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

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

Classes
class	LocalFunction

Public Types
using	Basis = B

using	TreePath = TP

using	Vector = V

using	GridView = typename Basis::GridView

using	EntitySet = GridViewEntitySet< GridView, 0 >

using	Tree = typename Basis::LocalView::Tree

using	SubTree = typename TypeTree::ChildForTreePath< Tree, TreePath >

using	NodeToRangeEntry = NTRE

using	Domain = typename EntitySet::GlobalCoordinate

using	Range = R

using	LocalDomain = typename EntitySet::LocalCoordinate

using	Element = typename EntitySet::Element

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

Public Member Functions
	DiscreteGlobalBasisFunction (const Basis &basis, const TreePath &treePath, const V &coefficients, const NodeToRangeEntry &nodeToRangeEntry)

	DiscreteGlobalBasisFunction (std::shared_ptr< const Basis > basis, const TreePath &treePath, std::shared_ptr< const V > coefficients, std::shared_ptr< const NodeToRangeEntry > nodeToRangeEntry)

const Basis &	basis () const

const TreePath &	treePath () const

const V &	dofs () const

const NodeToRangeEntry &	nodeToRangeEntry () const

Range	operator() (const Domain &x) const

const EntitySet &	entitySet () const
	Get associated EntitySet. More...

Friends
Traits::DerivativeInterface	derivative (const DiscreteGlobalBasisFunction &t)

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

Detailed Description

template<typename B, typename TP, typename V, typename NTRE = DefaultNodeToRangeMap<typename std::decay<decltype(std::declval().localView().tree().child(std::declval<TP>()))>::type>, typename R = typename V::value_type>
class Dune::Functions::DiscreteGlobalBasisFunction< B, TP, 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. The part of the spanned space that should be covered by the function is determined by a tree path that specifies the corresponding local ansatz tree.

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 N in the local ansatz subtree is associated to an entry RE of the range-type via the given node-to-range-entry-map.

Now let C be the coefficient block for a single basis function and V the value of this basis function at the evaluation point. Notice that both may be scalar, vector, matrix, or general container valued.

2.Each entry of C is associated with a flat index j via FlatVectorBackend. This is normally a lexicographic index. The total scalar dimension according to those flat indices is dim(C). 3.Each entry of V is associated with a flat index k via FlatVectorBackend. This is normally a lexicographic index. The total scalar dimension according to those flat indices dim(V). 4.Each entry of RE is associated with a flat index k via FlatVectorBackend. This is normally a lexicographic index. The total scalar dimension according to those flat indices dim(RE). 5.Via those flat indices we now interpret C,V, and RE as vectors and compute the diadic product (C x V). The entries of this product are mapped to the flat indices for RE lexicographically. I.e. we set

RE[j*dim(V)+k] = C[j] * V[k]

Hence the range entry RE must have dim(RE) = dim(C)*dim(V).

Template Parameters

B	Type of lobal basis
TP	Type of tree path specifying the requested subtree of ansatz functions
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