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

#include <partitionedspace.hh>

Detailed Description

template<class Tagger, class GV, class ScalarType = double>
class Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >

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

auto tagger = [](auto const& cell)
{
  auto x = cell.geometry().center();
  if (x[0]+x[1] > 1) return 0;
  if (x[0]>0.5) return 1;
  return 2;
};
using Tagger = decltype(tagger);
using BrokenH1 = FEFunctionSpace<PiecewiseContinuousLagrangeMapper<Tagger,LeafView>>;
BrokenH1 brokenH1 = (gridManager,gridManager.grid().leafGridView(),order,tagger);

Template Parameters

Tagger	a callable type mapping cells to subdomain tags
ScalarType	a scalar arithmetic type to be used as shape function value type
GV	grid view

Definition at line 683 of file partitionedspace.hh.

Inheritance diagram for Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >:

Classes
struct	Element

Public Types
typedef ScalarType	Scalar

typedef GV	GridView

typedef Base::ShapeFunctionSet	ShapeFunctionSet

typedef int	ConstructorArgument

template<int m>
using	Element_t = FunctionSpaceElement< FEFunctionSpace< PiecewiseContinuousLagrangeMapper >, m >
	Type of the FunctionSpaceElement, associated to the FEFunctionSpace. More...

typedef Implementation::Grid	Grid

using	Cell = Kaskade::Cell< Grid >

typedef Implementation::Converter	Converter

typedef Implementation::Combiner	Combiner

typedef GridView::IndexSet	IndexSet

typedef std::pair< size_t, int >	IndexPair
	Indexing information for localized ansatz functions. More...

typedef RangeView< GlobalIndexIterator >	GlobalIndexRange

typedef RangeView< SortedIndexIterator >	SortedIndexRange

Public Member Functions
	PiecewiseContinuousLagrangeMapper (GridView const &gridView, int order, Tagger const &tagger)
	Constructor. More...

GridView const &	gridView () const
	Returns the grid view used. More...

int	maxOrder () const
	Returns the maximal polynomial order of shape functions encountered in any cell. More...

GlobalIndexRange	initGlobalIndexRange () const
	Returns an empty range just for initialization purposes, since RangeView is not default constructible. More...

GlobalIndexRange	globalIndices (Cell const &cell) const
	Returns an immutable sequence containing the global indices of the ansatz functions with support intersecting this cell. More...

GlobalIndexRange	globalIndices (size_t n) const
	Returns an immutable sequence containing the global indices of the ansatz functions with support intersecting this cell. More...

SortedIndexRange	sortedIndices (Cell const &cell) const
	Returns an immutable sequence of (global index, local index) pairs sorted in ascending global index order. More...

SortedIndexRange	sortedIndices (size_t n) const
	Returns an immutable sequence of (global index, local index) pairs sorted in ascending global index order. More...

size_t	size () const
	Returns the number of global scalar degrees of freedom managed. More...

ShapeFunctionSet const &	shapefunctions (Cell const &cell, bool contained=false) const
	Returns the set of shape functions defined on this cell. More...

ShapeFunctionSet const &	shapefunctions (size_t n) const
	Returns the set of shape functions defined on this cell. More...

ShapeFunctionSet &	shapefunctions_non_const (Cell const &cell)

ShapeFunctionSet &	shapefunctions_non_const (size_t n)

ShapeFunctionSet const &	lowerShapeFunctions (Cell const &cell) const
	Returns a shape function set for a lower ansatz order (or an empty shape function set if there is no lower order). More...

Combiner	combiner (Cell const &cell, size_t index) const
	Returns a combiner for the given leaf cell. More...

std::pair< bool, size_t >	unrestrictedToRestrictedIndex (size_t unrestrictedIndex)

void	update ()
	(Re)computes the internal data. More...

Static Public Member Functions
static SortedIndexRange	initSortedIndexRange ()
	Returns an empty range just for initialization, since RangeView is not default constructible. More...

Static Public Attributes
static int const	continuity = -1

static bool const	globalSupport
	Whether the ansatz functions have global support (i.e. lead to dense matrices). More...

Protected Attributes
ContinuousLagrangeMapperImplementation< double, GV >	implementation

Member Typedef Documentation

◆ Cell

using Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::Cell = Kaskade::Cell<Grid>

inherited

Definition at line 238 of file partitionedspace.hh.

◆ Combiner

typedef Implementation::Combiner Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::Combiner

inherited

Definition at line 241 of file partitionedspace.hh.

◆ ConstructorArgument

template<class Tagger , class GV , class ScalarType = double>

typedef int Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::ConstructorArgument

Definition at line 693 of file partitionedspace.hh.

◆ Converter

typedef Implementation::Converter Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::Converter

inherited

Definition at line 240 of file partitionedspace.hh.

◆ Element_t

template<class Tagger , class GV , class ScalarType = double>

template<int m>

using Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::Element_t = FunctionSpaceElement<FEFunctionSpace<PiecewiseContinuousLagrangeMapper>,m>

Type of the FunctionSpaceElement, associated to the FEFunctionSpace.

Template Parameters

m	number of components

Definition at line 702 of file partitionedspace.hh.

◆ GlobalIndexRange

typedef RangeView<GlobalIndexIterator> Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::GlobalIndexRange

inherited

Definition at line 276 of file partitionedspace.hh.

◆ Grid

typedef Implementation::Grid Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::Grid

inherited

Definition at line 237 of file partitionedspace.hh.

◆ GridView

template<class Tagger , class GV , class ScalarType = double>

typedef GV Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::GridView

Definition at line 691 of file partitionedspace.hh.

◆ IndexPair

typedef std::pair<size_t,int> Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::IndexPair

inherited

Indexing information for localized ansatz functions.

Localized ansatz functions on a cell have global indices \( I \in {\bf N}^m \), compare the LocalToGlobalMapper concept. This index vector need not be sorted, in fact, as the extracted dofs are to be multiplied with the combiner matrix, their order matters. Consequently, there is a one-to-one mapping of cell-local indices (second component) and affected global indices (first component).

Definition at line 255 of file partitionedspace.hh.

◆ IndexSet

typedef GridView::IndexSet Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::IndexSet

inherited

Definition at line 244 of file partitionedspace.hh.

◆ Scalar

template<class Tagger , class GV , class ScalarType = double>

typedef ScalarType Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::Scalar

Definition at line 690 of file partitionedspace.hh.

◆ ShapeFunctionSet

template<class Tagger , class GV , class ScalarType = double>

typedef Base::ShapeFunctionSet Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::ShapeFunctionSet

Definition at line 692 of file partitionedspace.hh.

◆ SortedIndexRange

typedef RangeView<SortedIndexIterator> Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::SortedIndexRange

inherited

Definition at line 277 of file partitionedspace.hh.

Constructor & Destructor Documentation

◆ PiecewiseContinuousLagrangeMapper()

template<class Tagger , class GV , class ScalarType = double>

Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::PiecewiseContinuousLagrangeMapper	(	GridView const &	gridView,
		int	order,
		Tagger const &	tagger
	)

inline

Constructor.

Parameters

gridView	the grid view on which to define the space, usually a leaf grid view
order	polynomial ansatz order of shape functions (> 0)
tagger	a callable mapping cells to subdomain tags. The tagger is copied and stored in the space - make copying cheap.

Definition at line 717 of file partitionedspace.hh.

Member Function Documentation

◆ combiner()

Combiner Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::combiner	(	Cell const &	cell,
		size_t	index
	)		const

inlineinherited

Returns a combiner for the given leaf cell.

Parameters

cell	the grid cell for which the combiner is requested
index	the index of the cell

Definition at line 444 of file partitionedspace.hh.

◆ globalIndices() [1/2]

GlobalIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::globalIndices ( Cell const & cell ) const

inlineinherited

Returns an immutable sequence containing the global indices of the ansatz functions with support intersecting this cell.

Parameters

cell	the cell to inquire

Global indices start at 0 and are consecutive - in the range returned here, an unordered subset is contained.

Definition at line 334 of file partitionedspace.hh.

◆ globalIndices() [2/2]

GlobalIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::globalIndices ( size_t n ) const

inlineinherited

Returns an immutable sequence containing the global indices of the ansatz functions with support intersecting this cell.

Parameters

n	the index of the cell in the grid view used.

Global indices start at 0 and are consecutive - in the range returned here, an unordered subset is contained.

Definition at line 348 of file partitionedspace.hh.

◆ gridView()

GridView const & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::gridView ( ) const

inlineinherited

Returns the grid view used.

Definition at line 300 of file partitionedspace.hh.

◆ initGlobalIndexRange()

GlobalIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::initGlobalIndexRange ( ) const

inlineinherited

Returns an empty range just for initialization purposes, since RangeView is not default constructible.

Definition at line 318 of file partitionedspace.hh.

◆ initSortedIndexRange()

static SortedIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::initSortedIndexRange ( )

inlinestaticinherited

Returns an empty range just for initialization, since RangeView is not default constructible.

Definition at line 357 of file partitionedspace.hh.

◆ lowerShapeFunctions()

ShapeFunctionSet const & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::lowerShapeFunctions ( Cell const & cell ) const

inlineinherited

Returns a shape function set for a lower ansatz order (or an empty shape function set if there is no lower order).

Definition at line 431 of file partitionedspace.hh.

◆ maxOrder()

int Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::maxOrder ( ) const

inlineinherited

Returns the maximal polynomial order of shape functions encountered in any cell.

Definition at line 308 of file partitionedspace.hh.

◆ shapefunctions() [1/2]

ShapeFunctionSet const & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::shapefunctions	(	Cell const &	cell,
		bool	contained = `false`
	)		const

inlineinherited

Returns the set of shape functions defined on this cell.

Parameters

cell	the codim 0 entity of the grid for wich the shape functions are to be retrieved
contained	if true, the method may assume that the cell is contained in the index set of the space. (The other case occurs during interpolation between different grids).

Definition at line 399 of file partitionedspace.hh.

◆ shapefunctions() [2/2]

ShapeFunctionSet const & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::shapefunctions ( size_t n ) const

inlineinherited

Returns the set of shape functions defined on this cell.

Definition at line 416 of file partitionedspace.hh.

◆ shapefunctions_non_const() [1/2]

ShapeFunctionSet & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::shapefunctions_non_const ( Cell const & cell )

inlineinherited

Definition at line 408 of file partitionedspace.hh.

◆ shapefunctions_non_const() [2/2]

ShapeFunctionSet & Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::shapefunctions_non_const ( size_t n )

inlineinherited

Definition at line 422 of file partitionedspace.hh.

◆ size()

size_t Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::size ( ) const

inlineinherited

Returns the number of global scalar degrees of freedom managed.

Note that this does not correspond directly to the number of scalar coefficients in a FE function (if the FE function has more than one component).

Definition at line 388 of file partitionedspace.hh.

◆ sortedIndices() [1/2]

SortedIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::sortedIndices ( Cell const & cell ) const

inlineinherited

Returns an immutable sequence of (global index, local index) pairs sorted in ascending global index order.

Definition at line 367 of file partitionedspace.hh.

◆ sortedIndices() [2/2]

SortedIndexRange Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::sortedIndices ( size_t n ) const

inlineinherited

Returns an immutable sequence of (global index, local index) pairs sorted in ascending global index order.

Definition at line 376 of file partitionedspace.hh.

◆ unrestrictedToRestrictedIndex()

std::pair< bool, size_t > Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::unrestrictedToRestrictedIndex ( size_t unrestrictedIndex )

inlineinherited

Definition at line 453 of file partitionedspace.hh.

◆ update()

void Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::update ( )

inlineinherited

(Re)computes the internal data.

This has to be called after grid modifications and on construction.

Definition at line 463 of file partitionedspace.hh.

Member Data Documentation

◆ continuity

template<class Tagger , class GV , class ScalarType = double>

int const Kaskade::PiecewiseContinuousLagrangeMapper< Tagger, GV, ScalarType >::continuity = -1

static

Definition at line 694 of file partitionedspace.hh.

◆ globalSupport

bool const Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::globalSupport

staticinherited

Whether the ansatz functions have global support (i.e. lead to dense matrices).

Definition at line 282 of file partitionedspace.hh.

◆ implementation

ContinuousLagrangeMapperImplementation< double, GV > Kaskade::UniformPartitionedMapper< ContinuousLagrangeMapperImplementation< double, GV > , Tagger, PartitionedSpaceDetail::Empty >::implementation

protectedinherited

Definition at line 654 of file partitionedspace.hh.

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

partitionedspace.hh

Detailed Description

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Member Typedef Documentation

◆ Cell

◆ Combiner

◆ ConstructorArgument

◆ Converter

◆ Element_t

◆ GlobalIndexRange

◆ Grid

◆ GridView

◆ IndexPair

◆ IndexSet

◆ Scalar

◆ ShapeFunctionSet

◆ SortedIndexRange

Constructor & Destructor Documentation

◆ PiecewiseContinuousLagrangeMapper()

Member Function Documentation

◆ combiner()

◆ globalIndices() [1/2]

◆ globalIndices() [2/2]

◆ gridView()

◆ initGlobalIndexRange()

◆ initSortedIndexRange()

◆ lowerShapeFunctions()

◆ maxOrder()

◆ shapefunctions() [1/2]

◆ shapefunctions() [2/2]

◆ shapefunctions_non_const() [1/2]

◆ shapefunctions_non_const() [2/2]

◆ size()

◆ sortedIndices() [1/2]

◆ sortedIndices() [2/2]

◆ unrestrictedToRestrictedIndex()

◆ update()

Member Data Documentation

◆ continuity

◆ globalSupport

◆ implementation