A local-to-global mapper for continuous finite elements on a subdomain. More...

#include <lagrangespace.hh>

Detailed Description

template<class GV, class SupportOracle, class ScalarType = double>
class Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >

A local-to-global mapper for continuous finite elements on a subdomain.

Template Parameters

GV	the grid view on which the space is defined
SupportOracle	a callable that for each cell specifies whether it is contained in the subdomain (maximal support of the functions) or not
ScalarType

Using this mapper is tricky, since the support oracle is usually defined as a lambda function, the type of which has to be provided as a template parameter. Here, class template deduction as of C++ 17 helps:

FEFunctionSpace space(gridManager,ContinuousLagrangeMapperSubdomain(
                                       gridManager.grid().leafGridView(),order,
                                       [](auto& cell) { return cell.geometry().center()[0]>0; }));

Definition at line 674 of file lagrangespace.hh.

Inheritance diagram for Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, 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< ContinuousLagrangeMapperSubdomain >, 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

typedef RangeView< GlobalIndexIterator >	GlobalIndexRange

typedef RangeView< SortedIndexIterator >	SortedIndexRange

Public Member Functions
	ContinuousLagrangeMapperSubdomain (GridView const &gridView, int order, SupportOracle &&supportOracle)
	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 shape functions associated to this cell. More...

GlobalIndexRange	globalIndices (size_t n) const
	Returns an immutable sequence containing the global indices of the shape functions associated to 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 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

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
	Continuity of the functions in this space. If the support is restricted to a proper subdomain, the functions are discontinuous across the inner boundary - hence the low continuity even though inside the subdomain the functions are \( C^0 \). More...

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

Protected Attributes
ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double >	implementation

Member Typedef Documentation

◆ Cell

using Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::Cell = Kaskade::Cell<Grid>

inherited

Definition at line 208 of file scalarspace.hh.

◆ Combiner

typedef Implementation::Combiner Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::Combiner

inherited

Definition at line 211 of file scalarspace.hh.

◆ ConstructorArgument

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

typedef int Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::ConstructorArgument

Definition at line 684 of file lagrangespace.hh.

◆ Converter

typedef Implementation::Converter Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::Converter

inherited

Definition at line 210 of file scalarspace.hh.

◆ GlobalIndexRange

typedef RangeView<GlobalIndexIterator> Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::GlobalIndexRange

inherited

Definition at line 228 of file scalarspace.hh.

◆ Grid

typedef Implementation::Grid Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::Grid

inherited

Definition at line 207 of file scalarspace.hh.

◆ GridView

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

typedef GV Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::GridView

Definition at line 682 of file lagrangespace.hh.

◆ IndexPair

typedef std::pair<size_t,int> Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::IndexPair

inherited

Definition at line 215 of file scalarspace.hh.

◆ IndexSet

typedef GridView::IndexSet Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::IndexSet

inherited

Definition at line 214 of file scalarspace.hh.

◆ Scalar

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

typedef ScalarType Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::Scalar

Definition at line 681 of file lagrangespace.hh.

◆ ShapeFunctionSet

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

typedef Base::ShapeFunctionSet Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::ShapeFunctionSet

Definition at line 683 of file lagrangespace.hh.

◆ SortedIndexRange

typedef RangeView<SortedIndexIterator> Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::SortedIndexRange

inherited

Definition at line 229 of file scalarspace.hh.

Constructor & Destructor Documentation

◆ ContinuousLagrangeMapperSubdomain()

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

Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::ContinuousLagrangeMapperSubdomain	(	GridView const &	gridView,
		int	order,
		SupportOracle &&	supportOracle
	)

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)
supportOracle	a callable that for any cell

Definition at line 715 of file lagrangespace.hh.

Member Function Documentation

◆ combiner()

Combiner Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::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 370 of file scalarspace.hh.

◆ globalIndices() [1/2]

GlobalIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::globalIndices ( Cell const & cell ) const

inlineinherited

Returns an immutable sequence containing the global indices of the shape functions associated to this cell.

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

Definition at line 274 of file scalarspace.hh.

◆ globalIndices() [2/2]

GlobalIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::globalIndices ( size_t n ) const

inlineinherited

Returns an immutable sequence containing the global indices of the shape functions associated to this cell.

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

Definition at line 285 of file scalarspace.hh.

◆ gridView()

GridView const & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::gridView ( ) const

inlineinherited

Returns the grid view used.

Definition at line 244 of file scalarspace.hh.

◆ initGlobalIndexRange()

GlobalIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::initGlobalIndexRange ( ) const

inlineinherited

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

Definition at line 261 of file scalarspace.hh.

◆ initSortedIndexRange()

static SortedIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::initSortedIndexRange ( )

inlinestaticinherited

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

Definition at line 294 of file scalarspace.hh.

◆ lowerShapeFunctions()

ShapeFunctionSet const & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::lowerShapeFunctions ( Cell const & cell ) const

inlineinherited

Definition at line 357 of file scalarspace.hh.

◆ maxOrder()

int Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::maxOrder ( ) const

inlineinherited

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

Definition at line 252 of file scalarspace.hh.

◆ shapefunctions() [1/2]

ShapeFunctionSet const & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::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 331 of file scalarspace.hh.

◆ shapefunctions() [2/2]

ShapeFunctionSet const & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::shapefunctions ( size_t n ) const

inlineinherited

Returns the set of shape functions defined on this cell.

Definition at line 347 of file scalarspace.hh.

◆ shapefunctions_non_const() [1/2]

ShapeFunctionSet & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::shapefunctions_non_const ( Cell const & cell )

inlineinherited

Definition at line 339 of file scalarspace.hh.

◆ shapefunctions_non_const() [2/2]

ShapeFunctionSet & Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::shapefunctions_non_const ( size_t n )

inlineinherited

Definition at line 352 of file scalarspace.hh.

◆ size()

size_t Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::size ( ) const

inlineinherited

Returns the number of global degrees of freedom managed.

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

Definition at line 323 of file scalarspace.hh.

◆ sortedIndices() [1/2]

SortedIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::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 303 of file scalarspace.hh.

◆ sortedIndices() [2/2]

SortedIndexRange Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::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 311 of file scalarspace.hh.

◆ unrestrictedToRestrictedIndex()

std::pair< bool, size_t > Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::unrestrictedToRestrictedIndex ( size_t unrestrictedIndex )

inlineinherited

Definition at line 379 of file scalarspace.hh.

◆ update()

void Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::update ( )

inlineinherited

(Re)computes the internal data.

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

Definition at line 389 of file scalarspace.hh.

Member Data Documentation

◆ continuity

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

int const Kaskade::ContinuousLagrangeMapperSubdomain< GV, SupportOracle, ScalarType >::continuity = -1

static

Continuity of the functions in this space. If the support is restricted to a proper subdomain, the functions are discontinuous across the inner boundary - hence the low continuity even though inside the subdomain the functions are \( C^0 \).

Definition at line 692 of file lagrangespace.hh.

◆ globalSupport

bool const Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::globalSupport

staticinherited

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

Definition at line 234 of file scalarspace.hh.

◆ implementation

ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > Kaskade::UniformScalarMapper< ContinuousLagrangeMapperSubdomainImplementation< GV, SupportOracle, double > , ScalarSpaceDetail::Empty >::implementation

protectedinherited

Definition at line 528 of file scalarspace.hh.

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

lagrangespace.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

◆ GlobalIndexRange

◆ Grid

◆ GridView

◆ IndexPair

◆ IndexSet

◆ Scalar

◆ ShapeFunctionSet

◆ SortedIndexRange

Constructor & Destructor Documentation

◆ ContinuousLagrangeMapperSubdomain()

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