A representation of a finite element function space defined over a domain covered by a grid.
More...

#include <functionspace.hh>

Detailed Description

template<class LocalToGlobalMapper>
class Kaskade::FEFunctionSpace< LocalToGlobalMapper >

A representation of a finite element function space defined over a domain covered by a grid.

Elements of the space are defined in terms of shape functions defined over cells (codim 0 entities) of the grid and a LocalToglobalMapper (also known as node manager) combining local shape function coefficients on different cells to one global degree of freedom. Depending on the LocalToGlobalMapper, the finite element functions may be globally continuous or discontinuous, and may support pointwise evaluation of gradients besides the pointwise evaluation of function values.

The FEFunctionSpace defines an element type (a class that holds a certain function from the space) as well as evaluation cache classes that store global indices of local shape functions and values and possibly derivatives of shape functions at certain integration points.

See also: LocalToGlobalMapperConcept

Definition at line 1116 of file functionspace.hh.

Classes
struct	Element
	DEPRECATED use Element_t<m> instead. More...

struct	Evaluator
	A helper class that stores all informations necessary to evaluate FE functions at a certain point. More...

Public Types
using	GridView = typename LocalToGlobalMapper::GridView
	Type of grid view. More...

typedef GridView::Grid	Grid
	Type of grid. More...

typedef GridView::IndexSet	IndexSet
	Type of IndexSet. More...

typedef LocalToGlobalMapper::Scalar	Scalar

using	field_type = Scalar
	The scalar field type on which the linear (function) space is based. This is provided for consistency with Dune. More...

typedef Grid::ctype	ctype
	Coordinate Type. More...

typedef LocalToGlobalMapper	Mapper
	corresponding mapper More...

template<int m>
using	Element_t = FunctionSpaceElement< Self, m >
	Defines the element function type. More...

using	SfValueType = typename Evaluator::VarArg::ValueType
	type of shape function values More...

Public Member Functions
template<typename... Args>
	FEFunctionSpace (GridManagerBase< Grid > &gridMan, GridView const &gridView_, Args... args)
	Constructs a finite element space from a GridManager, a grid view, and possibly extra arguments passed to the node manager. More...

	FEFunctionSpace (GridManagerBase< Grid > &gridman_, Mapper &&m)
	Constructs a finite element space from a directly given mapper. More...

	FEFunctionSpace (FEFunctionSpace< LocalToGlobalMapper > const &fs)
	Copy constructor. More...

	~FEFunctionSpace ()

size_t	degreesOfFreedom () const
	Returns the dimension of the function space, i.e. the number of degrees of freedom of a one-component function from this space. More...

Grid const &	grid () const
	Provides access to the grid on which this finite element space is defined. More...

GridManagerBase< Grid > &	gridManager () const
	Access to the GridManager. More...

IndexSet const &	indexSet () const
	Provides access to the index set defining the part of the grid on which the space is defined. More...

GridView const &	gridView () const
	Provides access to the index set defining the potential support of the space. More...

LocalToGlobalMapper const &	mapper () const
	Provides read access to the node manager. More...

LocalToGlobalMapper &	mapper ()
	Provides read-write access to the node manager. More...

Evaluator	evaluator (ShapeFunctionCache< Grid, Scalar > *cache=nullptr, int deriv=1) const
	Creates a new evaluator for this space. More...

template<int m>
Element_t< m >	element () const
	Creates a new function in this function space. More...

std::vector< std::pair< size_t, SfValueType > >	linearCombination (Evaluator const &evaluator) const
	Returns the coefficients of the linear combination of global DoFs that define the value at the position specified by the given evaluator. More...

std::vector< std::pair< size_t, SfValueType > >	linearCombination (Cell< GridView > const &cell, LocalPosition< GridView > const &xi) const
	Returns the coefficients of the linear combination of global DoFs that define the value at the given position. More...

std::vector< std::pair< size_t, SfValueType > >	linearCombination (GlobalPosition< GridView > const &x) const
	Returns the coefficients of the linear combination of global DoFs that define the value at the given global position. More...

Public Attributes
boost::signals2::signal< void(typename TransferData< Self >::TransferMatrix const *) >	requestToRefine
	Signal for refinement. More...

Static Public Attributes
static int const	dim = Grid::dimension
	Grid dimension. More...

static int const	dimworld = Grid::dimensionworld
	spatial dimension More...

static int const	sfComponents = Mapper::ShapeFunctionSet::comps
	The number of components of shape functions. More...

static int const	continuity = Mapper::continuity
	Tells how often elements are globally continuously differentiable. More...

Member Typedef Documentation

◆ ctype

template<class LocalToGlobalMapper >

typedef Grid::ctype Kaskade::FEFunctionSpace< LocalToGlobalMapper >::ctype

Coordinate Type.

Definition at line 1138 of file functionspace.hh.

◆ Element_t

template<class LocalToGlobalMapper >

template<int m>

using Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Element_t = FunctionSpaceElement<Self,m>

Defines the element function type.

Template Parameters

m	number of "components" A "component" is understood as a full shape function value. This can be a multi-component value as well. With vectorial shape functions (e.g. Nedelec edge elements), m==2 means you end up with 2*dim entries of type Scalar in the function's values.

Definition at line 1181 of file functionspace.hh.

◆ field_type

template<class LocalToGlobalMapper >

using Kaskade::FEFunctionSpace< LocalToGlobalMapper >::field_type = Scalar

The scalar field type on which the linear (function) space is based. This is provided for consistency with Dune.

Definition at line 1135 of file functionspace.hh.

◆ Grid

template<class LocalToGlobalMapper >

typedef GridView::Grid Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Grid

Type of grid.

Definition at line 1124 of file functionspace.hh.

◆ GridView

template<class LocalToGlobalMapper >

using Kaskade::FEFunctionSpace< LocalToGlobalMapper >::GridView = typename LocalToGlobalMapper::GridView

Type of grid view.

Definition at line 1122 of file functionspace.hh.

◆ IndexSet

template<class LocalToGlobalMapper >

typedef GridView::IndexSet Kaskade::FEFunctionSpace< LocalToGlobalMapper >::IndexSet

Type of IndexSet.

Definition at line 1126 of file functionspace.hh.

◆ Mapper

template<class LocalToGlobalMapper >

typedef LocalToGlobalMapper Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Mapper

corresponding mapper

Definition at line 1141 of file functionspace.hh.

◆ Scalar

template<class LocalToGlobalMapper >

typedef LocalToGlobalMapper::Scalar Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Scalar

The scalar field type on which the linear (function) space is based.

Definition at line 1129 of file functionspace.hh.

◆ SfValueType

template<class LocalToGlobalMapper >

using Kaskade::FEFunctionSpace< LocalToGlobalMapper >::SfValueType = typename Evaluator::VarArg::ValueType

type of shape function values

Definition at line 1502 of file functionspace.hh.

Constructor & Destructor Documentation

◆ FEFunctionSpace() [1/3]

template<class LocalToGlobalMapper >

template<typename... Args>

Kaskade::FEFunctionSpace< LocalToGlobalMapper >::FEFunctionSpace	(	GridManagerBase< Grid > &	gridMan,
		GridView const &	gridView_,
		Args...	args
	)

inline

Constructs a finite element space from a GridManager, a grid view, and possibly extra arguments passed to the node manager.

Note that the grid has to exist during the whole lifetime of the function space.

The construction from a GridManager, rather than a Grid makes sure, that the FEFunctionSpace is informed about grid modifications, such that data can be transfered from the original grid to the modified grid.

Parameters

args	a parameter pack that is forwarded to the local to global mapper. If LocalToGlobalMapper is a LagrangeMapper or a HierarchicMapper, then the last argument arg denotes the polynomial order of the finite element space.

Definition at line 1522 of file functionspace.hh.

◆ FEFunctionSpace() [2/3]

template<class LocalToGlobalMapper >

Kaskade::FEFunctionSpace< LocalToGlobalMapper >::FEFunctionSpace	(	GridManagerBase< Grid > &	gridman_,
		Mapper &&	m
	)

inline

Constructs a finite element space from a directly given mapper.

This allows constructing a function space without specifying its complete type, which is inferred from the mapper argument (since C++17).

FEFunctionSpace space(gridman,ContinuousLagrangeMapper<double,GridView>(gridView,order));

Kaskade::ContinuousLagrangeMapper

A degrees of freedom manager for globally continuous FEFunctionSpace s of piecewise polynomials.

Definition: lagrangespace.hh:503

Kaskade::FEFunctionSpace

A representation of a finite element function space defined over a domain covered by a grid.

Definition: functionspace.hh:1117

Kaskade::FEFunctionSpace::gridView

GridView const & gridView() const

Provides access to the index set defining the potential support of the space.

Definition: functionspace.hh:1596

Parameters

m	the mapper, which is moved into the function space

Definition at line 1544 of file functionspace.hh.

◆ FEFunctionSpace() [3/3]

template<class LocalToGlobalMapper >

Kaskade::FEFunctionSpace< LocalToGlobalMapper >::FEFunctionSpace ( FEFunctionSpace< LocalToGlobalMapper > const & fs )

inline

Copy constructor.

Definition at line 1556 of file functionspace.hh.

◆ ~FEFunctionSpace()

template<class LocalToGlobalMapper >

Kaskade::FEFunctionSpace< LocalToGlobalMapper >::~FEFunctionSpace ( )

inline

Definition at line 1565 of file functionspace.hh.

Member Function Documentation

◆ degreesOfFreedom()

template<class LocalToGlobalMapper >

size_t Kaskade::FEFunctionSpace< LocalToGlobalMapper >::degreesOfFreedom ( ) const

inline

Returns the dimension of the function space, i.e. the number of degrees of freedom of a one-component function from this space.

Definition at line 1574 of file functionspace.hh.

Referenced by Kaskade::makeAuxiliarySpaceMultigridStack().

◆ element()

template<class LocalToGlobalMapper >

template<int m>

Element_t< m > Kaskade::FEFunctionSpace< LocalToGlobalMapper >::element ( ) const

inline

Creates a new function in this function space.

Template Parameters

m	the number of components The returned function is initialized to zero.

Definition at line 1621 of file functionspace.hh.

◆ evaluator()

template<class LocalToGlobalMapper >

Evaluator Kaskade::FEFunctionSpace< LocalToGlobalMapper >::evaluator	(	ShapeFunctionCache< Grid, Scalar > *	cache = `nullptr`,
		int	deriv = `1`
	)		const

inline

Creates a new evaluator for this space.

Parameters

cache	an (optional) shape function cache to be used
deriv	number of highest requested derivatives

Definition at line 1613 of file functionspace.hh.

Referenced by Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination().

◆ grid()

template<class LocalToGlobalMapper >

Grid const & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::grid ( ) const

inline

Provides access to the grid on which this finite element space is defined.

Definition at line 1580 of file functionspace.hh.

◆ gridManager()

template<class LocalToGlobalMapper >

GridManagerBase< Grid > & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::gridManager ( ) const

inline

Access to the GridManager.

Todo:: why is this a const function returning a non-const grid manager reference?

Definition at line 1586 of file functionspace.hh.

Referenced by Kaskade::prolongationStack().

◆ gridView()

template<class LocalToGlobalMapper >

GridView const & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::gridView ( ) const

inline

Provides access to the index set defining the potential support of the space.

Definition at line 1596 of file functionspace.hh.

Referenced by Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Evaluator::gridView(), Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination(), and Kaskade::prolongationStack().

◆ indexSet()

template<class LocalToGlobalMapper >

IndexSet const & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::indexSet ( ) const

inline

Provides access to the index set defining the part of the grid on which the space is defined.

Definition at line 1591 of file functionspace.hh.

Referenced by Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Evaluator::moveTo().

◆ linearCombination() [1/3]

template<class LocalToGlobalMapper >

std::vector< std::pair< size_t, SfValueType > > Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination	(	Cell< GridView > const &	cell,
		LocalPosition< GridView > const &	xi
	)		const

inline

Returns the coefficients of the linear combination of global DoFs that define the value at the given position.

Let \( u(x) = \sum_j u_j \varphi_j(x) \) and \( J(x) := \{ j\in \mathbf{N} \mid x\in \mathrm{supp} \varphi_j \} \). Then this method returns \( \{ (j,\varphi_j(x)) \mid j \in J(x) \} \). This provides information about which global dof affects the value at a certain position, and how much.

The same information can be extracted more efficiently but with less convenience from an evaluator.

Definition at line 1667 of file functionspace.hh.

◆ linearCombination() [2/3]

template<class LocalToGlobalMapper >

std::vector< std::pair< size_t, SfValueType > > Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination ( Evaluator const & evaluator ) const

inline

Returns the coefficients of the linear combination of global DoFs that define the value at the position specified by the given evaluator.

Let \( u(x) = \sum_j u_j \varphi_j(x) \) and \( J(x) := \{ j\in \mathbf{N} \mid x\in \mathrm{supp} \varphi_j \} \). Then this method returns \( \{ (j,\varphi_j(x)) \mid j \in J(x) \} \). This provides information about which global dof affects the value at a certain position, and how much.

The same information can be extracted more efficiently but with slightly less convenience directly from the evaluator.

Definition at line 1638 of file functionspace.hh.

Referenced by Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination().

◆ linearCombination() [3/3]

template<class LocalToGlobalMapper >

std::vector< std::pair< size_t, SfValueType > > Kaskade::FEFunctionSpace< LocalToGlobalMapper >::linearCombination ( GlobalPosition< GridView > const & x ) const

inline

Returns the coefficients of the linear combination of global DoFs that define the value at the given global position.

Let \( u(x) = \sum_j u_j \varphi_j(x) \) and \( J(x) := \{ j\in \mathbf{N} \mid x\in \mathrm{supp} \varphi_j \} \). Then this method returns \( \{ (j,\varphi_j(x)) \mid j \in J(x) \} \). This provides information about which global dof affects the value at a certain position, and how much.

The same information can be extracted much more efficiently but with less convenience from cell and local position.

Definition at line 1689 of file functionspace.hh.

◆ mapper() [1/2]

template<class LocalToGlobalMapper >

LocalToGlobalMapper & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::mapper ( )

inline

Provides read-write access to the node manager.

Definition at line 1606 of file functionspace.hh.

◆ mapper() [2/2]

template<class LocalToGlobalMapper >

LocalToGlobalMapper const & Kaskade::FEFunctionSpace< LocalToGlobalMapper >::mapper ( ) const

inline

Provides read access to the node manager.

Definition at line 1601 of file functionspace.hh.

Referenced by Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Evaluator::mapper(), Kaskade::FEFunctionSpace< LocalToGlobalMapper >::Evaluator::moveTo(), Kaskade::prolongationStack(), and Kaskade::Limex< Eq >::step().

Member Data Documentation

◆ continuity

template<class LocalToGlobalMapper >

int const Kaskade::FEFunctionSpace< LocalToGlobalMapper >::continuity = Mapper::continuity

static

Tells how often elements are globally continuously differentiable.

E.g., 0 means a globally continuous, but not differentiable function, -1 means a discontinuous function (with finite values), -2 may contain Dirac functionals etc.

Definition at line 1161 of file functionspace.hh.

◆ dim

template<class LocalToGlobalMapper >

int const Kaskade::FEFunctionSpace< LocalToGlobalMapper >::dim = Grid::dimension

static

Grid dimension.

Definition at line 1144 of file functionspace.hh.

◆ dimworld

template<class LocalToGlobalMapper >

int const Kaskade::FEFunctionSpace< LocalToGlobalMapper >::dimworld = Grid::dimensionworld

static

spatial dimension

Definition at line 1147 of file functionspace.hh.

◆ requestToRefine

template<class LocalToGlobalMapper >

boost::signals2::signal<void (typename TransferData<Self>::TransferMatrix const*) > Kaskade::FEFunctionSpace< LocalToGlobalMapper >::requestToRefine

mutable

Signal for refinement.

This signal is emitted after mesh refinement/coarsening. Clients are informed with a transfer matrix that allows to compute the new FE coefficients from the old ones. This is used by FEFunctions belonging to this space. Clients may start the transfer process asynchonously and return before completion.

If no transfer matrix is given (nullptr), clients are supposed to block until the transfer is finished.

Definition at line 1774 of file functionspace.hh.

◆ sfComponents

template<class LocalToGlobalMapper >

int const Kaskade::FEFunctionSpace< LocalToGlobalMapper >::sfComponents = Mapper::ShapeFunctionSet::comps

static

The number of components of shape functions.

Definition at line 1152 of file functionspace.hh.

The documentation for this class was generated from the following file:

functionspace.hh

Detailed Description

Classes

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Member Typedef Documentation

◆ ctype

◆ Element_t

◆ field_type

◆ Grid

◆ GridView

◆ IndexSet

◆ Mapper

◆ Scalar

◆ SfValueType

Constructor & Destructor Documentation

◆ FEFunctionSpace() [1/3]

◆ FEFunctionSpace() [2/3]

◆ FEFunctionSpace() [3/3]

◆ ~FEFunctionSpace()

Member Function Documentation

◆ degreesOfFreedom()

◆ element()

◆ evaluator()

◆ grid()

◆ gridManager()

◆ gridView()

◆ indexSet()

◆ linearCombination() [1/3]

◆ linearCombination() [2/3]

◆ linearCombination() [3/3]

◆ mapper() [1/2]

◆ mapper() [2/2]

Member Data Documentation

◆ continuity

◆ dim

◆ dimworld

◆ requestToRefine

◆ sfComponents