Implementations of the GlobalBasis concept. More...

Collaboration diagram for Function space basis implementations:

Classes
class	Dune::Functions::BSplineLocalBasis< GV, R >
	LocalBasis class in the sense of dune-localfunctions, presenting the restriction of a B-spline patch to a knot span. More...

class	Dune::Functions::BSplineLocalCoefficients< dim >
	Attaches a shape function to an entity. More...

class	Dune::Functions::BSplineLocalInterpolation< dim, LB >
	Local interpolation in the sense of dune-localfunctions, for the B-spline basis on tensor-product grids. More...

class	Dune::Functions::BSplineLocalFiniteElement< GV, R >
	LocalFiniteElement in the sense of dune-localfunctions, for the B-spline basis on tensor-product grids. More...

class	Dune::Functions::BSplineNodeFactory< GV, MI >
	Node factory for B-spline basis. More...

class	Dune::Functions::CompositeNodeFactory< MI, IMS, SF >
	A factory for composite bases. More...

class	Dune::Functions::PQ1NodeFactory< GV, MI >
	Factory for a first order PQ-lagrange basis. More...

class	Dune::Functions::PQkNodeFactory< GV, k, MI >
	A factory for PQ-lagrange bases with given order. More...

class	Dune::Functions::TaylorHoodNodeFactory< GV, MI, HI >
	Factory for lowest order Taylor-Hood basis. More...

Typedefs
template<typename GV >
using	Dune::Functions::BSplineBasis = DefaultGlobalBasis< BSplineNodeFactory< GV, FlatMultiIndex< std::size_t >> >
	A global B-spline basis. More...

template<typename GV , int k>
using	Dune::Functions::LagrangeBasis = DefaultGlobalBasis< PQkNodeFactory< GV, k, FlatMultiIndex< std::size_t >> >
	Nodal basis of a scalar k-th-order Lagrangean finite element space. More...

template<typename GV , int k>
using	Dune::Functions::LagrangeDGBasis = DefaultGlobalBasis< LagrangeDGNodeFactory< GV, k, FlatMultiIndex< std::size_t >> >
	Basis of a scalar k-th-order Lagrangean-DG finite element space. More...

template<typename GV >
using	Dune::Functions::PQ1NodalBasis = DefaultGlobalBasis< PQ1NodeFactory< GV, FlatMultiIndex< std::size_t >> >
	Nodal basis of a scalar first-order Lagrangian finite element space. More...

template<typename GV , int k>
using	Dune::Functions::PQkNodalBasis = DefaultGlobalBasis< PQkNodeFactory< GV, k, FlatMultiIndex< std::size_t >> >
	Nodal basis of a scalar k-th-order Lagrangean finite element space. More...

template<typename GV >
using	Dune::Functions::TaylorHoodBasis = DefaultGlobalBasis< TaylorHoodNodeFactory< GV, std::array< std::size_t, 2 >> >
	Nodal basis for a lowest order Taylor-Hood Lagrangean finite element space. More...

Functions
template<typename... Args, std::enable_if_t< Concept::isIndexMergingStrategy< typename LastType< Args... >::type >(), int > = 0>
auto	Dune::Functions::BasisBuilder::composite (Args &&... args)
	Create a factory builder that can build a CompositeNodeFactory. More...

template<std::size_t k, class SubFactoryTag , class IndexMergingStrategy >
Imp::PowerNodeFactoryBuilder< k, IndexMergingStrategy, SubFactoryTag >	Dune::Functions::BasisBuilder::power (SubFactoryTag &&tag, const IndexMergingStrategy &ims)
	Create a factory builder that can build a PowerNodeFactory. More...

template<std::size_t k, class SubFactoryTag >
Imp::PowerNodeFactoryBuilder< k, LeafBlockedInterleaved, SubFactoryTag >	Dune::Functions::BasisBuilder::power (SubFactoryTag &&tag)
	Create a factory builder that can build a PowerNodeFactory. More...

template<std::size_t k>
Imp::PQkNodeFactoryBuilder< k >	Dune::Functions::BasisBuilder::pq ()
	Create a factory builder that can build a PQkNodeFactory. More...

Detailed Description

Implementations of the GlobalBasis concept.

Typedef Documentation

§ BSplineBasis

template<typename GV >

using Dune::Functions::BSplineBasis = typedef DefaultGlobalBasis<BSplineNodeFactory<GV, FlatMultiIndex<std::size_t>> >

A global B-spline basis.

Template Parameters

GV	The GridView that the space is defined on

§ LagrangeBasis

template<typename GV , int k>

using Dune::Functions::LagrangeBasis = typedef DefaultGlobalBasis<PQkNodeFactory<GV, k, FlatMultiIndex<std::size_t>> >

Nodal basis of a scalar k-th-order Lagrangean finite element space.

Note

This only works for certain grids. The following restrictions hold

If k is no larger than 2, then the grids can have any dimension
If k is larger than 3 then the grid must be two-dimensional
If k is 3, then the grid can be 3d if it is a simplex grid

All arguments passed to the constructor will be forwarded to the constructor of PQkNodeFactory.

Template Parameters

GV	The GridView that the space is defined on
k	The order of the basis

§ LagrangeDGBasis

template<typename GV , int k>

using Dune::Functions::LagrangeDGBasis = typedef DefaultGlobalBasis<LagrangeDGNodeFactory<GV, k, FlatMultiIndex<std::size_t>> >

Basis of a scalar k-th-order Lagrangean-DG finite element space.

Template Parameters

GV	The GridView that the space is defined on
k	The order of the basis

§ PQ1NodalBasis

template<typename GV >

using Dune::Functions::PQ1NodalBasis = typedef DefaultGlobalBasis<PQ1NodeFactory<GV, FlatMultiIndex<std::size_t>> >

Nodal basis of a scalar first-order Lagrangian finite element space.

Template Parameters

GV	The GridView that the space is defined on

Note: This mainly serves as an example, since PQkNodalBasis<GV,1> provides the same functionality.

§ PQkNodalBasis

template<typename GV , int k>

using Dune::Functions::PQkNodalBasis = typedef DefaultGlobalBasis<PQkNodeFactory<GV, k, FlatMultiIndex<std::size_t>> >

Nodal basis of a scalar k-th-order Lagrangean finite element space.

Note

This only works for certain grids. The following restrictions hold

If k is no larger than 2, then the grids can have any dimension
If k is larger than 3 then the grid must be two-dimensional
If k is 3, then the grid can be 3d if it is a simplex grid

All arguments passed to the constructor will be forwarded to the constructor of PQkNodeFactory.

Template Parameters

GV	The GridView that the space is defined on
k	The order of the basis

§ TaylorHoodBasis

template<typename GV >

using Dune::Functions::TaylorHoodBasis = typedef DefaultGlobalBasis<TaylorHoodNodeFactory<GV, std::array<std::size_t, 2>> >

Nodal basis for a lowest order Taylor-Hood Lagrangean finite element space.

Template Parameters

GV	The GridView that the space is defined on.

Note: This mainly serves as an example, since you can construct a basis with the same functionality manually using
static const int k = 1;
auto taylorHoodBasis = makeBasis(
gridView,
composite(
power<dim>(
lagrange<k+1>(),
flatInterleaved()),
lagrange<k>()
));

Function Documentation

§ composite()

template<typename... Args, std::enable_if_t< Concept::isIndexMergingStrategy< typename LastType< Args... >::type >(), int > = 0>

auto Dune::Functions::BasisBuilder::composite ( Args &&... args )

Create a factory builder that can build a CompositeNodeFactory.

Template Parameters

Args	Types of child factory builders and IndexMergingStrategy type

Parameters

args	Child factory builder objects and an IndexMergingStrategy

This is the overload used if the last argument is an IndexMergingStrategy.

Template Parameters

Args	Types of child factory builders

Parameters

args	Child factory builder objects

This is the overload used if no IndexMergingStrategy is supplied. In this case the BasisBuilder::BlockedLexicographic strategy is used.

§ power() [1/2]

template<std::size_t k, class SubFactoryTag , class IndexMergingStrategy >

Imp::PowerNodeFactoryBuilder<k, IndexMergingStrategy, SubFactoryTag> Dune::Functions::BasisBuilder::power	(	SubFactoryTag &&	tag,
		const IndexMergingStrategy &	ims
	)

Create a factory builder that can build a PowerNodeFactory.

Template Parameters

SubFactoryTag	Types of child factory builder and IndexMergingStrategy type
IndexMergingStrategy	An IndexMergingStrategy type

Parameters

tag	Child factory builder objects and an IndexMergingStrategy
ims	IndexMergingStrategy to be used

This overload can be used to explicitly supply an IndexMergingStrategy.

§ power() [2/2]

template<std::size_t k, class SubFactoryTag >

Imp::PowerNodeFactoryBuilder<k, LeafBlockedInterleaved, SubFactoryTag> Dune::Functions::BasisBuilder::power ( SubFactoryTag && tag )

Create a factory builder that can build a PowerNodeFactory.

Template Parameters

SubFactoryTag Types of child factory builder and IndexMergingStrategy type

Parameters

tag	Child factory builder objects and an IndexMergingStrategy

This overload will select the BasisBuilder::BlockedLexicographic strategy.

§ pq()

template<std::size_t k>

Imp::PQkNodeFactoryBuilder<k> Dune::Functions::BasisBuilder::pq ( )

Create a factory builder that can build a PQkNodeFactory.

Template Parameters

k	The polynomial order of ansatz functions

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

§ BSplineBasis

§ LagrangeBasis

§ LagrangeDGBasis

§ PQ1NodalBasis

§ PQkNodalBasis

§ TaylorHoodBasis

Function Documentation

§ composite()

§ power() [1/2]

§ power() [2/2]

§ pq()