Dune Core Modules (2.8.0)
Pre-basis for B-spline basis. More...
#include <dune/functions/functionspacebases/bsplinebasis.hh>
Public Types | |
using | GridView = GV |
The grid view that the FE space is defined on. | |
using | IndexSet = Impl::DefaultNodeIndexSet< BSplinePreBasis > |
Type of created tree node index set. More... | |
using | MultiIndex = MI |
Type used for global numbering of the basis vectors. | |
Public Member Functions | |
BSplinePreBasis (const GridView &gridView, const std::vector< double > &knotVector, unsigned int order, bool makeOpen=true) | |
Construct a B-spline basis for a given grid view and set of knot vectors. More... | |
BSplinePreBasis (const GridView &gridView, const FieldVector< double, dim > &lowerLeft, const FieldVector< double, dim > &upperRight, const std::array< unsigned int, dim > &elements, unsigned int order, bool makeOpen=true) | |
Construct a B-spline basis for a given grid view with uniform knot vectors. More... | |
void | initializeIndices () |
Initialize the global indices. | |
const GridView & | gridView () const |
Obtain the grid view that the basis is defined on. | |
void | update (const GridView &gv) |
Update the stored grid view, to be called if the grid has changed. | |
Node | makeNode () const |
Create tree node. | |
IndexSet | makeIndexSet () const |
Create tree node index set. More... | |
size_type | size (const SizePrefix prefix) const |
Return number of possible values for next position in multi index. | |
size_type | dimension () const |
Get the total dimension of the space spanned by this basis. | |
size_type | maxNodeSize () const |
Get the maximal number of DOFs associated to node for any element. | |
template<typename It > | |
It | indices (const Node &node, It it) const |
Maps from subtree index set [0..size-1] to a globally unique multi index in global basis. | |
unsigned int | size () const |
Total number of B-spline basis functions. | |
unsigned int | size (size_t d) const |
Number of shape functions in one direction. | |
void | evaluateFunction (const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldVector< R, 1 > > &out, const std::array< unsigned, dim > ¤tKnotSpan) const |
Evaluate all B-spline basis functions at a given point. | |
void | evaluateJacobian (const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldMatrix< R, 1, dim > > &out, const std::array< unsigned, dim > ¤tKnotSpan) const |
Evaluate Jacobian of all B-spline basis functions. More... | |
template<size_type k> | |
void | evaluate (const typename std::array< int, k > &directions, const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldVector< R, 1 > > &out, const std::array< unsigned, dim > ¤tKnotSpan) const |
Evaluate Derivatives of all B-spline basis functions. | |
Static Public Member Functions | |
static std::array< unsigned int, dim > | getIJK (typename GridView::IndexSet::IndexType idx, std::array< unsigned int, dim > elements) |
Compute integer element coordinates from the element index. More... | |
static void | evaluateFunction (const typename GV::ctype &in, std::vector< R > &out, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan) |
Evaluate all one-dimensional B-spline functions for a given coordinate direction. More... | |
static void | evaluateFunctionFull (const typename GV::ctype &in, DynamicMatrix< R > &out, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan) |
Evaluate all one-dimensional B-spline functions for a given coordinate direction. More... | |
static void | evaluateAll (const typename GV::ctype &in, std::vector< R > &out, bool evaluateJacobian, std::vector< R > &outJac, bool evaluateHessian, std::vector< R > &outHess, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan) |
Evaluate the second derivatives of all one-dimensional B-spline functions for a given coordinate direction. More... | |
Detailed Description
class Dune::Functions::BSplinePreBasis< GV, MI >
Pre-basis for B-spline basis.
- Template Parameters
-
GV The GridView that the space is defined on MI Type to be used for multi-indices
The BSplinePreBasis can be used to embed a BSplineBasis in a larger basis for the construction of product spaces.
Member Typedef Documentation
◆ IndexSet
using Dune::Functions::BSplinePreBasis< GV, MI >::IndexSet = Impl::DefaultNodeIndexSet<BSplinePreBasis> |
Type of created tree node index set.
Constructor & Destructor Documentation
◆ BSplinePreBasis() [1/2]
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inline |
Construct a B-spline basis for a given grid view and set of knot vectors.
The grid must match the knot vectors, i.e.:
- The grid must be structured and Cartesian, and have cube elements only
- The number of elements in each direction must match the number of knot spans in that direction
- In fact, the element spacing in any direction must match the knot spacing in that direction (disregarding knot multiplicities)
- When ordering the grid elements according to their indices, the resulting order must be lexicographical, with the x-index increasing fastest.
Unfortunately, not all of these conditions can be checked for automatically.
- Parameters
-
knotVector A single knot vector, which will be used for all coordinate directions order B-spline order, will be used for all coordinate directions makeOpen If this is true, then knots are prepended and appended to the knot vector to make the knot vector 'open'. i.e., start and end with 'order+1' identical knots. Basis functions from such knot vectors are interpolatory at the end of the parameter interval.
- Todo:
- maybe test whether the knot vector is already open?
References Dune::Hybrid::accumulate(), Dune::Functions::BSplinePreBasis< GV, MI >::elements_, Dune::Functions::BSplinePreBasis< GV, MI >::knotVectors_, Dune::Functions::BSplinePreBasis< GV, MI >::order_, and Dune::TypeTree::push_back().
◆ BSplinePreBasis() [2/2]
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inline |
Construct a B-spline basis for a given grid view with uniform knot vectors.
The grid must match the knot vectors, i.e.:
- The grid must be structured and Cartesian, and have cube elements only
- Bounding box and number of elements of the grid must match the corresponding arguments given to this constructor.
- The element spacing must be uniform
- When ordering the grid elements according to their indices, the resulting order must be lexicographical, with the x-index increasing fastest.
Unfortunately, not all of these conditions can be checked for automatically.
- Parameters
-
gridView The grid we are defining the basis on lowerLeft Lower left corner of the structured grid upperRight Upper right corner of the structured grid elements Number of elements in each coordinate direction order B-spline order, will be used for all coordinate directions makeOpen If this is true, then knots are prepended and appended to the knot vector to make the knot vector 'open'. i.e., start and end with 'order+1' identical knots. Basis functions from such knot vectors are interpolatory at the end of the parameter interval.
- Todo:
- maybe test whether the knot vector is already open?
References Dune::Hybrid::accumulate(), Dune::Functions::BSplinePreBasis< GV, MI >::elements_, Dune::Functions::BSplinePreBasis< GV, MI >::knotVectors_, Dune::Functions::BSplinePreBasis< GV, MI >::order_, and Dune::TypeTree::push_back().
Member Function Documentation
◆ evaluateAll()
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inlinestatic |
Evaluate the second derivatives of all one-dimensional B-spline functions for a given coordinate direction.
- Parameters
-
in Scalar(!) coordinate where to evaluate the functions enableEvaluations switches calculation of desired derivatives on [out] out Vector containing the values of all B-spline derivatives at 'in' [out] outJac Vector containing the first derivatives of all B-spline derivatives at 'in' (only if calculation was switched on by enableEvaluations) [out] outHess Vector containing the second derivatives of all B-spline derivatives at 'in' (only if calculation was switched on by enableEvaluations)
References Dune::Functions::BSplinePreBasis< GV, MI >::evaluateFunctionFull(), Dune::Functions::BSplinePreBasis< GV, MI >::evaluateJacobian(), Dune::Simd::Overloads::max(), and Dune::DynamicMatrix< K >::resize().
Referenced by Dune::Functions::BSplinePreBasis< GV, MI >::evaluate().
◆ evaluateFunction()
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inlinestatic |
Evaluate all one-dimensional B-spline functions for a given coordinate direction.
This implementations was based on the explanations in the book of Cottrell, Hughes, Bazilevs, "Isogeometric Analysis"
- Parameters
-
in Scalar(!) coordinate where to evaluate the functions [out] out Vector containing the values of all B-spline functions at 'in'
- Todo:
- We only hand out function values for those basis functions whose support overlaps the current knot span. However, in the preceding loop we still computed all values_. This won't scale.
References Dune::Simd::Overloads::max().
◆ evaluateFunctionFull()
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inlinestatic |
Evaluate all one-dimensional B-spline functions for a given coordinate direction.
This implementations was based on the explanations in the book of Cottrell, Hughes, Bazilevs, "Isogeometric Analysis"
- Todo:
- This method is a hack! I computes the derivatives of ALL B-splines, even the ones that are zero on the current knot span. I need it as an intermediate step to get the derivatives working. It will/must be removed as soon as possible.
- Parameters
-
in Scalar(!) coordinate where to evaluate the functions [out] out Vector containing the values of all B-spline functions at 'in'
References Dune::DynamicMatrix< K >::resize().
Referenced by Dune::Functions::BSplinePreBasis< GV, MI >::evaluateAll(), and Dune::Functions::BSplinePreBasis< GV, MI >::evaluateJacobian().
◆ evaluateJacobian()
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inline |
Evaluate Jacobian of all B-spline basis functions.
In theory this is easy: just look up the formula in a B-spline text of your choice. The challenge is compute only the values needed for the current knot span.
References Dune::Functions::BSplinePreBasis< GV, MI >::evaluateFunctionFull(), Dune::Functions::BSplinePreBasis< GV, MI >::knotVectors_, Dune::Simd::Overloads::max(), Dune::Functions::BSplinePreBasis< GV, MI >::order_, and Dune::Functions::BSplinePreBasis< GV, MI >::size().
Referenced by Dune::Functions::BSplinePreBasis< GV, MI >::evaluateAll().
◆ getIJK()
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inlinestatic |
Compute integer element coordinates from the element index.
- Warning
- This method makes strong assumptions about the grid, namely that it is structured, and that indices are given in a x-fastest fashion.
Referenced by Dune::Functions::BSplinePreBasis< GV, MI >::indices().
◆ makeIndexSet()
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inline |
Create tree node index set.
Create an index set suitable for the tree node obtained by makeNode().
The documentation for this class was generated from the following file:
- dune/functions/functionspacebases/bsplinebasis.hh