Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R > Class Template Reference

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

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

Public Member Functions
const EntitySet &	entitySet () const
	Get associated EntitySet.

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 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 flatVectorView. 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 flatVectorView. 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 flatVectorView. 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
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

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

• dune/functions/gridfunctions/discreteglobalbasisfunction.hh