Degrees of freedom manager for H(div) conforming elements. More...

#include <nedelecspace.hh>

Detailed Description

template<class ScalarType, class GV>
class Kaskade::HdivMapper< ScalarType, GV >

Degrees of freedom manager for H(div) conforming elements.

Template Parameters

ScalarType	scalar type
GV	grid view

Definition at line 234 of file nedelecspace.hh.

Classes
class	Combiner
	A class implementing a matrix \( K \) mapping a subset of global degrees of freedom (those given by globalIndices()) to local degrees of freedom (shape functions). More...

Public Types
typedef ScalarType	Scalar

typedef GV	GridView

typedef GridView::Grid	Grid

typedef GridView::IndexSet	IndexSet

typedef int	ConstructorArgument

typedef RangeView< std::vector< size_t >::const_iterator >	GlobalIndexRange

typedef std::pair< size_t, int >	IndexPair

typedef std::vector< IndexPair >::const_iterator	SortedIndexIterator

typedef RangeView< SortedIndexIterator >	SortedIndexRange

typedef Grid::template Codim< 0 >::Entity	Cell

typedef HdivShapeFunctionSetContainer< typenameGrid::ctype, dim, Scalar >::value_type	ShapeFunctionSet

typedef HdivConverter< GridView >	Converter
	A class mapping local shape function values and derivatives to global shape function values and derivatives. More...

Public Member Functions
	HdivMapper (GridView const &gridView_, int order_)
	Constructs an HdivMapper for a given grid view. More...

virtual	~HdivMapper ()

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

ShapeFunctionSet const &	shapefunctions (size_t) const

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 a const sequence containing the global indices of the shape functions associated to this cell. Global indices start at 0 and are consecutive. More...

GlobalIndexRange	globalIndices (size_t n) const
	Returns a const sequence containing the global indices of the shape functions associated to the cell with index n. Global indices start at 0 and are consecutive. 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...

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

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	dim = Grid::dimension

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

static int const	continuity = -1

Member Typedef Documentation

◆ Cell

template<class ScalarType , class GV >

typedef Grid::template Codim<0>::Entity Kaskade::HdivMapper< ScalarType, GV >::Cell

Definition at line 258 of file nedelecspace.hh.

◆ ConstructorArgument

template<class ScalarType , class GV >

typedef int Kaskade::HdivMapper< ScalarType, GV >::ConstructorArgument

Definition at line 250 of file nedelecspace.hh.

◆ Converter

template<class ScalarType , class GV >

typedef HdivConverter<GridView> Kaskade::HdivMapper< ScalarType, GV >::Converter

A class mapping local shape function values and derivatives to global shape function values and derivatives.

Definition at line 359 of file nedelecspace.hh.

◆ GlobalIndexRange

template<class ScalarType , class GV >

typedef RangeView<std::vector<size_t>::const_iterator> Kaskade::HdivMapper< ScalarType, GV >::GlobalIndexRange

Definition at line 252 of file nedelecspace.hh.

◆ Grid

template<class ScalarType , class GV >

typedef GridView::Grid Kaskade::HdivMapper< ScalarType, GV >::Grid

Definition at line 240 of file nedelecspace.hh.

◆ GridView

template<class ScalarType , class GV >

typedef GV Kaskade::HdivMapper< ScalarType, GV >::GridView

Definition at line 239 of file nedelecspace.hh.

◆ IndexPair

template<class ScalarType , class GV >

typedef std::pair<size_t,int> Kaskade::HdivMapper< ScalarType, GV >::IndexPair

Definition at line 254 of file nedelecspace.hh.

◆ IndexSet

template<class ScalarType , class GV >

typedef GridView::IndexSet Kaskade::HdivMapper< ScalarType, GV >::IndexSet

Definition at line 241 of file nedelecspace.hh.

◆ Scalar

template<class ScalarType , class GV >

typedef ScalarType Kaskade::HdivMapper< ScalarType, GV >::Scalar

Definition at line 237 of file nedelecspace.hh.

◆ ShapeFunctionSet

template<class ScalarType , class GV >

typedef HdivShapeFunctionSetContainer<typenameGrid::ctype,dim,Scalar>::value_type Kaskade::HdivMapper< ScalarType, GV >::ShapeFunctionSet

Definition at line 259 of file nedelecspace.hh.

◆ SortedIndexIterator

template<class ScalarType , class GV >

typedef std::vector<IndexPair>::const_iterator Kaskade::HdivMapper< ScalarType, GV >::SortedIndexIterator

Definition at line 255 of file nedelecspace.hh.

◆ SortedIndexRange

template<class ScalarType , class GV >

typedef RangeView<SortedIndexIterator> Kaskade::HdivMapper< ScalarType, GV >::SortedIndexRange

Definition at line 256 of file nedelecspace.hh.

Constructor & Destructor Documentation

◆ HdivMapper()

template<class ScalarType , class GV >

Kaskade::HdivMapper< ScalarType, GV >::HdivMapper	(	GridView const &	gridView_,
		int	order_
	)

inline

Constructs an HdivMapper for a given grid view.

Parameters

order ansatz function order (at least 1).

Definition at line 265 of file nedelecspace.hh.

◆ ~HdivMapper()

template<class ScalarType , class GV >

virtual Kaskade::HdivMapper< ScalarType, GV >::~HdivMapper ( )

inlinevirtual

Definition at line 273 of file nedelecspace.hh.

Member Function Documentation

◆ combiner()

template<class ScalarType , class GV >

Combiner Kaskade::HdivMapper< ScalarType, GV >::combiner	(	Cell const &	cell,
		size_t	index
	)		const

inline

Returns a combiner for the given cell.

Parameters

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

Definition at line 408 of file nedelecspace.hh.

◆ globalIndices() [1/2]

template<class ScalarType , class GV >

GlobalIndexRange Kaskade::HdivMapper< ScalarType, GV >::globalIndices ( Cell const & cell ) const

inline

Returns a const sequence containing the global indices of the shape functions associated to this cell. Global indices start at 0 and are consecutive.

Definition at line 312 of file nedelecspace.hh.

Referenced by Kaskade::HdivMapper< ScalarType, GV >::globalIndices().

◆ globalIndices() [2/2]

template<class ScalarType , class GV >

GlobalIndexRange Kaskade::HdivMapper< ScalarType, GV >::globalIndices ( size_t n ) const

inline

Returns a const sequence containing the global indices of the shape functions associated to the cell with index n. Global indices start at 0 and are consecutive.

Definition at line 321 of file nedelecspace.hh.

◆ initGlobalIndexRange()

template<class ScalarType , class GV >

GlobalIndexRange Kaskade::HdivMapper< ScalarType, GV >::initGlobalIndexRange ( ) const

inline

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

Definition at line 303 of file nedelecspace.hh.

◆ initSortedIndexRange()

template<class ScalarType , class GV >

static SortedIndexRange Kaskade::HdivMapper< ScalarType, GV >::initSortedIndexRange ( )

inlinestatic

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

Definition at line 329 of file nedelecspace.hh.

◆ maxOrder()

template<class ScalarType , class GV >

int Kaskade::HdivMapper< ScalarType, GV >::maxOrder ( ) const

inline

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

Definition at line 295 of file nedelecspace.hh.

◆ shapefunctions() [1/2]

template<class ScalarType , class GV >

ShapeFunctionSet const & Kaskade::HdivMapper< ScalarType, GV >::shapefunctions	(	Cell const &	cell,
		bool
	)		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 281 of file nedelecspace.hh.

Referenced by Kaskade::HdivMapper< ScalarType, GV >::combiner(), and Kaskade::HdivMapper< ScalarType, GV >::update().

◆ shapefunctions() [2/2]

template<class ScalarType , class GV >

ShapeFunctionSet const & Kaskade::HdivMapper< ScalarType, GV >::shapefunctions ( size_t ) const

inline

Definition at line 287 of file nedelecspace.hh.

◆ size()

template<class ScalarType , class GV >

size_t Kaskade::HdivMapper< ScalarType, GV >::size ( ) const

inline

Returns the number of global degrees of freedom managed.

Definition at line 354 of file nedelecspace.hh.

◆ sortedIndices() [1/2]

template<class ScalarType , class GV >

SortedIndexRange Kaskade::HdivMapper< ScalarType, GV >::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 338 of file nedelecspace.hh.

Referenced by Kaskade::HdivMapper< ScalarType, GV >::sortedIndices().

◆ sortedIndices() [2/2]

template<class ScalarType , class GV >

SortedIndexRange Kaskade::HdivMapper< ScalarType, GV >::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 346 of file nedelecspace.hh.

◆ update()

template<class ScalarType , class GV >

void Kaskade::HdivMapper< ScalarType, GV >::update ( )

inline

(Re)computes the internal data.

This has to be called after grid modifications.

In Hdiv conforming spaces, there are two types of ansatz functions: (i) cell-interior functions (with vanishing normal components on the boundary) and (ii) face functions (with Lagrangian property on normal component at the face/edge/vertex nodes). They are ordered

Definition at line 423 of file nedelecspace.hh.

Referenced by Kaskade::HdivMapper< ScalarType, GV >::HdivMapper().

Member Data Documentation

◆ continuity

template<class ScalarType , class GV >

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

static

Definition at line 251 of file nedelecspace.hh.

◆ dim

template<class ScalarType , class GV >

int const Kaskade::HdivMapper< ScalarType, GV >::dim = Grid::dimension

static

Definition at line 243 of file nedelecspace.hh.

Referenced by Kaskade::HdivMapper< ScalarType, GV >::Combiner::Combiner(), and Kaskade::HdivMapper< ScalarType, GV >::update().

◆ globalSupport

template<class ScalarType , class GV >

bool const Kaskade::HdivMapper< ScalarType, GV >::globalSupport = false

static

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

Definition at line 248 of file nedelecspace.hh.

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

nedelecspace.hh

Detailed Description

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ Cell

◆ ConstructorArgument

◆ Converter

◆ GlobalIndexRange

◆ Grid

◆ GridView

◆ IndexPair

◆ IndexSet

◆ Scalar

◆ ShapeFunctionSet

◆ SortedIndexIterator

◆ SortedIndexRange

Constructor & Destructor Documentation

◆ HdivMapper()

◆ ~HdivMapper()

Member Function Documentation

◆ combiner()

◆ globalIndices() [1/2]

◆ globalIndices() [2/2]

◆ initGlobalIndexRange()

◆ initSortedIndexRange()

◆ maxOrder()

◆ shapefunctions() [1/2]

◆ shapefunctions() [2/2]

◆ size()

◆ sortedIndices() [1/2]

◆ sortedIndices() [2/2]

◆ update()

Member Data Documentation

◆ continuity

◆ dim

◆ globalSupport