Degrees of freedom manager for Morley nonconforming elements. More...

#include <morleyspace.hh>

Detailed Description

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

Degrees of freedom manager for Morley nonconforming elements.

The Morley elements are piecewise quadratic, continuous at the mesh vertices, and have continuous edge-normal derivatives at the edge midpoints.

Template Parameters

ScalarType	scalar type
GV	grid view

Definition at line 38 of file morleyspace.hh.

Classes
class	Combiner
	A combiner 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 LagrangeShapeFunctionSetContainer< typenameGrid::ctype, dim, Scalar >::value_type	ShapeFunctionSet

typedef LagrangeSimplexShapeFunctionSet< typename Grid::ctype, dim, ScalarType >	ShapeFunctionSetImplementation

typedef ScalarConverter< Cell, Scalar >	Converter
	The converter type. More...

Public Member Functions
	MorleyMapper (GridView const &gridView_)
	Constructs a MorleyMapper for a given grid view. More...

virtual	~MorleyMapper ()

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

ShapeFunctionSet const &	shapefunctions (Cell const &cell) const

ShapeFunctionSet const &	shapefunctions (size_t) const

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

GlobalIndexRange	globalIndices (Cell const &cell) const

GlobalIndexRange	globalIndices (size_t n) const
	Returns a const 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...

Combiner	combiner (Cell const &cell, size_t index) const

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 int const	dimw = Grid::template Codim<0>::Entity::Geometry::coorddimension

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::MorleyMapper< ScalarType, GV >::Cell

Definition at line 67 of file morleyspace.hh.

◆ ConstructorArgument

template<class ScalarType , class GV >

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

Definition at line 59 of file morleyspace.hh.

◆ Converter

template<class ScalarType , class GV >

typedef ScalarConverter<Cell,Scalar> Kaskade::MorleyMapper< ScalarType, GV >::Converter

The converter type.

Morley basis functions do not change their value due to the mapping from reference to actual element, hence we can use the standard converter for scalar functions here.

Definition at line 172 of file morleyspace.hh.

◆ GlobalIndexRange

template<class ScalarType , class GV >

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

Definition at line 61 of file morleyspace.hh.

◆ Grid

template<class ScalarType , class GV >

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

Definition at line 45 of file morleyspace.hh.

◆ GridView

template<class ScalarType , class GV >

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

Definition at line 44 of file morleyspace.hh.

◆ IndexPair

template<class ScalarType , class GV >

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

Definition at line 63 of file morleyspace.hh.

◆ IndexSet

template<class ScalarType , class GV >

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

Definition at line 46 of file morleyspace.hh.

◆ Scalar

template<class ScalarType , class GV >

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

Definition at line 41 of file morleyspace.hh.

◆ ShapeFunctionSet

template<class ScalarType , class GV >

typedef LagrangeShapeFunctionSetContainer<typenameGrid::ctype,dim,Scalar>::value_type Kaskade::MorleyMapper< ScalarType, GV >::ShapeFunctionSet

Definition at line 68 of file morleyspace.hh.

◆ ShapeFunctionSetImplementation

template<class ScalarType , class GV >

typedef LagrangeSimplexShapeFunctionSet<typename Grid::ctype,dim,ScalarType> Kaskade::MorleyMapper< ScalarType, GV >::ShapeFunctionSetImplementation

Definition at line 70 of file morleyspace.hh.

◆ SortedIndexIterator

template<class ScalarType , class GV >

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

Definition at line 64 of file morleyspace.hh.

◆ SortedIndexRange

template<class ScalarType , class GV >

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

Definition at line 65 of file morleyspace.hh.

Constructor & Destructor Documentation

◆ MorleyMapper()

template<class ScalarType , class GV >

Kaskade::MorleyMapper< ScalarType, GV >::MorleyMapper ( GridView const & gridView_ )

inline

Constructs a MorleyMapper for a given grid view.

Definition at line 75 of file morleyspace.hh.

◆ ~MorleyMapper()

template<class ScalarType , class GV >

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

inlinevirtual

Definition at line 82 of file morleyspace.hh.

Member Function Documentation

◆ combiner()

template<class ScalarType , class GV >

Combiner Kaskade::MorleyMapper< 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 312 of file morleyspace.hh.

◆ globalIndices() [1/2]

template<class ScalarType , class GV >

GlobalIndexRange Kaskade::MorleyMapper< 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 116 of file morleyspace.hh.

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

◆ globalIndices() [2/2]

template<class ScalarType , class GV >

GlobalIndexRange Kaskade::MorleyMapper< ScalarType, GV >::globalIndices ( size_t n ) 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 126 of file morleyspace.hh.

◆ initGlobalIndexRange()

template<class ScalarType , class GV >

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

inline

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

Definition at line 106 of file morleyspace.hh.

◆ initSortedIndexRange()

template<class ScalarType , class GV >

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

inlinestatic

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

Definition at line 134 of file morleyspace.hh.

◆ maxOrder()

template<class ScalarType , class GV >

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

inline

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

Definition at line 87 of file morleyspace.hh.

◆ shapefunctions() [1/2]

template<class ScalarType , class GV >

ShapeFunctionSet const & Kaskade::MorleyMapper< ScalarType, GV >::shapefunctions ( Cell const & cell ) const

inline

Definition at line 92 of file morleyspace.hh.

◆ shapefunctions() [2/2]

template<class ScalarType , class GV >

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

inline

Definition at line 98 of file morleyspace.hh.

◆ size()

template<class ScalarType , class GV >

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

inline

Returns the number of global degrees of freedom managed.

This is just the number of vertices plus the number of edges.

Definition at line 161 of file morleyspace.hh.

◆ sortedIndices() [1/2]

template<class ScalarType , class GV >

SortedIndexRange Kaskade::MorleyMapper< 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 143 of file morleyspace.hh.

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

◆ sortedIndices() [2/2]

template<class ScalarType , class GV >

SortedIndexRange Kaskade::MorleyMapper< 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 151 of file morleyspace.hh.

◆ update()

template<class ScalarType , class GV >

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

inline

(Re)computes the internal data.

This has to be called after grid modifications.

Definition at line 323 of file morleyspace.hh.

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

Member Data Documentation

◆ continuity

template<class ScalarType , class GV >

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

static

Definition at line 60 of file morleyspace.hh.

◆ dim

template<class ScalarType , class GV >

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

static

Definition at line 48 of file morleyspace.hh.

Referenced by Kaskade::MorleyMapper< ScalarType, GV >::shapefunctions(), and Kaskade::MorleyMapper< ScalarType, GV >::size().

◆ dimw

template<class ScalarType , class GV >

int const Kaskade::MorleyMapper< ScalarType, GV >::dimw = Grid::template Codim<0>::Entity::Geometry::coorddimension

static

Definition at line 50 of file morleyspace.hh.

◆ globalSupport

template<class ScalarType , class GV >

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

static

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

Definition at line 56 of file morleyspace.hh.

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

morleyspace.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

◆ ShapeFunctionSetImplementation

◆ SortedIndexIterator

◆ SortedIndexRange

Constructor & Destructor Documentation

◆ MorleyMapper()

◆ ~MorleyMapper()

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

◆ dimw

◆ globalSupport