Function space basis implementations

Implementations of the GlobalBasis concept. More...

Collaboration diagram for Function space basis implementations:

Classes
class	Dune::Functions::BSplineLocalBasis< GV, R, MI >
	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, MI >
	LocalFiniteElement in the sense of dune-localfunctions, for the B-spline basis on tensor-product grids. More...
class	Dune::Functions::BSplinePreBasis< GV, MI >
	Pre-basis for B-spline basis. More...
class	Dune::Functions::CompositePreBasis< MI, IMS, SPB >
	A pre-basis for composite bases. More...
class	Dune::Functions::LagrangePreBasis< GV, k, MI, R >
	A pre-basis for a PQ-lagrange bases with given order. More...
class	Dune::Functions::RannacherTurekPreBasis< GV, MI >
	Pre-basis for a Rannacher-Turek basis. More...
class	Dune::Functions::TaylorHoodPreBasis< GV, MI, HI >
	Pre-basis for lowest order Taylor-Hood basis. More...

Typedefs
template<typename GV >
using	Dune::Functions::BSplineBasis = DefaultGlobalBasis< BSplinePreBasis< GV, FlatMultiIndex< std::size_t > > >
	A global B-spline basis. More...
template<typename GV , int k = -1, typename R = double>
using	Dune::Functions::LagrangeBasis = DefaultGlobalBasis< LagrangePreBasis< GV, k, FlatMultiIndex< std::size_t >, R > >
	Nodal basis of a scalar k-th-order Lagrangean finite element space. More...
template<typename GV , int k>
using	Dune::Functions::LagrangeDGBasis = DefaultGlobalBasis< LagrangeDGPreBasis< 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::RannacherTurekBasis = DefaultGlobalBasis< RannacherTurekPreBasis< GV, FlatMultiIndex< std::size_t > > >
	Rannacher-Turek basis. More...
template<typename GV >
using	Dune::Functions::TaylorHoodBasis = DefaultGlobalBasis< TaylorHoodPreBasis< GV, Dune::ReservedVector< std::size_t, 2 > > >
	Nodal basis for a lowest order Taylor-Hood Lagrangean finite element space. More...

Functions
template<std::size_t k>
auto	Dune::Functions::BasisFactory::brezziDouglasMarini ()
	Create a pre-basis factory that can create a Brezzi-Douglas-Marini pre-basis. More...
auto	Dune::Functions::BasisFactory::bSpline (const std::vector< double > &knotVector, unsigned int order, bool makeOpen=true)
	Create a pre-basis factory that can create a B-spline pre-basis. More...
template<typename... Args, std::enable_if_t< Concept::isIndexMergingStrategy< typename LastType< Args... >::type >(), int > = 0>
auto	Dune::Functions::BasisFactory::composite (Args &&... args)
	Create a factory builder that can build a CompositePreBasis. More...
template<std::size_t k, typename R = double>
auto	Dune::Functions::BasisFactory::lagrange ()
	Create a pre-basis factory that can create a Lagrange pre-basis. More...
template<typename R = double>
auto	Dune::Functions::BasisFactory::lagrange (int order)
	Create a pre-basis factory that can create a Lagrange pre-basis with a run-time order. More...
template<std::size_t k>
auto	Dune::Functions::BasisFactory::lagrangeDG ()
	Create a pre-basis factory that can create a LagrangeDG pre-basis. More...
template<std::size_t k, class ChildPreBasisFactory , class IndexMergingStrategy >
auto	Dune::Functions::BasisFactory::power (ChildPreBasisFactory &&childPreBasisFactory, const IndexMergingStrategy &ims)
	Create a pre-basis factory that can build a PowerPreBasis. More...
template<std::size_t k, class ChildPreBasisFactory >
auto	Dune::Functions::BasisFactory::power (ChildPreBasisFactory &&childPreBasisFactory)
	Create a factory builder that can build a PowerPreBasis. More...
template<class Dummy = void>
auto	Dune::Functions::BasisFactory::rannacherTurek ()
	Create a pre-basis factory that can create a Rannacher-Turek pre-basis. More...
template<std::size_t k>
auto	Dune::Functions::BasisFactory::raviartThomas ()
	Create a pre-basis factory that can create a Raviart-Thomas pre-basis. More...
auto	Dune::Functions::BasisFactory::taylorHood ()
	Create a pre-basis factory that can create a Taylor-Hood pre-basis. More...

Detailed Description

Implementations of the GlobalBasis concept.

Typedef Documentation

BSplineBasis

template<typename GV >

using Dune::Functions::BSplineBasis = typedef DefaultGlobalBasis<BSplinePreBasis<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 = -1, typename R = double>

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

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 LagrangePreBasis.

Warning

The implementation of the basis with run-time order order uses the LagrangeFiniteElement implementation of dune-localfunctions, which is known to violate strict-aliasing rules (see https://gitlab.dune-project.org/core/dune-localfunctions/issues/14) Keep this in mind if ever you experience difficult-to-explain crashes or wrong results.

Template Parameters

GV	The GridView that the space is defined on
k	The order of the basis; -1 means 'order determined at run-time'
R	The range type of the local basis

LagrangeDGBasis

template<typename GV , int k>

using Dune::Functions::LagrangeDGBasis = typedef DefaultGlobalBasis<LagrangeDGPreBasis<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

RannacherTurekBasis

template<typename GV >

using Dune::Functions::RannacherTurekBasis = typedef DefaultGlobalBasis<RannacherTurekPreBasis<GV, FlatMultiIndex<std::size_t> > >

Rannacher-Turek basis.

These are Crouzeix-Raviart-elements for quadrilateral elements. See Rolf Rannacher and Stefan Turek. Simple nonconforming quadrilateral Stokes element. Numerical Methods for Partial Differential Equations, 8:97–111, 1992.

Template Parameters

GV	The GridView that the space is defined on

TaylorHoodBasis

template<typename GV >

using Dune::Functions::TaylorHoodBasis = typedef DefaultGlobalBasis<TaylorHoodPreBasis<GV, Dune::ReservedVector<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

brezziDouglasMarini()

template<std::size_t k>

auto Dune::Functions::BasisFactory::brezziDouglasMarini

(

)

Create a pre-basis factory that can create a Brezzi-Douglas-Marini pre-basis.

Template Parameters

k	Order of the Brezzi-Douglas-Marini element

bSpline()

auto Dune::Functions::BasisFactory::bSpline	(	const std::vector< double > &	knotVector,
		unsigned int	order,
		bool	makeOpen = true
	)

Create a pre-basis factory that can create a B-spline pre-basis.

composite()

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

auto Dune::Functions::BasisFactory::composite

(

Args &&...

args

)

Create a factory builder that can build a CompositePreBasis.

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 BasisFactory::BlockedLexicographic strategy is used.

lagrange() [1/2]

template<std::size_t k, typename R = double>

auto Dune::Functions::BasisFactory::lagrange

(

)

Create a pre-basis factory that can create a Lagrange pre-basis.

Template Parameters

k	The polynomial order of the ansatz functions; -1 means 'order determined at run-time'
R	The range type of the local basis

lagrange() [2/2]

template<typename R = double>

auto Dune::Functions::BasisFactory::lagrange

(

int

order

)

Create a pre-basis factory that can create a Lagrange pre-basis with a run-time order.

Template Parameters

R	The range type of the local basis

lagrangeDG()

template<std::size_t k>

auto Dune::Functions::BasisFactory::lagrangeDG

(

)

Create a pre-basis factory that can create a LagrangeDG pre-basis.

Template Parameters

k	The polynomial order of the ansatz functions

power() [1/2]

template<std::size_t k, class ChildPreBasisFactory >

auto Dune::Functions::BasisFactory::power

(

ChildPreBasisFactory &&

childPreBasisFactory

)

Create a factory builder that can build a PowerPreBasis.

Template Parameters

ChildPreBasisFactory

Types of child pre-basis factory

Parameters

childPreBasisFactory

Child pre-basis factory

This overload will select the BasisFactory::BlockedInterleaved strategy.

power() [2/2]

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

auto Dune::Functions::BasisFactory::power	(	ChildPreBasisFactory &&	childPreBasisFactory,
		const IndexMergingStrategy &	ims
	)

Create a pre-basis factory that can build a PowerPreBasis.

Template Parameters

ChildPreBasisFactory	Types of child pre-basis factory
IndexMergingStrategy	An IndexMergingStrategy type

Parameters

childPreBasisFactory	Child pre-basis factory
ims	IndexMergingStrategy to be used

This overload can be used to explicitly supply an IndexMergingStrategy.

rannacherTurek()

template<class Dummy = void>

auto Dune::Functions::BasisFactory::rannacherTurek

(

)

Create a pre-basis factory that can create a Rannacher-Turek pre-basis.

raviartThomas()

template<std::size_t k>

auto Dune::Functions::BasisFactory::raviartThomas

(

)

Create a pre-basis factory that can create a Raviart-Thomas pre-basis.

Template Parameters

k	Order of the Raviart-Thomas element

taylorHood()

auto Dune::Functions::BasisFactory::taylorHood

(

)

Create a pre-basis factory that can create a Taylor-Hood pre-basis.