A grid function induced by a global basis and a coefficient vector. More...

#include <dune/functions/gridfunctions/discreteglobalbasisfunction.hh>

Inheritance diagram for Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >:

Classes
class	LocalFunction

Public Types
using	Basis = typename Base::Basis

using	Vector = typename Base::Vector

using	Domain = typename Base::Domain

using	Range = R

using	Traits = Imp::GridFunctionTraits< Range(Domain), typename Base::EntitySet, DefaultDerivativeTraits, 16 >

using	Coefficient = Dune::AutonomousValue< decltype(std::declval< Vector >()[std::declval< typename Basis::MultiIndex >()])>

using	GridView = typename Basis::GridView

using	EntitySet = GridViewEntitySet< GridView, 0 >

using	Tree = typename Basis::LocalView::Tree

using	NodeToRangeEntry = NTRE

using	LocalDomain = typename EntitySet::LocalCoordinate

using	Element = typename EntitySet::Element

Public Member Functions
template<class B_T , class V_T , class NTRE_T >
	DiscreteGlobalBasisFunction (B_T &&basis, V_T &&coefficients, NTRE_T &&nodeToRangeEntry)
	Create a grid-function, by wrapping the arguments in `std::shared_ptr`.

	DiscreteGlobalBasisFunction (std::shared_ptr< const Basis > basis, std::shared_ptr< const V > coefficients, std::shared_ptr< const typename Base::NodeToRangeEntry > nodeToRangeEntry)
	Create a grid-function, by moving the arguments in `std::shared_ptr`.

Range	operator() (const Domain &x) const
	Evaluate at a point given in world coordinates.

const Basis &	basis () const
	Return a const reference to the stored basis.

const Vector &	dofs () const
	Return the coefficients of this discrete function by reference.

const NodeToRangeEntry &	nodeToRangeEntry () const
	Return the stored node-to-range map.

const EntitySet &	entitySet () const
	Get associated set of entities the local-function can be bound to.

Protected Attributes
std::shared_ptr< const Data >	data_

Friends
DiscreteGlobalBasisFunctionDerivative< DiscreteGlobalBasisFunction >	derivative (const DiscreteGlobalBasisFunction &f)
	Derivative of the `DiscreteGlobalBasisFunction`

LocalFunction	localFunction (const DiscreteGlobalBasisFunction &t)
	Construct local function from a DiscreteGlobalBasisFunction.

Related Symbols
(Note that these are not member symbols.)
template<typename R , typename B , typename V >
auto	makeDiscreteGlobalBasisFunction (B &&basis, V &&vector)
	Generate a DiscreteGlobalBasisFunction.

Detailed Description

template<typename B, typename V, typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>
class Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >

A grid function induced by a global basis and a coefficient vector.

This implements the grid function interface by combining a given global basis and a coefficient vector.

This class supports mapping of subtrees to multi-component ranges, vector-valued shape functions, and implicit product spaces given by vector-valued coefficients. The mapping of these to the range type is done via the following multistage procedure:

1.Each leaf node in the local ansatz subtree is associated to an entry RE of the range-type via the given node-to-range-entry-map. Based on this mapping each node is processed independently in the following way:

2.Now let the coefficients type C per basis function be dim_C-dimensional. Then we compute the dim(C) linear combinations (one for each coefficient index) of the shape function values with type V independently storing them in a std::array<V,dim_C>.

3.Finally the resulting array of function values is assigned to the nodal range entry RE. Since both types may be different their entries are mapped to one another via flatVectorView(). This will recursive enumerate the entries of the types in lexicographic order (unless flatVectorView is specialized differently for a certain type).

As a consequence the nodal range entry is required to have a total dimension dim_RE = dim_C * dim_V and to be compatible with flatVectorView().

Template Parameters

B	Type of global basis
V	Type of coefficient vectors
NTRE	Type of node-to-range-entry-map that associates each leaf node in the local ansatz subtree with an entry in the range type
R	Range type of this function

Requirements:

Type R is default constructible
default constructed R has correct "shape" to hold the components of the range and to be accessible using the node-to-range-entry map NTRE.
This requirements applies recursively to the derivative ranges.

Member Typedef Documentation

◆ Basis

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

using Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::Basis = typename Base::Basis

◆ Coefficient

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::Coefficient = Dune::AutonomousValue<decltype(std::declval<Vector>()[std::declval<typename Basis::MultiIndex>()])>

inherited

◆ Domain

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

using Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::Domain = typename Base::Domain

◆ Element

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::Element = typename EntitySet::Element

inherited

◆ EntitySet

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::EntitySet = GridViewEntitySet<GridView, 0>

inherited

◆ GridView

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::GridView = typename Basis::GridView

inherited

◆ LocalDomain

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::LocalDomain = typename EntitySet::LocalCoordinate

inherited

◆ NodeToRangeEntry

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::NodeToRangeEntry = NTRE

inherited

◆ Range

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

using Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::Range = R

◆ Traits

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

using Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::Traits = Imp::GridFunctionTraits<Range(Domain), typename Base::EntitySet, DefaultDerivativeTraits, 16>

◆ Tree

template<typename B , typename V , typename NTRE >

using Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::Tree = typename Basis::LocalView::Tree

inherited

◆ Vector

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

using Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::Vector = typename Base::Vector

Constructor & Destructor Documentation

◆ DiscreteGlobalBasisFunction() [1/2]

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

template<class B_T , class V_T , class NTRE_T >

Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::DiscreteGlobalBasisFunction	(	B_T &&	basis,
		V_T &&	coefficients,
		NTRE_T &&	nodeToRangeEntry
	)

inline

Create a grid-function, by wrapping the arguments in std::shared_ptr.

◆ DiscreteGlobalBasisFunction() [2/2]

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::DiscreteGlobalBasisFunction	(	std::shared_ptr< const Basis >	basis,
		std::shared_ptr< const V >	coefficients,
		std::shared_ptr< const typename Base::NodeToRangeEntry >	nodeToRangeEntry
	)

inline

Create a grid-function, by moving the arguments in std::shared_ptr.

Member Function Documentation

◆ basis()

template<typename B , typename V , typename NTRE >

const Basis & Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::basis ( ) const

inlineinherited

Return a const reference to the stored basis.

◆ dofs()

template<typename B , typename V , typename NTRE >

const Vector & Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::dofs ( ) const

inlineinherited

Return the coefficients of this discrete function by reference.

◆ entitySet()

template<typename B , typename V , typename NTRE >

const EntitySet & Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::entitySet ( ) const

inlineinherited

Get associated set of entities the local-function can be bound to.

◆ nodeToRangeEntry()

template<typename B , typename V , typename NTRE >

const NodeToRangeEntry & Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::nodeToRangeEntry ( ) const

inlineinherited

Return the stored node-to-range map.

◆ operator()()

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

Range Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >::operator() ( const Domain & x ) const

inline

Evaluate at a point given in world coordinates.

Warning: This has to find the element that the evaluation point is in. It is therefore very slow.

Friends And Related Symbol Documentation

◆ derivative

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

DiscreteGlobalBasisFunctionDerivative< DiscreteGlobalBasisFunction > derivative ( const DiscreteGlobalBasisFunction< B, V, NTRE, R > & f )

friend

Derivative of the DiscreteGlobalBasisFunction

◆ localFunction

template<typename B , typename V , typename NTRE = HierarchicNodeToRangeMap, typename R = typename V::value_type>

LocalFunction localFunction ( const DiscreteGlobalBasisFunction< B, V, NTRE, R > & t )

friend

Construct local function from a DiscreteGlobalBasisFunction.

The obtained local function satisfies the concept Dune::Functions::Concept::LocalFunction. It must be bound to an entity from the entity set of the DiscreteGlobalBasisFunction before it can be used.

Member Data Documentation

◆ data_

template<typename B , typename V , typename NTRE >

std::shared_ptr<const Data> Dune::Functions::ImplDoc::DiscreteGlobalBasisFunctionBase< B, V, NTRE >::data_

protectedinherited

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

discreteglobalbasisfunction.hh

Classes

Public Types

Public Member Functions

Protected Attributes

Friends

Related Symbols

Detailed Description

Member Typedef Documentation

◆ Basis

◆ Coefficient

◆ Domain

◆ Element

◆ EntitySet

◆ GridView

◆ LocalDomain

◆ NodeToRangeEntry

◆ Range

◆ Traits

◆ Tree

◆ Vector

Constructor & Destructor Documentation

◆ DiscreteGlobalBasisFunction() [1/2]

◆ DiscreteGlobalBasisFunction() [2/2]

Member Function Documentation

◆ basis()

◆ dofs()

◆ entitySet()

◆ nodeToRangeEntry()

◆ operator()()

Friends And Related Symbol Documentation

◆ derivative

◆ localFunction

Member Data Documentation

◆ data_