Base class for piecewise continuous mappers. More...

#include <partitionedspace.hh>

Detailed Description

template<class Implementation, class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>
class Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >

Base class for piecewise continuous mappers.

This class manages degrees of freedom for ansatz spaces that are piecewise continuous as given by a piece tag for each cell. To all entity-tag incidences with the same entity type there are the same number of global degrees of freedom associated. This means that on each cell there is the same number of global dofs, but on faces there can be nf or 2*nf dofs, on edges (in 3D) m*ne dofs with m>=1, and on vertices m*1 dofs with m>=1. On each cell live the same number of shape functions.

We call a degree of freedom associated to an incidence (e,t) of entity e of the grid and tag t

if the support of the ansatz function is contained within the union of the cells (codim 0 entitites) with tag t 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 as well as piecewise continuous polynomial FE spaces.

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	a policy class for specifying the actual shape function sets
Tagger	a policy class for providing tags of cells. Functions are supposed to be continuous on the subdomain given by a specific tag, but can be discontinuous across tag boundaries. The default is a single tag for all cells.ſ
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. The default is empty, i.e. no additional data.

Definition at line 234 of file partitionedspace.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
	Indexing information for localized ansatz functions. More...

typedef RangeView< GlobalIndexIterator >	GlobalIndexRange

typedef RangeView< SortedIndexIterator >	SortedIndexRange

Public Member Functions
	UniformPartitionedMapper (Implementation const &impl, 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 &	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
	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 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 Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

using Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::Cell = Kaskade::Cell<Grid>

Definition at line 238 of file partitionedspace.hh.

◆ Combiner

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::Combiner Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::Combiner

Definition at line 241 of file partitionedspace.hh.

◆ Converter

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::Converter Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::Converter

Definition at line 240 of file partitionedspace.hh.

◆ GlobalIndexRange

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef RangeView<GlobalIndexIterator> Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::GlobalIndexRange

Definition at line 276 of file partitionedspace.hh.

◆ Grid

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::Grid Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::Grid

Definition at line 237 of file partitionedspace.hh.

◆ GridView

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::GridView Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::GridView

Definition at line 243 of file partitionedspace.hh.

◆ IndexPair

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

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

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef GridView::IndexSet Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::IndexSet

Definition at line 244 of file partitionedspace.hh.

◆ Scalar

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::Scalar Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::Scalar

Definition at line 242 of file partitionedspace.hh.

◆ ShapeFunctionSet

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef Implementation::ShapeFunctionSet Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::ShapeFunctionSet

Definition at line 239 of file partitionedspace.hh.

◆ SortedIndexRange

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

typedef RangeView<SortedIndexIterator> Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::SortedIndexRange

Definition at line 277 of file partitionedspace.hh.

Constructor & Destructor Documentation

◆ UniformPartitionedMapper()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::UniformPartitionedMapper	(	Implementation const &	impl,
		Tagger const &	tagger_
	)

inline

Constructor.

Parameters

impl	a policy object defining the actual shape function sets. It is copied to a member variable.
tagger	a policy object providing cell tags. It is copied to a member variable.

Definition at line 290 of file partitionedspace.hh.

Member Function Documentation

◆ combiner()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

Combiner Kaskade::UniformPartitionedMapper< Implementation, Tagger, 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 444 of file partitionedspace.hh.

◆ globalIndices() [1/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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.

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

◆ globalIndices() [2/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

Returns the grid view used.

Definition at line 300 of file partitionedspace.hh.

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

◆ initGlobalIndexRange()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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

Definition at line 318 of file partitionedspace.hh.

◆ initSortedIndexRange()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inlinestatic

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

Definition at line 357 of file partitionedspace.hh.

◆ lowerShapeFunctions()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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

Definition at line 308 of file partitionedspace.hh.

◆ shapefunctions() [1/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

ShapeFunctionSet const & Kaskade::UniformPartitionedMapper< Implementation, Tagger, 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 399 of file partitionedspace.hh.

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

◆ shapefunctions() [2/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

Returns the set of shape functions defined on this cell.

Definition at line 416 of file partitionedspace.hh.

◆ shapefunctions_non_const() [1/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

Definition at line 408 of file partitionedspace.hh.

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

◆ shapefunctions_non_const() [2/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

Definition at line 422 of file partitionedspace.hh.

◆ size()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

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.

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

◆ sortedIndices() [1/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

SortedIndexRange Kaskade::UniformPartitionedMapper< Implementation, Tagger, 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 367 of file partitionedspace.hh.

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

◆ sortedIndices() [2/2]

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

SortedIndexRange Kaskade::UniformPartitionedMapper< Implementation, Tagger, 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 376 of file partitionedspace.hh.

◆ unrestrictedToRestrictedIndex()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

inline

Definition at line 453 of file partitionedspace.hh.

◆ update()

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

void Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::update ( )

inline

(Re)computes the internal data.

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

Definition at line 463 of file partitionedspace.hh.

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

Member Data Documentation

◆ globalSupport

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

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

static

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

Definition at line 282 of file partitionedspace.hh.

◆ implementation

template<class Implementation , class Tagger = PartitionedSpaceDetail::SingleTagger, class SFData = PartitionedSpaceDetail::Empty>

Implementation Kaskade::UniformPartitionedMapper< Implementation, Tagger, SFData >::implementation

protected

Definition at line 654 of file partitionedspace.hh.

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

partitionedspace.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

◆ UniformPartitionedMapper()

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