Definition at line 1750 of file comp_step.hh.

adjustEdgeTangents() [1/2]

template<class Index , class ctype >

void Kaskade::adjustEdgeTangents	(	BoundaryStar< Index, ctype, 2 > &	star,
		std::map< std::array< Index, 2 >, Dune::FieldVector< ctype, 2 > > &	orientedEdges,
		GeometricFeatureDetector< Index, ctype, 2 > const &	features
	)

adjustEdgeTangents() [2/2]

template<class Index , class ctype >

void Kaskade::adjustEdgeTangents	(	BoundaryStar< Index, ctype, 3 > &	star,
		std::map< std::array< Index, 2 >, Dune::FieldVector< ctype, 3 > > &	orientedEdges,
		GeometricFeatureDetector< Index, ctype, 3 > const &	features
	)

Detects feature edges and adjusts the edge tangent vectors accordingly.

Feature edges are determined according to two criteria:

• the normals \( n_1, n_2 \) of the incident faces deviate from each other significantly, i.e. \( n_1^T n_2 < \alpha \), where \( \alpha \) is the feature edge threshold
• the set \( \{p_1,p_2\} \) of incident faces' patch types occurs in the featureEdges list (the order of \( p_1, p_2 \) is not relevant).

If any of these two criteria is satisfied, the edge is classified as feature edge.

If exactly two feature edges meet in one vertex, and their normalized emanating tangent vectors \( t_a, t_b \) are approximately parallel (i.e. \( \|t_a + t_b\| < \beta \), where \( \beta \) is the feature curve threshold), these two tangent vectors are modified such as to be collinear.

Parameters

	star	vertices and faces around a boundary vertex
[out]	orientedEdges	all boundary half-edges, indexed

Referenced by Kaskade::BoundaryTangents< dim, Index, ctype >::BoundaryTangents().

appendDate()

std::string & Kaskade::appendDate

(

std::string &

str

)

append current date to string str

appendDateAndTime()

std::string & Kaskade::appendDateAndTime

(

std::string &

str

)

append current time and date to string str

approximateGlobalValues()

template<class Space >

void Kaskade::approximateGlobalValues	(	Space const &	space,
		typename Space::Grid::template Codim< 0 >::Entity const &	cell,
		DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &	globalValues,
		DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, 1, 1 > > &	coeff
	)

Parameters

cell	the cell on which to interpolate. This has to be contained in the space's grid view.

Definition at line 159 of file fetransfer.hh.

Referenced by interpolateGloballyWeak().

assignIfNegative()

template<class Value >

void Kaskade::assignIfNegative	(	Value &	val,
		Value	newVal
	)

Definition at line 21 of file kaskadeBridge.hh.

Referenced by Kaskade::Bridge::KaskadeLinearization< Functional >::cols(), Kaskade::Bridge::KaskadeLinearization< Functional >::d2axpy(), Kaskade::Bridge::NormalStepLinearization< Functional, stateId, adjointId >::d2axpy(), Kaskade::Bridge::TangentialStepLinearization< Functional, stateId, adjointId >::d2axpy(), Kaskade::Bridge::KaskadeLinearization< Functional >::d2taxpy(), Kaskade::Bridge::KaskadeLinearization< Functional >::ddtxpy(), Kaskade::Bridge::KaskadeLinearization< Functional >::ddxpy(), Kaskade::Bridge::NormalStepLinearization< Functional, stateId, adjointId >::ddxpy(), Kaskade::Bridge::TangentialStepLinearization< Functional, stateId, adjointId >::ddxpy(), Kaskade::Bridge::KaskadeLinearization< Functional >::evald(), Kaskade::Bridge::NormalStepLinearization< Functional, stateId, adjointId >::getMatrixBlocks(), Kaskade::Bridge::TangentialStepLinearization< Functional, stateId, adjointId >::getMatrixBlocks(), and Kaskade::Bridge::KaskadeLinearization< Functional >::rows().

bigEndian()

bool Kaskade::bigEndian

(

)

Return true if byte order is big endian.

biggerThanAbs()

bool Kaskade::biggerThanAbs	(	const std::pair< double, int > &	x1,
		const std::pair< double, int > &	x2
	)

Definition at line 34 of file goalOrientedErrorEstimator.hh.

Referenced by Kaskade::GoalOrientedErrorEstimator< TemplateFunctional, OriginalVariableSetDescription, ExtensionVariableSetDescription, ExtensionSpace >::refineGrid().

bisection()

template<class Equation >

double Kaskade::bisection	(	double	a,
		double	b,
		Equation const &	f,
		double	accuracy,
		int &	iterations
	)

Performs bisection algorithm to find a zero of a.

Definition at line 290 of file homotopy_base.hh.

Referenced by corrTangent(), and InteriorPointTangentialPredictor< IPF, DomainVector >::muOnSuccess().

boundaryL2Norm()

template<class FEFunction >

auto Kaskade::boundaryL2Norm

(

FEFunction const &

function

)

boundaryL2Norm computes the L2-norm of an FE function on the whole boundary of the underlying grid.

Parameters

function

is the FE function to be integrated.

Template Parameters

FEFunction

is the type of the integrand.

Returns

value of integral

Definition at line 135 of file norms.hh.

bsplineDifferentiationMatrix()

template<class Scalar >

void Kaskade::bsplineDifferentiationMatrix	(	Dune::DynamicVector< Scalar > const &	t,
		Dune::DynamicVector< Scalar > const &	s,
		int	p,
		Dune::DynamicMatrix< Scalar > &	d
	)

computes the differentiation matrix for bspline interpolation of order p on t

B-Splines of order p define an interpolation \( u(t) \) for all \( t \) between the \( n+1 \) timepoints \( t_i \) with given values \( u(t_i) \). The derivative's values \( u'(t_i) \) at the \( m+1 \) timepoints \( s_i \) can then be computed as a linear combination of the values \( u(t_i) \):

\[ u'(s_i) = \sum_{k=0}^n d_{ik} u(t_k) \]

For \( p=n \), the interpolation is classical polynomial interpolation.

Parameters

[in]	t	the time points from which to interpolate. Entries have to be strictly increasing.
[in]	s	the time points from which to interpolate. Entries have to be strictly increasing.
[in]	p	the order of B-spline interpolation (nonnegative)
[out]	d	the \( m+1 \times n+1 \) differentiation matrix

bsplineEvaluationMatrix()

template<class Scalar >

void Kaskade::bsplineEvaluationMatrix	(	Dune::DynamicVector< Scalar > const &	t,
		Dune::DynamicVector< Scalar > const &	s,
		int	p,
		Dune::DynamicMatrix< Scalar > &	e
	)

computes the evaluation on s matrix for bspline interpolation of order p on t

B-Splines of order p define an interpolation \( u(t) \) for all \( t \) between the \( n+1 \) timepoints \( t_i \) with given values \( u(t_i) \). The values \( u(s_i) \) can then be computed as a linear combination of the values \( u(t_i) \):

\[ u(s_i) = \sum_{k=0}^n e_{ik} u(t_k) \]

For \( p=n \), the interpolation is classical polynomial interpolation.

Parameters

[in]	t	the time points from which to interpolate. Entries have to be strictly increasing.
[in]	s	the time points from which to interpolate. Entries have to be strictly increasing.
[in]	p	the order of B-spline interpolation (nonnegative)
[out]	e	the \( m+1 \times n+1 \) evaluation matrix

castMatrixEntries()

template<class ScalarA , class ScalarB , int r, int c>

Dune::FieldMatrix< ScalarA, r, c > Kaskade::castMatrixEntries

(

Dune::FieldMatrix< ScalarB, r, c > const &

m

)

Copies matrix into another matrix with possibly different entry type (e.g. from double to float).

Definition at line 29 of file converter.hh.

clearVarArgs()

template<class ArgYL , class ArgYH , class ArgUL , class ArgUH , class ArgPL , class ArgPH >

void Kaskade::clearVarArgs	(	ArgYL &	yl,
		ArgYH &	yh,
		ArgUL &	ul,
		ArgUH &	uh,
		ArgPL &	pl,
		ArgPH &	ph
	)

Definition at line 70 of file errorDistribution.hh.

Referenced by Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::BoundaryCache::evaluateAt(), and Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::DomainCache::evaluateAt().

column()

template<class Scalar , int n, int m>

Dune::FieldVector< Scalar, n > Kaskade::column	(	Dune::FieldMatrix< Scalar, n, m > const &	A,
		int	j
	)

Extracts the j-th column of the given matrix A.

Definition at line 445 of file fixdune.hh.

Referenced by Kaskade::DerivativeChecker< Functional, checkD1, SparseInt >::checkSecondDerivative(), and Kaskade::DerivativeCheck::d2().

component()

template<int m, class Scalar , class Sequence >

auto & Kaskade::component

(

LinearProductSpace< Scalar, Sequence > &

x

)

Definition at line 463 of file linearspace.hh.

Referenced by Kaskade::AbstractFunctionSpaceElement::applyAsDualTo(), Kaskade::AbstractFunctionSpaceElement::axpy(), Kaskade::AmiraMeshReader::ImplementationDetails::exceptionMessage(), Kaskade::Bridge::VectorTraits< VariableSet< Descr > >::getRole(), and Kaskade::Bridge::Vector< Implementation >::getRole().

computeBoundaryStars()

template<class GridView >

std::map< typename GridView::IndexSet::IndexType, BoundaryStar< typename GridView::IndexSet::IndexType, typename GridView::ctype, GridView::dimension > > Kaskade::computeBoundaryStars

(

GridView const &

gv

)

Computes the boundary stars (i.e. corners around a vertex) for all boundary vertices of the grid view.

Parameters

gv	the grid view to use, usually the level 0 coarse grid view.

Returns

a map that maps indices of boundary vertices to their star

Definition at line 275 of file boundaryInterpolation.hh.

Referenced by Kaskade::BoundaryTangents< dim, Index, ctype >::BoundaryTangents().

computeH1HalfError()

template<class ArgU , class ArgY , class ArgP >

double Kaskade::computeH1HalfError	(	ArgU const &	u,
		ArgY const &	y,
		ArgP const &	p
	)

Definition at line 87 of file errorDistribution.hh.

Referenced by Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::DomainCache::d1().

computeL2Error()

template<class ArgU , class ArgY , class ArgP >

double Kaskade::computeL2Error	(	ArgU const &	u,
		ArgY const &	y,
		ArgP const &	p
	)

Definition at line 81 of file errorDistribution.hh.

Referenced by Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::DomainCache::d1(), and Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::BoundaryCache::d1().

computeSimplexSfPermutation()

template<class ShapeFunctionSet >

void Kaskade::computeSimplexSfPermutation	(	ShapeFunctionSet const &	sfs,
		int const *	vPermutation,
		int *	sfPermutation,
		int *	sign
	)

For a given shape function set

• sfs which is defined on a simplex and permits a simple coupling, and a given permutation
• vPermutation of the vertices of the simplex defining an affine spatial transformation \( f \), this function returns a permutation
• sfPermutation of the shape functions and a sign vector
• sign, such that

\[ \mathrm{sign[k]}\phi_{\mathrm{sfPermutation[k]}}(f(x)) = \phi_k(x). \]

Definition at line 401 of file pshapefunctions.hh.

conjugation()

template<class Scalar , class Entry >

void Kaskade::conjugation	(	Dune::BCRSMatrix< Entry > &	C,
		Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 > > const &	P,
		Dune::BCRSMatrix< Entry > const &	A,
		bool	onlyLowerTriangle = false
	)

Computes the triple sparse matrix product \( C = C + P^T A P \).

Parameters

C	has to have a sparsity pattern that is a superset of the sparsity pattern of \( P^T A P \).

Definition at line 286 of file conjugation.hh.

Referenced by Kaskade::AdditiveMultiGrid< Smoother, Prolongation, CoarsePreconditioner >::AdditiveMultiGrid(), makeAuxiliarySpaceMultigridStack(), Lossy_Detail::MlStack< Grd >::MlStack(), Kaskade::MultiGridStack< Prolongation, Entry, Index >::MultiGridStack(), and Kaskade::MultiGridSolver_Detail::MultiLevelStack< Grid, Scalar, nComponents, Matrix >::MultiLevelStack().

conjugationPattern()

template<class Scalar , class Entry >

std::unique_ptr< Dune::MatrixIndexSet > Kaskade::conjugationPattern	(	Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 > > const &	P,
		Dune::BCRSMatrix< Entry > const &	A,
		bool	onlyLowerTriangle = false
	)

Creates the sparsity pattern of \( P^T A P\).

Out now: onlyLowerTriangle. If parameter is set true, we will only touch the lower triangle of A and only create the lower triangle of the resulting matrix P^T A P

Definition at line 43 of file conjugation.hh.

Referenced by Kaskade::MultiGridSolver_Detail::MultiLevelStack< Grid, Scalar, nComponents, Matrix >::MultiLevelStack().

copyFromFunctionSpaceElement()

template<int rbegin, int rend, class FSE , class CoeffVector >

void Kaskade::copyFromFunctionSpaceElement	(	FSE const &	fse,
		CoeffVector &	coeffVector
	)

Definition at line 1744 of file comp_step.hh.

copyHeader()

template<class GridView >

void Kaskade::copyHeader	(	GridView const &	gridView,
		std::string const &	file_in,
		std::string const &	file_out
	)

This method copies/adapts the header of an Amira-file containing additional information about the materials. (e.g which material id belongs to which material)

Parameters

gridView	gridView, i.e. LeafGridView
file_in	file, from which the additional material data is read (header in Amira-file)
file_out	file to be written in. Should be the same file as in the call of writeAMIRAFile

Definition at line 210 of file amira.hh.

Referenced by writeAMIRAFile().

createFileName()

std::string Kaskade::createFileName	(	std::string const &	desiredName,
		std::string const &	ending = std::string(),
		bool	useEnding = true,
		int	length = 3
	)

create file name

Checks if a file called <fileName><ending> exists. If this is the case tries fileName0...0ending - fileName9...9ending, where the number of added digits can be controlled via variable length

Parameters

desiredName	desired file name
ending	(i.e. '.doc', '.cpp', '.vtu', ...)
useEnding	true: create file name with ending, false: use ending only for checking file name candidates
length	length of the extension if file name exists

createFileNameInFolder()

std::string Kaskade::createFileNameInFolder	(	std::string	folderName,
		std::string const &	desiredName,
		std::string const &	ending = std::string(),
		bool const	useEnding = true,
		int const	length = 3
	)

createFolder()

bool Kaskade::createFolder

(

std::string

folder_name

)

ddxpy_template()

template<class Assembler , class Lin , int rbegin, int rend, int cbegin, int cend>

void Kaskade::ddxpy_template	(	Lin &	lin,
		AbstractFunctionSpaceElement &	y,
		AbstractFunctionSpaceElement const &	x
	)

Definition at line 1756 of file comp_step.hh.

deleteAllAboveLevel()

template<class Grid , class T >

void Kaskade::deleteAllAboveLevel	(	CellData< Grid, T > &	ic,
		int	maxlevel
	)

Delete all error entries of entities which are above a certain level.

This may be sensible, if the geometry resolution is coarse, such that too deep refinement is not useful

Definition at line 250 of file celldata.hh.

dgetrf_()

void Kaskade::dgetrf_	(	int *	m,
		int *	n,
		double *	a,
		int *	lda,
		int *	ipiv,
		int *	info
	)

Referenced by clapack_dgetrf(), dgetrf(), and Kaskade::AdditiveSchwarzPreconditioner< Op >::init().

dgetrs_()

void Kaskade::dgetrs_	(	char *	trans,
		int *	n,
		int *	nrhs,
		double *	a,
		int *	lda,
		int *	ipiv,
		double *	b,
		int *	ldb,
		int *	info
	)

Referenced by Kaskade::AdditiveSchwarzPreconditioner< Op >::apply().

directInverseOperator() [1/2]

template<class GOP , int firstRow, int lastRow, int firstCol, int lastCol>

InverseLinearOperator< DirectSolver< typename AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol >::Domain, typename AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol >::Range > > Kaskade::directInverseOperator	(	AssembledGalerkinOperator< GOP, firstRow, lastRow, firstCol, lastCol > const &	A,
		DirectType	directType,
		MatrixProperties	properties
	)

Definition at line 618 of file direct.hh.

Referenced by Kaskade::InexactTangentSpacePreconditioner< Functional, Assembler, components, exactConstraint >::apply(), directInverseOperator(), Kaskade::GoalOrientedErrorEstimator< TemplateFunctional, OriginalVariableSetDescription, ExtensionVariableSetDescription, ExtensionSpace >::operator()(), Kaskade::HierarchicalBasisErrorEstimator< Functional, ExtensionVariableSetDescription, ExtensionSpace, NormFunctional, AdjustRHS >::operator()(), and Kaskade::Limex< Eq >::step().

directInverseOperator() [2/2]

template<class Matrix , class Domain , class Range >

InverseLinearOperator< DirectSolver< Domain, Range > > Kaskade::directInverseOperator	(	MatrixRepresentedOperator< Matrix, Domain, Range > const &	A,
		DirectType	directType = DirectType::UMFPACK,
		MatrixProperties	properties = MatrixProperties::GENERAL
	)

Definition at line 626 of file direct.hh.

endianness()

Endian Kaskade::endianness

(

)

Return endianness.

errorL2()

template<class Indicator >

Indicator Kaskade::errorL2

(

Indicator const &

indi

)

Scale error indicators for H^1, such that L_2 indicators are the result.

This is done by the heuristics that the L_2 error is h * H^1-error.

Definition at line 316 of file celldata.hh.

evalCellProperties()

template<class View , class Space >

CellData< typenameSpace::Grid, Dune::FieldVector< double, 1 > >::CellDataVector Kaskade::evalCellProperties

(

Space const &

space

)

Evaluate WeakFunctionViews and construct CellData.

Definition at line 360 of file functionviews.hh.

evaluateData()

template<class OriginalEvaluators , class ExtensionEvaluators , class Functional , class ArgYH , class ArgYE , class ArgUH , class ArgUE , class ArgPH , class ArgPE >

void Kaskade::evaluateData	(	OriginalEvaluators &	originalEvaluators,
		ExtensionEvaluators &	extendedEvaluators,
		Functional const &	f,
		ArgYH &	yl,
		ArgYE &	yh,
		ArgUH &	ul,
		ArgUE &	uh,
		ArgPH &	pl,
		ArgPE &	ph,
		double	w
	)

Definition at line 43 of file errorDistribution.hh.

Referenced by Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::BoundaryCache::evaluateAt(), and Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::DomainCache::evaluateAt().

evaluateGlobalShapeFunctions()

template<class Space >

void Kaskade::evaluateGlobalShapeFunctions	(	Space const &	space,
		Cell< typename Space::GridView > const &	cell,
		std::vector< LocalPosition< typename Space::GridView > > const &	x,
		DynamicMatrix< Dune::FieldMatrix< typename Space::Scalar, Space::sfComponents, 1 > > &	sfValues
	)

Definition at line 93 of file fetransfer.hh.

extendMarks()

template<typename FSElement >

void Kaskade::extendMarks	(	FSElement &	fse,
		FSElement const &	fu,
		int	neighboursForMarking
	)

Definition at line 333 of file celldata.hh.

Referenced by Kaskade::Bridge::extendMarkings().

forEachCell()

template<class GridView , class Functor >

void Kaskade::forEachCell	(	GridView const &	gridView,
		Functor	functor
	)

DEPRECATED: use range based for loops and Dune::elements() directly. iterates over each cell and applies functor to cell. Each cell is visited exactly once.

Definition at line 33 of file forEach.hh.

Referenced by markCells().

forEachCellAndEachFace()

template<class GridView , class Functor >

void Kaskade::forEachCellAndEachFace	(	GridView const &	gridView,
		Functor	functor
	)

iterates over each cell and applies functor to cell and then iterates over each face of cell and applies functor to face

Definition at line 110 of file forEach.hh.

forEachFace()

template<class GridView , class Functor >

void Kaskade::forEachFace	(	GridView const &	gridView,
		Functor	functor
	)

DEPRECATED: use range based for loops and Dune::intersections() directly.iterates over each face and applies functor to face. Each boundary face is visited exactly once and each inner face is visited exactly twice (from each neighbouring cell) and so the functor is applied twice to inner faces.

Definition at line 52 of file forEach.hh.

Referenced by forEachInnerFace().

forEachFaceOfCell()

template<class GridView , class Functor >

void Kaskade::forEachFaceOfCell	(	GridView const &	gridView,
		Functor	functor
	)

same as forEachFace, but the functor is applied to the face and the cell from which the face is visited

Definition at line 63 of file forEach.hh.

forEachInnerFace()

template<class GridView , class Functor >

void Kaskade::forEachInnerFace	(	GridView const &	gridView,
		Functor	functor
	)

iterates over each inner face and applies functor to face. Each inner face is visited exactly twice (and so functor is applied twice).

Definition at line 99 of file forEach.hh.

forEachVertex()

template<class GridView , class Functor >

void Kaskade::forEachVertex	(	GridView const &	gridView,
		Functor	functor
	)

DEPRECATED: use range based for loops and Dune::vertices() directly. iterates over each vertex and applies functor to vertex. Each vertex is visited exactly once.

Definition at line 42 of file forEach.hh.

frobenius_norm2()

template<class Entry >

EntryTraits< Entry >::real_type Kaskade::frobenius_norm2

(

Entry const &

x

)

Definition at line 111 of file scalar.hh.

Referenced by Kaskade::NumaDenseMatrix< Entry >::frobenius_norm2(), Kaskade::InverseLocalMatrixStorageBase::regularize(), and Kaskade::NumaVector< Entry >::two_norm2().

getBCRSIndicesFromTriplet()

template<class SparseInt >

std::vector< std::vector< SparseInt > > Kaskade::getBCRSIndicesFromTriplet	(	SparseInt	nrows,
		std::vector< SparseInt > const &	ridx,
		std::vector< SparseInt > const &	cidx,
		int	nr = 1,
		int	nc = 1
	)

Sorts the sparse matrix nonzero positions into row buckets.

From the row and column indices of a sparse matrix with scalar entries, e.g., in triplet format, obtain the row and column indices of a sparse matrix with nr-by-nc block-entries, as in Dune::BCRSMatrix<Dune::FieldMatrix<Scalar,nr,nc>>. The indices are stored by row.

Parameters

nrows	number of rows of BCRS target matrix (i.e. rows of triplet source / nr)
ridx	vector of row indices
cidx	vector of column indices
nr	row size of sparse matrix entries
nc	column size of sparse matrix entries

Definition at line 456 of file crsutil.hh.

Referenced by Kaskade::AssemblyDetail::Fill< Dune::BCRSMatrix< Dune::FieldMatrix< Scalar, 1, 1 >, Allocator > >::apply().

getDate()

std::string Kaskade::getDate

(

)

getDateAndTime()

std::string Kaskade::getDateAndTime

(

)

gridIterate() [1/2]

template<class VariableList , class Collector , class Functions , class Spaces >

void Kaskade::gridIterate	(	VariableList const &	vars,
		Functions const &	functions,
		Spaces const &	spaces,
		Collector &	f
	)

A function that supports general iterations over a spatial domain and supports efficient evaluation of FE functions at the iterated quadrature points. This is a low-level function working directly on variable lists and function lists. There's a convenience overload working on VariableSets.

Template Parameters

Collector

a type implementing the Collector concept

For each quadrature point \( \xi \) in all cells \( T \), this calls

\[ f(T, i, \xi, w, u), \]

where \( i \) is the cell index, \( u \) is the sequence of function values and \( w \) is the integration weight. This is performed in parallel on several copies of \( f \). After the integration, the provided collector joins the data of its copies.

Parameters

vars	a heterogeneous container of VariableDescription structures
functions	a heterogeneous container of FE functions or function views that can be evaluated given an Evaluator of the associated space.
spaces	a heterogeneous container of pointers to FE function spaces. VariableDescription classes that give the mapping of functions in data to their associated spaces.
f	the functor that does the work. On each quadrature point, its operator() is called with a heterogeneous container of the values of the functions in data.

Definition at line 121 of file iterate_grid.hh.

Referenced by gridIterate(), scaledTwoNormSquared(), and uniformEmbeddedErrorEstimation().

gridIterate() [2/2]

template<class VariableSet , class Collector >

void Kaskade::gridIterate	(	VariableSet const &	functions,
		Collector &	f
	)

A function that supports general iterations over a spatial domain and supports efficient evaluation of FE functions at the iterated quadrature points.

This is a convenience overload for the usual case that the FE spaces are just those listed in the VariableDescriptions.

Definition at line 148 of file iterate_grid.hh.

hdivShapeFunctionSet()

template<class ctype , int dimension, class T = double>

HdivShapeFunctionSetContainer< ctype, dimension, T >::value_type const & Kaskade::hdivShapeFunctionSet	(	Dune::GeometryType	type,
		int	order
	)

Returns a Hdiv shape function set for given reference element type and given polynomial order. Singleton function.

Definition at line 542 of file nedelecshapefunctions.hh.

hierarchicExtensionShapeFunctionSet()

template<class ctype , int dimension, class Scalar >

HierarchicExtensionShapeFunctionSetContainer< ctype, dimension, Scalar >::value_type const & Kaskade::hierarchicExtensionShapeFunctionSet	(	Dune::GeometryType	type,
		int	order
	)

Returns a Hierarchic shape function set for given reference element type and given polynomial order. Singleton function.

Definition at line 750 of file hierarchicshapefunctions.hh.

hierarchicShapeFunctionSet()

template<class ctype , int dimension, class Scalar >

HierarchicShapeFunctionSetContainer< ctype, dimension, Scalar >::value_type const & Kaskade::hierarchicShapeFunctionSet	(	Dune::GeometryType	type,
		int	order
	)

Returns a Hierarchic shape function set for given reference element type and given polynomial order. Singleton function.

Definition at line 570 of file hierarchicshapefunctions.hh.

horzcat() [1/4]

template<class Scalar , int n, int m>

auto Kaskade::horzcat

(

Dune::FieldMatrix< Scalar, n, m > const &

a

)

Definition at line 381 of file fixdune.hh.

horzcat() [2/4]

template<class Scalar , int n, int m, class ... Rest>

auto Kaskade::horzcat	(	Dune::FieldMatrix< Scalar, n, m > const &	a,
		Rest ...	rest
	)

Definition at line 387 of file fixdune.hh.

horzcat() [3/4]

template<class Scalar , int n>

auto Kaskade::horzcat

(

Dune::FieldVector< Scalar, n > const &

c1

)

Definition at line 328 of file fixdune.hh.

Referenced by horzcat().

horzcat() [4/4]

template<class Scalar , int n>

Dune::FieldMatrix< Scalar, n, 3 > Kaskade::horzcat	(	Dune::FieldVector< Scalar, n > const &	col1,
		Dune::FieldVector< Scalar, n > const &	col2,
		Dune::FieldVector< Scalar, n > const &	col3
	)

Definition at line 429 of file fixdune.hh.

insertMatrixBlockEntries()

template<class BMatrix >

void Kaskade::insertMatrixBlockEntries	(	BMatrix &	globalMatrix,
		BMatrix const &	matrixBlock,
		typename BMatrix::size_type	startRow,
		typename BMatrix::size_type	startCol
	)

Add entries of a sparse matrix block to a global sparse matrix, which already has the suitable sparsity pattern assigned.

Definition at line 182 of file matrixBlocks.hh.

insertMatrixBlockIndices() [1/2]

template<class Entry >

void Kaskade::insertMatrixBlockIndices	(	Dune::MatrixIndexSet &	globalIndexSet,
		Dune::BCRSMatrix< Entry > const &	matrixBlock,
		Dune::MatrixIndexSet::size_type	startRow,
		Dune::MatrixIndexSet::size_type	startCol
	)

Add indices of a sparse matrix block to a global sparse matrix (creator).

Definition at line 164 of file matrixBlocks.hh.

insertMatrixBlockIndices() [2/2]

template<class Entry , class Index >

void Kaskade::insertMatrixBlockIndices	(	NumaCRSPatternCreator< Index > &	globalCreator,
		NumaBCRSMatrix< Entry, Index > const &	matrixBlock,
		typename NumaBCRSMatrix< Entry, Index >::size_type	startRow,
		typename NumaBCRSMatrix< Entry, Index >::size_type	startCol
	)

Add indices of a sparse matrix block to a global sparse matrix (creator).

Definition at line 131 of file matrixBlocks.hh.

insertVectorBlock()

template<class BVector >

void Kaskade::insertVectorBlock	(	BVector &	globalVector,
		BVector const &	vectorBlock,
		typename BVector::size_type	startIdx
	)

Add entries of a vector block to a global vector.

Definition at line 203 of file matrixBlocks.hh.

integral()

template<class WeakFunctionView , class Space >

auto Kaskade::integral	(	WeakFunctionView const &	f,
		Space const &	space
	)

Definition at line 301 of file integration.hh.

lagrangeShapeFunctionSet()

template<class ctype , int dimension, class Scalar = double, bool restricted = false>

LagrangeShapeFunctionSetContainer< ctype, dimension, Scalar, restricted >::value_type const & Kaskade::lagrangeShapeFunctionSet	(	Dune::GeometryType	type,
		int	order
	)

Returns a Lagrange shape function set for given reference element type and given polynomial order. Singleton function.

Template Parameters

restricted

docme!

Definition at line 872 of file lagrangeshapefunctions.hh.

LeastSquares()

void Kaskade::LeastSquares	(	SLAPMatrix< double >	a,
		std::vector< double > const &	b,
		std::vector< double > &	x
	)

Solve linear least squares problem, given by a*x=b.

Preferrably used like the following:

LeastSquares(SLAPMatrix<double>(A),b,x)

Here A models the Dune Matrix concept.

Referenced by Kaskade::PolynomialModel::computeCoefficients().

linearizationDifference()

template<class Functional >

LinearizationDifferenceAt< Functional > Kaskade::linearizationDifference	(	Functional const &	f,
		typename Functional::OriginVars::VariableSet const &	u1,
		typename Functional::OriginVars::VariableSet const &	u2
	)

Convenience routine: construct linearization without having to know the type of the functional.

Definition at line 885 of file functional_aux.hh.

littleEndian()

bool Kaskade::littleEndian

(

)

Return true if byte order is little endian.

localH1SemiNorm()

template<class Function >

CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector Kaskade::localH1SemiNorm

(

Function const &

f

)

local (cellwise) H1-semi-norms

Definition at line 100 of file norms.hh.

localL2Norm()

template<class Function >

CellData< typenameFunction::Space::Grid, typenameFunction::ValueType >::CellDataVector Kaskade::localL2Norm

(

Function const &

f

)

local (cellwise) L2-norms

Definition at line 114 of file norms.hh.

localProlongationMatrix()

template<class ChildSpace , class FatherSpace >

void Kaskade::localProlongationMatrix	(	ChildSpace const &	childSpace,
		Cell< typename ChildSpace::Grid > const &	child,
		FatherSpace const &	fatherSpace,
		Cell< typename FatherSpace::Grid > const &	father,
		DynamicMatrix< Dune::FieldMatrix< typename ChildSpace::Scalar, 1, 1 > > &	prolongation,
		typename ChildSpace::Mapper::ShapeFunctionSet const &	childSfs,
		typename FatherSpace::Mapper::ShapeFunctionSet const &	fatherSfs
	)

Computes a local prolongation matrix for global shape functions from father cell to child cell.

Returns

In the notation of LocalToGlobalMapperConcept ( \(\Phi_{ij}\) is the matrix of shape function values \(\phi_j\) at interpolation nodes \( \xi_i \), and \(\Psi \) is the diagonal matrix of converter values \( \psi(x_i)\)), the returned value is

\[ p \leftarrow \Phi_c^+ \Psi_c^{-1} \Psi_f \Phi_f. \]

This means, \( p \in \R^{n_c \times n_f} \) is a matrix, where the entries \( p_{ij} \) give the contribution of the \( j \)-th father global shape function to the \( i \)-th child global shape function. \( n_f \) and \( n_c \) are the number of father and child shape functions, respectively.

Although suggestively called father and child, the only geometric relation required is that all interpolation nodes of the child cell are also contained inside the father cell.

Note that the FE spaces on father and child may be different, providing interpolation matrices for different FE approximations. The requirement is that the scalar type and the number of shape function components coincide.

Parameters

childSfs	a shape function set to use for the child space on the given child cell (which need not be contained in the child space's grid view)
fatherSfs	a shape function set to use for the father space on the given father cell (which need not be contained in the fathers space's grid view)

Definition at line 195 of file fetransfer.hh.

Referenced by localProlongationMatrix(), Kaskade::CoarseningDetail::GetLocalTransferProjection< Cell >::operator()(), and Kaskade::TransferData< Space, CoarseningPolicy >::transferMatrix().

makeAuxiliarySpaceMultigridStack()

template<class Space , class Entry , class Index >

MultiGridStack< Prolongation, Entry, Index > Kaskade::makeAuxiliarySpaceMultigridStack	(	Space const &	space,
		NumaBCRSMatrix< Entry, Index > const &	A,
		double	volumeRatio = 100
	)

creates a semi-geometric multigrid preconditioner based on an auxiliary space

Template Parameters

Space

the finite element space for which the stiffness matrix A has been computed. Currently this is restricted to a P1 finite element space.

Todo:

: implement for general spaces

Template Parameters

Entry

the type of matrix entries in the stiffness matrix

Returns

a multigrid stack with prolongations and (Galerkin-projected) stiffness matrices

Definition at line 378 of file amg.hh.

markByBulkCriterion()

template<class Grid , class T >

CellData< Grid, int >::CellDataVector Kaskade::markByBulkCriterion	(	CellData< Grid, T > &	ic,
		double	Theta
	)

Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "bulk criterion".

To be used together with GridManager::mark(...)

Definition at line 224 of file celldata.hh.

Referenced by Kaskade::Bridge::AdaptiveGrid< GridManager, Estimate >::mark().

markByMaxCriterion()

template<class Grid , class T >

CellData< Grid, int >::CellDataVector Kaskade::markByMaxCriterion	(	CellData< Grid, T > &	ic,
		double	Ratio
	)

Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion".

Definition at line 262 of file celldata.hh.

markCells()

template<class GridManager , class Functor >

void Kaskade::markCells	(	GridManager &	gridManager,
		Functor	functor
	)

Definition at line 121 of file forEach.hh.

markWithinInterval()

template<class Grid , class T >

CellData< Grid, int >::CellDataVector Kaskade::markWithinInterval	(	CellData< Grid, T > &	ic,
		double	lower,
		double	upper,
		int	times
	)

Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion".

Definition at line 280 of file celldata.hh.

matrix_to_triplet()

template<class Matrix , class OutIteratorI , class OutIteratorD >

void Kaskade::matrix_to_triplet	(	Matrix const &	a,
		OutIteratorI	i,
		OutIteratorI	j,
		OutIteratorD	z
	)

converts a matrix to the coordinate (triplet) format.

The Matrix type needs to satisfy the Dune matrix interface.

Definition at line 418 of file crsutil.hh.

MatrixKT_A_K()

void Kaskade::MatrixKT_A_K	(	SLAPMatrix< double >	A,
		SLAPMatrix< double > &	K,
		SLAPMatrix< double > &	out
	)

MatrixMultiplication()

void Kaskade::MatrixMultiplication	(	SLAPMatrix< double >	A,
		SLAPMatrix< double > &	B,
		SLAPMatrix< double > &	AB
	)

maxNorm()

template<class Vector >

Vector::field_type Kaskade::maxNorm

(

std::vector< Vector > const &

values

)

A function to compute the partial \(\max-\)norm or \(L^{\infty}-\)norm of a vector of vectors. If \(\mathbf{x}\) denotes a vector of vectors, where \(\mathbf{x} = \{ \mathbf{x_1},\ldots , \mathbf{x_n}\}^{T}\), then \(\| \mathbf{x} \|_{\infty} = \max_{1 \leq i \leq N} \|\mathbf{x_i}\|$\f. Here the norm \)|.| \( is some arbitrary norm and in the current template function it is implemented as a \)\max- \(norm. \tparam Vector, a vector type, usually Dune::DenseVector \param[in]values a vector of vectors. \return the \)\infty-.

  \brief A function to compute the partial \f$1-\f$norm or \f$L^{1}-\f$norm of a vector of vectors.
  If \f$\mathbf{x}\f$ denotes a vector of vectors, where \f$\mathbf{x} = \{ \mathbf{x_1},\ldots , \mathbf{x_n}\}^{T}\f$,
  then \f$\| \mathbf{x} \|_1 = \sum_{i=1}^N \|\mathbf{x_i}\|$\f. Here the norm \f$\|.\| \f$ is some arbitrary norm and
  in the current template function it is implemented as a \f$1-\f$norm.

  \tparam Vector, a vector type, usually Dune::DenseVector

  \param[in]values a vector of vectors.

  \return the \f$1-\f$norm of the vector values, usually a double.
*/

template<class Vector> typename Vector::field_type oneNorm(std::vector<Vector> const& values) { return std::accumulate(values.begin(),values.end(),0.0,[](double init, Vector const& v) { return init + v.one_norm(); }); // auto norm = 0.0;

// for (auto i = 0u; i < values.size(); ++i) // //one_norm: public member function of Dune::DenseVector // norm += values[i].one_norm();

// return norm; }

/**

Definition at line 54 of file sdc_euler.hh.

moveEvaluatorsToCell() [1/2]

template<class Evaluators , class Cell >

void Kaskade::moveEvaluatorsToCell	(	Evaluators &	evals,
		Cell const &	cell
	)

Moves all provided evaluators to the given cell.

Definition at line 1888 of file functionspace.hh.

Referenced by PointwiseCorrection< PolyEquation >::correct(), corrTangent(), edgeAveragingFull(), Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::BoundaryCache::evaluateAt(), Kaskade::ErrorDistribution< Functional, ExtendedAnsatzVars >::DomainCache::evaluateAt(), Kaskade::GridIterateDetail::gridIterateRange(), and projectHierarchically().

moveEvaluatorsToCell() [2/2]

template<class Evaluators , class Cell , class Index >

void Kaskade::moveEvaluatorsToCell	(	Evaluators &	evals,
		Cell const &	cell,
		Index	idx
	)

Moves all provided evaluators to the given cell with provided index.

As index lookups may be relatively expensive, providing the index here once for all spaces/evaluators may improve performance.

Definition at line 1900 of file functionspace.hh.

nedelecShapeFunctionSet()

template<class ctype , int dimension, class T >

NedelecShapeFunctionSetContainer< ctype, dimension, T >::value_type const & Kaskade::nedelecShapeFunctionSet	(	Dune::GeometryType	type,
		int	order
	)

Returns a Nedelec shape function set for given reference element type and given polynomial order. Singleton function.

Definition at line 309 of file nedelecshapefunctions.hh.

nestedDissection()

std::array< std::vector< size_t >, 3 > Kaskade::nestedDissection	(	std::vector< std::pair< size_t, size_t > > const &	edges,
		std::vector< size_t > const &	edgeStart
	)

Computes a nested dissection of the given graph.

Parameters

edges	a sequence \( E \) of edges \( (v,w) \), given as pairs of vertices, sorted lexicographically. The edges are assumed to be symmetric, i.e. \( (v,w)\in E \Rightarrow (w,v)\in E \), and shall not contain the diagonal, i.e. \( (v,v) \not\in E \).
edgeStart	an index sequence such that all edges \( (v,w) \) for some particular \( v \) are in the half-open range [edgeStart(v),edgeStart(v+1)[ of edges.

The vertices are assumed to be a contiguous range \( 0, \dots, n-1 \) of integers.

Returns

a tuple \( (v_1, v_2, s) \) of vertices, forming the two sets \( v_1, v_2 \) separated by \( s \).

If no proper partitioning can be found, both \( v_1, v_2 \) are empty and \( s \) contains all vertices. If the graph is disconnected, \( s \) is empty.

nestUzawa()

template<class Scalar , class Sequence >

auto Kaskade::nestUzawa

(

LinearProductSpace< Scalar, Sequence > const &

z

)

Convenience function for creating Uzawa domain/range arguments.

If the UzawaSolver is created by providing AssembledGalerkinOperator data for A, B, and Bt, their domain and range spaces are LinearProductSpace types containing (usually) just one component. Then, domain and range of the UzawaSolver are doubly nested, [[u],[p]], but extracting two consecutive components from an assembler leads to the flat LinearProductSpace [u,p]. This function takes [u,p] and outputs [[u],[p]].

Definition at line 299 of file uzawa.hh.

operator+()

template<class Index , class Index2 >

NumaCRSPattern< Index > Kaskade::operator+	(	NumaCRSPattern< Index > const &	pa,
		NumaCRSPattern< Index2 > const &	pb
	)

Definition at line 2037 of file threadedMatrix.hh.

operator<<() [1/8]

template<class B , class A >

std::ostream & Kaskade::operator<<	(	std::ostream &	out,
		Dune::BCRSMatrix< B, A > const &	a
	)

Definition at line 474 of file crsutil.hh.

operator<<() [2/8]

template<class Entry , bool diagonal, class SortedRowIdx , class SortedColIdx >

std::ostream & Kaskade::operator<<	(	std::ostream &	out,
		LocalMatrix< Entry, diagonal, SortedRowIdx, SortedColIdx > const &	A
	)

Definition at line 146 of file localMatrices.hh.

operator<<() [3/8]

std::ostream & Kaskade::operator<<	(	std::ostream &	out,
		MGProlongation const &	p
	)

operator<<() [4/8]

template<typename Prolongations , typename Entry , typename Index >

std::ostream & Kaskade::operator<<	(	std::ostream &	out,
		MultiGridStack< Prolongations, Entry, Index > const &	mgStack
	)

Definition at line 855 of file prolongation.hh.

operator<<() [5/8]

template<class Entry , int ... Sizes>

std::ostream & Kaskade::operator<<	(	std::ostream &	out,
		Tensor< Entry, Sizes... > const &	t
	)

Definition at line 307 of file tensor.hh.

operator<<() [6/8]

template<typename Scalar , typename SparseIndexInt >

std::ostream & Kaskade::operator<<	(	std::ostream &	s,
		MatrixAsTriplet< Scalar, SparseIndexInt > const &	mat
	)

Definition at line 773 of file triplet.hh.

operator<<() [7/8]

template<typename Scalar >

std::ostream & Kaskade::operator<<	(	std::ostream &	s,
		std::vector< Scalar > const &	vec
	)

Definition at line 47 of file dune_bridge.hh.

operator<<() [8/8]

std::ostream & Kaskade::operator<<	(	std::ostream &	stream,
		VTKReader::FunctionInfo const &	info
	)

pseudoinverse()

template<class Scalar >

void Kaskade::pseudoinverse	(	SLAPMatrix< Scalar >	A,
		SLAPMatrix< Scalar > &	Ainv
	)

Computes the pseudoinverse.

• A The input matrix. Will be overwritten with unspecified data.
• Ainv the pseudoinverse. Needs to have the shape of A transposed.

rangeView()

template<class It >

RangeView< It > Kaskade::rangeView	(	It	first,
		It	last
	)

Convenience function for constructing range views on the fly.

Definition at line 59 of file views.hh.

Referenced by Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::combiner(), and Kaskade::UniformScalarMapper< Implementation, SFData >::combiner().

relativeError()

template<class Variables , class OutIter , class Functions , class Spaces , class Scaling >

void Kaskade::relativeError	(	Variables const &	varDesc,
		Functions const &	f1,
		Functions const &	f2,
		Functions const &	f3,
		Spaces const &	spaces,
		Scaling const &	scaling,
		OutIter	out
	)

For each variable, this function computes the following pair of values:

\[ (\|f_1-f_2\|,\|f_3\|) \]

Template Parameters

Variables	a boost::fusion sequence of variable descriptions
OutIter	an output iterator with value type std::pair(double,double)
Functions	a boost::fusion sequence of finite element functions, referenced by the variable descriptions
Spaces	a boost::fusion sequence of pointers to spaces, referenced by the variable descriptions
Scaling

Definition at line 382 of file iterate_grid.hh.

Referenced by Kaskade::Limex< Eq >::estimateError().

removeConst()

template<class T >

T * Kaskade::removeConst

(

T const *

t

)

Definition at line 36 of file typeTraits.hh.

reshapeBlocks() [1/2]

template<int dimIn, int dimOut>

Dune::BlockVector< Dune::FieldVector< double, dimOut > > Kaskade::reshapeBlocks

(

Dune::BlockVector< Dune::FieldVector< double, dimIn > > const &

b

)

reshapes a Dune::BlockVector block structure

Reshapes a Dune::BlockVector with entry-type Dune::FieldVector<double,dimIn> to entry type Dune::FieldVector<double,dimOut>, i.e. the size of the contained blocks are reshaped. Block sizes must be such that dimIn == 1 or dimOut == 1.

Template Parameters

dimIn	reshape block size from dimIn
dimOut	to desired block size dimOut

Parameters

b	A Dune::BlockVector<> whose entry-type is to be reshaped

Definition at line 1037 of file dynamicMatrix.hh.

reshapeBlocks() [2/2]

template<class Kb , int nb, int mb, class Ka , int na, int ma>

DynamicMatrix< Dune::FieldMatrix< Kb, nb, mb > > Kaskade::reshapeBlocks

(

DynamicMatrix< Dune::FieldMatrix< Ka, na, ma > > const &

A

)

Definition at line 64 of file reshape.hh.

scaledTwoNormSquared()

template<class Variables , class Functions , class Spaces , class Scaling , class Collector >

void Kaskade::scaledTwoNormSquared	(	Variables const &	varDesc,
		Functions const &	f,
		Spaces const &	spaces,
		Scaling const &	scaling,
		Collector &	sum
	)

Evaluates the square of the scaled \(L^2\)-norms of a set of functions.

Template Parameters

Variables	a boost::fusion sequence of VariableDescription types
Functions	a boost::fusion sequence of FE function types (or types providing the required interface subset)
Spaces
Scaling
Collector

Parameters

varDesc	a boost::fusion sequence of VariableDescription entries, e.g. obtained from VariableSetDescription::Variables()
f	a matching boost::fusion sequence of FE functions

The required interface subset of FE functions includes the value() and the space() methods.

Definition at line 304 of file iterate_grid.hh.

Referenced by coarsening(), Kaskade::EmbeddedErrorEstimator< VariableSetDescription, Scaling >::estimate(), and relativeError().

sdcExEulerIterationStep()

template<class Vector >

Vector::field_type Kaskade::sdcExEulerIterationStep	(	Kaskade::SDCTimeGrid const &	grid,
		std::vector< Vector > &	yi,
		std::vector< Vector > &	dyi,
		std::function< Vector(typename Vector::field_type, Vector const &)>	rhsFunc,
		std::function< typename Vector::field_type(std::vector< Vector > const &)>	normFunc,
		bool	verbose = false
	)

A single spectral defect correction iteration sweep based on explicit Euler method.

This function performs one spectral defect correction (SDC) iteration for a system of ODE's of the form:

\[y'(t) = f(y(t)),\,\, y(0) = y_0 \textrm{ and } t \in [0, T].\]

using the explicit Euler method on a given time grid. Here SDC is interpreted as fixed point iteration. Given an approximate solution \(y^{[j]} \in \mathbb{P}_N\), the error function

\[\delta^{[j]} = y - y^{[j]}\]

satisfies the defect equation

\[\delta^{[j]}'(t) = y'(t) - y^{[j]}'(t) = f(y(t)) - y^{[j]}'(t).\]

The equivalent Picard equation is

\[\delta^{[j]}(t) = \int_{\tau=0}^t \left( f(y^{[j]}(\tau)+\delta^{[j]}(\tau)) - {y^{[j]}}'(\tau) \right) \,d\tau.\]

Evaluated at the grid nodes \( t_i\) we obtain

\[ \delta^{[j]}_i &= \delta^{[j]}_{i-1} + \int_{\tau=t_{i-1}}^{t_i} \left( f(y^{[j]}(\tau)+\delta^{[j]}(\tau)) - {y^{[j]}}'(\tau) \right) \,d\tau \\ &= \delta^{[j]}_{i-1} + \int_{\tau=t_{i-1}}^{t_i} \left( f(y^{[j]}(\tau)+\delta^{[j]}(\tau)) - f(y^{[j]}(\tau))\right) \,d\tau \\ &\quad + \int_{\tau=t_{i-1}}^{t_i} \hspace{-0.5em}f(y^{[j]}(\tau)) \,d\tau - ( y^{[j]}_i-y^{[j]}_{i-1}) \]

starting at \(\delta_0^{[j]} = 0.\) Using left looking rectangular rule for approximating the first integral, and the canonical quadrature by polynomial interpolation on the nodes \( t_1,\ldots t_N\) for second integral, approximate values \( \hat{\delta}_i^{[j]}\) for \( \delta_i^{[j]}\) can be evaluated. With the left looking rectangular rule, we obtain the explicit scheme

\[ \hat\delta^{[j]}_i &= \hat\delta^{[j]}_{i-1} + (t_i-t_{i-1}) \left( f(y^{[j]}_{i-1}+\hat{\delta}^{[j]}_{i-1}) - f(y^{[j]}_{i-1})\right) + \sum_{k=1}^N S_{ik} f(y^{[j]}_k) - y^{[j]}_i+y^{[j]}_{i-1}, \]

where the entries of the spectral quadrature matrix \( S \in \mathbb{R}^{N \times N}\) are defined in terms of the Lagrange polynomials \(L_k \in \mathbb{P}_N\) satisfying \(L_k(t_i) = \delta_{ik}\) as

\[ S_{ik} = \int_{\tau=t_{i-1}}^{t_i} L_k(\tau) \,d\tau, \quad i,k =1,\dots, N. \]

An improved approximation \( y^{[j+1]}\) is then obtained by polynomial interpolation of \(\hat \delta^{[j]}_i \),

\[y^{[j+1]} = y^{[j]} + \hat\delta^{[j]}.\]

The norm of the correction \(\hat\delta^{[j]}\) is returned.

Template Parameters

Vector,a

vector type, usually Dune::DenseVector.

Parameters

[in]	grid	the collocation time grid
[out]	yi	stores the current iterate of the solution \(y\).
[out]	dyi	is the approximate correction \(\delta y \)
[in]	rhsFunc	is the function which represents the right hand side \(f\) and is used in th computation of \( \delta y\).
[in]	normFunc	represents the norm that would be used in the computation of norm of \( \delta y\).
[in]	verbose	a boolean used to print out the iterates of \(y\).

Returns

the norm of dyi, the type of the norm is determined by input parameter normFunc.

Definition at line 117 of file sdc_euler.hh.

Referenced by Kaskade::EulerSDC< Vector, TimeGrid >::integrate(), and Kaskade::EulerSDC< Vector, TimeGrid >::integrateTOL().

spaceTransfer()

template<class Fu1 , class Fu2 >

void Kaskade::spaceTransfer	(	Fu1 &	f1,
		Fu2 const &	f2
	)

DEPRECATED. Use interpolateGlobally instead.

Definition at line 1119 of file fetransfer.hh.

Referenced by Kaskade::Bridge::SpaceTransfer::operator()().

submatrix()

template<class Target , class Source , class RowIndices , class ColIndices >

Target Kaskade::submatrix ( Source const &  A, RowIndices const &  ri, ColIndices const &  ci  )

related

Referenced by Kaskade::NumaBCRSMatrix< Entry, Index >::eraseRowsNCols().

SymmetricEigenvalues()

void Kaskade::SymmetricEigenvalues	(	SLAPMatrix< double >	a,
		std::vector< double > &	eig
	)

transpose()

template<class T , typename = std::enable_if_t<std::is_arithmetic<T>::value>>

T Kaskade::transpose

(

T

x

)

Definition at line 750 of file dynamicMatrix.hh.

Referenced by Kaskade::Elastomechanics::HyperelasticVariationalFunctional< HyperelasticEnergy, StrainTensor >::cauchyStress(), Kaskade::NumaBCRSMatrix< Entry, Index >::conjugation(), Kaskade::ThreadedMatrixDetail::MatrixEntry< To, From, scalarsMatch >::copy(), Kaskade::Elastomechanics::LinearizedGreenLagrangeTensor< Scalar, dim, byValue >::d0(), Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d0(), Kaskade::Elastomechanics::SurfaceGreenLagrangeTensor< Scalar, dim, byValue >::d0(), Kaskade::Elastomechanics::ExtendedGreenLagrangeTensor< Scalar, dim, byValue >::d0(), Kaskade::Cofactor< dimension, Source >::d0(), Kaskade::Elastomechanics::SurfaceGreenLagrangeTensor< Scalar, dim, byValue >::d1(), Kaskade::Elastomechanics::ExtendedGreenLagrangeTensor< Scalar, dim, byValue >::d1(), Kaskade::Cofactor< dimension, Source >::d1(), Kaskade::Elastomechanics::LinearizedGreenLagrangeTensor< Scalar, dim, byValue >::d1(), Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d1(), Kaskade::Elastomechanics::SurfaceGreenLagrangeTensor< Scalar, dim, byValue >::d2(), Kaskade::Elastomechanics::ExtendedGreenLagrangeTensor< Scalar, dim, byValue >::d2(), Kaskade::Cofactor< dimension, Source >::d2(), Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d2(), Kaskade::Cofactor< dimension, Source >::d3(), Kaskade::BoundaryInterpolationDisplacement< GridView >::derivative(), Kaskade::VectorialConverterBase< GridView >::global(), Kaskade::ScalarConverter< Cell, Scalar >::global(), Kaskade::ThreadedMatrixDetail::CopyMatrixToChunk< Entry, Matrix, true, transposed, Index >::init(), Kaskade::ThreadedMatrixDetail::CopyMatrixToChunk< Entry, Matrix, false, true, Index >::init(), and Kaskade::DynamicMatrix< K >::transpose().

TransposedMatrixMultiply()

void Kaskade::TransposedMatrixMultiply	(	SLAPMatrix< double >	A,
		std::vector< double > &	in,
		std::vector< double > &	out
	)

tripletToCompressedColumn()

template<class Scalar , class Index >

void Kaskade::tripletToCompressedColumn	(	Index	nRows,
		Index	nCols,
		size_t	nNonZeros,
		std::vector< Index > const &	ridx,
		std::vector< Index > const &	cidx,
		std::vector< Scalar > const &	values,
		std::vector< Index > &	Ap,
		std::vector< Index > &	Ai,
		std::vector< Scalar > &	Az
	)

Converts a matrix in triplet format to a compressed column format.

Template Parameters

Scalar	the matrix entry type
Index	the row/column index type

Referenced by Kaskade::SUPERLUFactorization< Scalar >::SUPERLUFactorization(), and Kaskade::UMFFactorization< Scalar, UMFPackIndex >::UMFFactorization().

umfpack_solve()

void Kaskade::umfpack_solve	(	std::vector< int > const &	ridx,
		std::vector< int > const &	cidx,
		std::vector< double > const &	values,
		std::vector< double > const &	b,
		std::vector< double > &	x
	)

unmarkOutOf()

template<class Grid >

CellData< Grid, int >::CellDataVector Kaskade::unmarkOutOf	(	CellData< Grid, int > const &	ic,
		Dune::FieldVector< typename Grid::ctype, Grid::dimension >	center,
		double	radius
	)

Create a CellDataVector, in which the largest entities of *this are marked by 1, using the "max criterion".

Definition at line 296 of file celldata.hh.

unnestUzawa()

template<class Scalar , class Sequence >

auto Kaskade::unnestUzawa

(

LinearProductSpace< Scalar, Sequence > const &

z

)

Convenience function for unpacking Uzawa domain/range results.

This unwraps nested LinearProductSpace arguments.

Parameters

z	a nested Uzawa domain/range type of structure [[u],[p]]

Returns

a flattend representation of structure [u,p]

Definition at line 319 of file uzawa.hh.

uzawa()

template<class MatA , class SolA , class MatB , class MatBt , class PrecS >

auto Kaskade::uzawa	(	MatA &	A,
		SolA &	invA,
		MatB &	B,
		MatBt &	Bt,
		PrecS &	precS,
		double	reduction = 1e-3,
		int	maxit = 1000,
		int	verbose = 0
	)

Convenience function for constructing an UzawaSolver. \tparem MatA derived from Dune::LinearOperator<X,X>

Template Parameters

SolA	derived from Dune::InverseOperator<X,X>
MatB	derived from Dune::LinearOperator<X,Y>
MatBt	derived from Dune::LinearOperator<Y,X>
PrecS	derived from Dune::Preconditioner<Y,Y>

Definition at line 280 of file uzawa.hh.

vectorFromSequence() [1/5]

template<class InIter >

InIter Kaskade::vectorFromSequence	(	double &	x,
		InIter	iter
	)

Definition at line 97 of file crsutil.hh.

vectorFromSequence() [2/5]

template<class K , int size, class InIter >

InIter Kaskade::vectorFromSequence	(	Dune::FieldVector< K, size > &	v,
		InIter	iter
	)

Definition at line 111 of file crsutil.hh.

vectorFromSequence() [3/5]

template<class InIter >

InIter Kaskade::vectorFromSequence	(	float &	x,
		InIter	iter
	)

Definition at line 104 of file crsutil.hh.

vectorFromSequence() [4/5]

template<class Space , int m, class InIter >

InIter Kaskade::vectorFromSequence	(	FunctionSpaceElement< Space, m > &	v,
		InIter	in
	)

Definition at line 1045 of file functionspace.hh.

Referenced by Kaskade::DirectSolver< Domain_, Range_ >::apply(), Kaskade::DirectPreconditioner< Op >::apply(), and vectorFromSequence().

vectorFromSequence() [5/5]

template<class K , class InIter >

InIter Kaskade::vectorFromSequence	(	std::vector< K > &	v,
		InIter	iter
	)

Definition at line 135 of file crsutil.hh.

vectorToSequence() [1/4]

template<class OutIter >

OutIter Kaskade::vectorToSequence	(	double	x,
		OutIter	iter
	)

Definition at line 30 of file crsutil.hh.

Referenced by Kaskade::DirectSolver< Domain_, Range_ >::apply(), Kaskade::DirectPreconditioner< Op >::apply(), Kaskade::DirectPreconditionerFloatWrapper< Domain, Range, SparseIndex >::apply(), Kaskade::EnergyScalarProduct< X >::operator()(), Kaskade::VariationalFunctionalAssembler< F, SparseIndex, BoundaryDetector, QuadRule >::BlockToSequence< DataOutIter >::operator()(), vectorToSequence(), and Kaskade::FunctionSpaceElement< FunctionSpace, m >::vectorToSequence().

vectorToSequence() [2/4]

template<class K , int size, class OutIter >

OutIter Kaskade::vectorToSequence	(	Dune::FieldVector< K, size > const &	v,
		OutIter	iter
	)

Definition at line 45 of file crsutil.hh.

vectorToSequence() [3/4]

template<class OutIter >

OutIter Kaskade::vectorToSequence	(	float	x,
		OutIter	iter
	)

Definition at line 37 of file crsutil.hh.

vectorToSequence() [4/4]

template<class K , class OutIter >

OutIter Kaskade::vectorToSequence	(	std::vector< K > const &	v,
		OutIter	iter
	)

Definition at line 84 of file crsutil.hh.

vertcat()

template<class Entry , class A >

Dune::BlockVector< Entry, A > Kaskade::vertcat	(	Dune::BlockVector< Entry, A > const &	x,
		Dune::BlockVector< Entry, A > const &	y
	)

Definition at line 31 of file vectorOps.hh.

vertexids()

void Kaskade::vertexids ( int  d, int  c, int  k, int *  idx  )

inline

Computes the d-c+1 local vertex indices of the vertices incident to the k-th subentity of codimension c in the reference simplex of dimension d.

Parameters

d	spatial dimension of the reference simplex
c	codimension of the considered subentity
k	number of the subentity (among all of given codimension c)
idx	output iterator, where d-c+1 values are stored

Definition at line 117 of file gridcombinatorics.hh.

Referenced by computeBoundaryStars(), Kaskade::ContinuousHierarchicMapperImplementation< Scalar, GV, ShapeFunctionFilter >::entityIndex(), Kaskade::ContinuousHierarchicExtensionMapperImplementation< Scalar, GV, ShapeFunctionFilter >::entityIndex(), and Kaskade::BoundaryInterpolationDetail::getIsBoundaryFace().

writeAMIRAFile()

template<class GridView , class VariableSet >

void Kaskade::writeAMIRAFile	(	GridView const &	gridView,
		VariableSet const &	vars,
		std::string	file_out,
		IoOptions	options = ioOptions_default,
		Dune::BlockVector< Dune::FieldVector< double, 1 > >	materialData = Dune::BlockVector<Dune::FieldVector<double, 1>>(),
		std::string	file_in = ""
	)

This procedure writes data in AmiraMesh with cell material data to ascii/binary format, e.g. for visualization in AMIRA software.

Parameters

gridView	gridView, i.e. LeafGridView
description	variable set description
vars	data of variables
file_out	name of output file
options	defines the format for the output,e.g., ascii/binary
material	material data of underlying grid. Typically called as material.coefficients(), where material is a is a FunctionSpaceElement.
file_in	the Amira-input file the material data was read from

Definition at line 276 of file amira.hh.

writeMarc()

template<class Material >

void Kaskade::writeMarc	(	Material const &	material,
		std::string const &	filename,
		double const	scale = 1.0,
		IoOptions	options = IoOptions()
	)

Writes grid and material IDs given as FE function to a Marc input file.

This creates an input file for the Marc finite element solver by MSC Software. The created file is intended for heat simulations (not mechanics), and provides dummy thermal material parameters which need to be fixed before submitting the file to MARC.

The underlying grid must contain just one type of cell.

Parameters

material	a scalar integer-valued piecewise constant FE function defining the material id
filename	file name (without trailing ".marc" suffix)
scale	a scaling factor for the geometry. All lengths and positions are scaled by this factor.

Definition at line 69 of file marcwriter.hh.

writeToMatlab()

template<class Assembler >

void Kaskade::writeToMatlab	(	Assembler const &	assembler,
		std::string const &	path,
		std::string const &	basename,
		int	precision = 16
	)

Definition at line 237 of file matlab.hh.

Variable Documentation

contiguousStorage

template<class Vec >

constexpr bool Kaskade::contiguousStorage = Crsutil_Detail::VectorTraits<Vec>::contiguous

constexpr

Definition at line 167 of file crsutil.hh.

ioOptions_default

IoOptions Kaskade::ioOptions_default

extern

symmetryCheck

template<class Functional , int n>

constexpr bool Kaskade::symmetryCheck = Functional_Aux_Detail::checkSymmetry<Functional,n>::pass

constexpr

Definition at line 249 of file functional_aux.hh.