Base class for uniform scalar local to global mappers. More...

#include <scalarspace.hh>

Detailed Description

template<class Implementation, class SFData = ScalarSpaceDetail::Empty>
class Kaskade::UniformScalarMapper< Implementation, SFData >

Base class for uniform scalar local to global mappers.

It manages degrees of freedom for ansatz spaces where to each type of entity of the grid the same number of global degrees of freedom is associated and on each cell live the same number of shape functions.

We call a degree of freedom associated to an entity e of the grid

if the support of the ansatz function is contained within the union of the cells (codim 0 entitites) which are incident to e and
the ansatz function vanishes on all subentities of incident cells with a codimension not less than e. This includes the usual polynomial FE spaces of arbitrary but fixed order.

With each shape function on each cell, we associate its global degree of freedom and additional data the type of is specified as template parameter SFData.

Template Parameters

Implementation
SFData	type of (optional) additional data associated to global degrees of freedom. This is used, e.g., for associating a sign to shape functions in hiearchic spaces.

Definition at line 204 of file scalarspace.hh.

Public Types
typedef Implementation::Grid	Grid

using	Cell = Kaskade::Cell< Grid >

typedef Implementation::ShapeFunctionSet	ShapeFunctionSet

typedef Implementation::Converter	Converter

typedef Implementation::Combiner	Combiner

typedef Implementation::Scalar	Scalar

typedef Implementation::GridView	GridView

typedef GridView::IndexSet	IndexSet

typedef std::pair< size_t, int >	IndexPair

typedef RangeView< GlobalIndexIterator >	GlobalIndexRange

typedef RangeView< SortedIndexIterator >	SortedIndexRange

Public Member Functions
	UniformScalarMapper (Implementation const &impl)

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 &	shapefunctions_non_const (Cell const &cell)

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

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

Protected Attributes
Implementation	implementation

Member Typedef Documentation

◆ Cell

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

using Kaskade::UniformScalarMapper< Implementation, SFData >::Cell = Kaskade::Cell<Grid>

Definition at line 208 of file scalarspace.hh.

◆ Combiner

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::Combiner Kaskade::UniformScalarMapper< Implementation, SFData >::Combiner

Definition at line 211 of file scalarspace.hh.

◆ Converter

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::Converter Kaskade::UniformScalarMapper< Implementation, SFData >::Converter

Definition at line 210 of file scalarspace.hh.

◆ GlobalIndexRange

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef RangeView<GlobalIndexIterator> Kaskade::UniformScalarMapper< Implementation, SFData >::GlobalIndexRange

Definition at line 228 of file scalarspace.hh.

◆ Grid

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::Grid Kaskade::UniformScalarMapper< Implementation, SFData >::Grid

Definition at line 207 of file scalarspace.hh.

◆ GridView

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::GridView Kaskade::UniformScalarMapper< Implementation, SFData >::GridView

Definition at line 213 of file scalarspace.hh.

◆ IndexPair

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef std::pair<size_t,int> Kaskade::UniformScalarMapper< Implementation, SFData >::IndexPair

Definition at line 215 of file scalarspace.hh.

◆ IndexSet

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef GridView::IndexSet Kaskade::UniformScalarMapper< Implementation, SFData >::IndexSet

Definition at line 214 of file scalarspace.hh.

◆ Scalar

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::Scalar Kaskade::UniformScalarMapper< Implementation, SFData >::Scalar

Definition at line 212 of file scalarspace.hh.

◆ ShapeFunctionSet

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef Implementation::ShapeFunctionSet Kaskade::UniformScalarMapper< Implementation, SFData >::ShapeFunctionSet

Definition at line 209 of file scalarspace.hh.

◆ SortedIndexRange

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

typedef RangeView<SortedIndexIterator> Kaskade::UniformScalarMapper< Implementation, SFData >::SortedIndexRange

Definition at line 229 of file scalarspace.hh.

Constructor & Destructor Documentation

◆ UniformScalarMapper()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

Kaskade::UniformScalarMapper< Implementation, SFData >::UniformScalarMapper ( Implementation const & impl )

inline

Definition at line 236 of file scalarspace.hh.

Member Function Documentation

◆ combiner()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

Combiner Kaskade::UniformScalarMapper< Implementation, SFData >::combiner	(	Cell const &	cell,
		size_t	index
	)		const

inline

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]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

GlobalIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::globalIndices ( Cell const & cell ) const

inline

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.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::globalIndices(), and Kaskade::UniformScalarMapper< Implementation, SFData >::lowerShapeFunctions().

◆ globalIndices() [2/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

GlobalIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::globalIndices ( size_t n ) const

inline

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()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

GridView const & Kaskade::UniformScalarMapper< Implementation, SFData >::gridView ( ) const

inline

Returns the grid view used.

Definition at line 244 of file scalarspace.hh.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::update().

◆ initGlobalIndexRange()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

GlobalIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::initGlobalIndexRange ( ) const

inline

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

Definition at line 261 of file scalarspace.hh.

◆ initSortedIndexRange()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

static SortedIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::initSortedIndexRange ( )

inlinestatic

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

Definition at line 294 of file scalarspace.hh.

◆ lowerShapeFunctions()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

ShapeFunctionSet const & Kaskade::UniformScalarMapper< Implementation, SFData >::lowerShapeFunctions ( Cell const & cell ) const

inline

Definition at line 357 of file scalarspace.hh.

◆ maxOrder()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

int Kaskade::UniformScalarMapper< Implementation, SFData >::maxOrder ( ) const

inline

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

Definition at line 252 of file scalarspace.hh.

◆ shapefunctions() [1/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

ShapeFunctionSet const & Kaskade::UniformScalarMapper< Implementation, SFData >::shapefunctions	(	Cell const &	cell,
		bool	contained = `false`
	)		const

inline

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.

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

◆ shapefunctions() [2/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

ShapeFunctionSet const & Kaskade::UniformScalarMapper< Implementation, SFData >::shapefunctions ( size_t n ) const

inline

Returns the set of shape functions defined on this cell.

Definition at line 347 of file scalarspace.hh.

◆ shapefunctions_non_const() [1/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

ShapeFunctionSet & Kaskade::UniformScalarMapper< Implementation, SFData >::shapefunctions_non_const ( Cell const & cell )

inline

Definition at line 339 of file scalarspace.hh.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::shapefunctions_non_const().

◆ shapefunctions_non_const() [2/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

ShapeFunctionSet & Kaskade::UniformScalarMapper< Implementation, SFData >::shapefunctions_non_const ( size_t n )

inline

Definition at line 352 of file scalarspace.hh.

◆ size()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

size_t Kaskade::UniformScalarMapper< Implementation, SFData >::size ( ) const

inline

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.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::update().

◆ sortedIndices() [1/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

SortedIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::sortedIndices ( Cell const & cell ) const

inline

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

Definition at line 303 of file scalarspace.hh.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::sortedIndices().

◆ sortedIndices() [2/2]

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

SortedIndexRange Kaskade::UniformScalarMapper< Implementation, SFData >::sortedIndices ( size_t n ) const

inline

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()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

std::pair< bool, size_t > Kaskade::UniformScalarMapper< Implementation, SFData >::unrestrictedToRestrictedIndex ( size_t unrestrictedIndex )

inline

Definition at line 379 of file scalarspace.hh.

Referenced by Kaskade::FunctionSpaceElement< FunctionSpace, m >::operator=().

◆ update()

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

void Kaskade::UniformScalarMapper< Implementation, SFData >::update ( )

inline

(Re)computes the internal data.

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

Definition at line 389 of file scalarspace.hh.

Referenced by Kaskade::UniformScalarMapper< Implementation, SFData >::UniformScalarMapper().

Member Data Documentation

◆ globalSupport

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

bool const Kaskade::UniformScalarMapper< Implementation, SFData >::globalSupport = false

static

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

Definition at line 234 of file scalarspace.hh.

◆ implementation

template<class Implementation , class SFData = ScalarSpaceDetail::Empty>

Implementation Kaskade::UniformScalarMapper< Implementation, SFData >::implementation

protected

Definition at line 528 of file scalarspace.hh.

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

scalarspace.hh

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Member Typedef Documentation

◆ Cell

◆ Combiner

◆ Converter

◆ GlobalIndexRange

◆ Grid

◆ GridView

◆ IndexPair

◆ IndexSet

◆ Scalar

◆ ShapeFunctionSet

◆ SortedIndexRange

Constructor & Destructor Documentation

◆ UniformScalarMapper()

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

◆ globalSupport

◆ implementation