3#ifndef DUNE_FUNCTIONS_FUNCTIONSPACEBASES_LAGRANGEBASIS_HH
4#define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_LAGRANGEBASIS_HH
7#include <dune/common/exceptions.hh>
9#include <dune/localfunctions/lagrange.hh>
10#include <dune/localfunctions/lagrange/equidistantpoints.hh>
11#include <dune/localfunctions/lagrange/pqkfactory.hh>
32template<
typename GV,
int k,
typename R=
double>
35template<
typename GV,
int k,
class MI,
typename R=
double>
36class LagrangePreBasis;
55template<
typename GV,
int k,
class MI,
typename R>
58 static const int dim = GV::dimension;
59 static const bool useDynamicOrder = (k<0);
73 using IndexSet = Impl::DefaultNodeIndexSet<LagrangePreBasis>;
90 if (!useDynamicOrder &&
order!=std::numeric_limits<unsigned int>::max())
91 DUNE_THROW(RangeError,
"Template argument k has to be -1 when supplying a run-time order!");
93 for (
int i=0; i<=dim; i++)
153 [[deprecated(
"Warning: The IndexSet typedef and the makeIndexSet method are deprecated. "\
154 "As a replacement use the indices() method of the PreBasis directly.")]]
187 DUNE_THROW(Dune::NotImplemented,
"No size method for " << dim <<
"d grids available yet!");
193 assert(prefix.size() == 0 || prefix.size() == 1);
194 return (prefix.size() == 0) ?
size() : 0;
208 return power(
order()+1, (
unsigned int)GV::dimension);
211 template<
typename It>
216 Dune::LocalKey localKey = node.
finiteElement().localCoefficients().localKey(i);
217 const auto& gridIndexSet =
gridView().indexSet();
218 const auto& element = node.
element();
221 auto dofDim = dim - localKey.codim();
228 if (k==1 || dofDim==0) {
229 *it = {{ (
size_type)(gridIndexSet.subIndex(element,localKey.subEntity(),dim)) }};
239 + localKey.index() }};
244 const auto refElement
245 = Dune::referenceElement<double,dim>(element.type());
249 auto v0 = (
size_type)gridIndexSet.subIndex(element,refElement.subEntity(localKey.subEntity(),localKey.codim(),0,dim),dim);
250 auto v1 = (
size_type)gridIndexSet.subIndex(element,refElement.subEntity(localKey.subEntity(),localKey.codim(),1,dim),dim);
251 bool flip = (v0 > v1);
254 +
dofsPerCube(1)*((
size_type)gridIndexSet.subIndex(element,localKey.subEntity(),localKey.codim()))
257 +
dofsPerCube(1)*((
size_type)gridIndexSet.subIndex(element,localKey.subEntity(),localKey.codim()))
258 + localKey.index() }};
267 if (element.type().isTriangle())
272 else if (element.type().isQuadrilateral())
278 DUNE_THROW(Dune::NotImplemented,
"2d elements have to be triangles or quadrilaterals");
281 const auto refElement
282 = Dune::referenceElement<double,dim>(element.type());
285 DUNE_THROW(Dune::NotImplemented,
"LagrangeNodalBasis for 3D grids is only implemented if k<=3");
287 if (
order()==3 and !refElement.type(localKey.subEntity(), localKey.codim()).isTriangle())
288 DUNE_THROW(Dune::NotImplemented,
"LagrangeNodalBasis for 3D grids with k==3 is only implemented if the grid is a simplex grid");
299 if (element.type().isTetrahedron())
304 else if (element.type().isHexahedron())
309 else if (element.type().isPrism())
314 else if (element.type().isPyramid())
320 DUNE_THROW(Dune::NotImplemented,
"3d elements have to be tetrahedra, hexahedra, prisms, or pyramids");
322 DUNE_THROW(Dune::NotImplemented,
"Grids of dimension larger than 3 are no supported");
324 DUNE_THROW(Dune::NotImplemented,
"Grid contains elements not supported for the LagrangeNodalBasis");
334 return (useDynamicOrder) ?
order_ : k;
365 return order() == 0 ? (dim == simplexDim ? 1 : 0) : Dune::binomial(std::size_t(
order()-1),simplexDim);
371 return order() == 0 ? (dim == cubeDim ? 1 : 0) : Dune::power(
order()-1, cubeDim);
403template<
typename GV,
int k,
typename R>
408 template<
typename Domain,
typename Range,
int dim>
409 class LagrangeRunTimeLFECache
412 using FiniteElementType = LagrangeLocalFiniteElement<EquidistantPointSet,dim,Domain,Range>;
414 const FiniteElementType& get(GeometryType type)
416 auto i = data_.find(type);
418 i = data_.emplace(type,FiniteElementType(type,order_)).first;
422 std::map<GeometryType, FiniteElementType> data_;
426 static constexpr int dim = GV::dimension;
427 static constexpr bool useDynamicOrder = (k<0);
429 using FiniteElementCache =
typename std::conditional<(useDynamicOrder),
430 LagrangeRunTimeLFECache<typename GV::ctype, R, dim>,
431 PQkLocalFiniteElementCache<typename GV::ctype, R, dim, k>
437 using Element =
typename GV::template Codim<0>::Entity;
453 if constexpr (useDynamicOrder)
484 return (useDynamicOrder) ?
order_ : k;
497namespace BasisFactory {
501template<
int k,
typename R=
double>
502class LagrangePreBasisFactory
504 static const bool useDynamicOrder = (k<0);
506 static const std::size_t requiredMultiIndexSize = 1;
509 LagrangePreBasisFactory() : order_(0)
513 LagrangePreBasisFactory(
unsigned int order)
517 template<
class MultiIndex,
class Gr
idView>
518 auto makePreBasis(
const GridView& gridView)
const
520 return (useDynamicOrder)
541template<std::
size_t k,
typename R=
double>
544 return Imp::LagrangePreBasisFactory<k,R>();
554template<
typename R=
double>
557 return Imp::LagrangePreBasisFactory<-1,R>(order);
587template<
typename GV,
int k=-1,
typename R=
double>
auto lagrange()
Create a pre-basis factory that can create a Lagrange pre-basis.
Definition: lagrangebasis.hh:542
Definition: polynomial.hh:10
Global basis for given pre-basis.
Definition: defaultglobalbasis.hh:47
Definition: lagrangebasis.hh:406
LagrangeNode(unsigned int order)
Constructor with a run-time order.
Definition: lagrangebasis.hh:447
unsigned int order() const
Definition: lagrangebasis.hh:482
const FiniteElement & finiteElement() const
Return the LocalFiniteElement for the element we are bound to.
Definition: lagrangebasis.hh:467
const Element * element_
Definition: lagrangebasis.hh:492
const Element & element() const
Return current element, throw if unbound.
Definition: lagrangebasis.hh:458
FiniteElementCache cache_
Definition: lagrangebasis.hh:490
typename FiniteElementCache::FiniteElementType FiniteElement
Definition: lagrangebasis.hh:438
void bind(const Element &e)
Bind to element.
Definition: lagrangebasis.hh:473
typename GV::template Codim< 0 >::Entity Element
Definition: lagrangebasis.hh:437
const FiniteElement * finiteElement_
Definition: lagrangebasis.hh:491
unsigned int order_
Definition: lagrangebasis.hh:488
std::size_t size_type
Definition: lagrangebasis.hh:436
LagrangeNode()
Constructor without order (uses the compile-time value)
Definition: lagrangebasis.hh:441
A pre-basis for a PQ-lagrange bases with given order.
Definition: lagrangebasis.hh:57
Node makeNode() const
Create tree node.
Definition: lagrangebasis.hh:141
size_type dimension() const
Get the total dimension of the space spanned by this basis.
Definition: lagrangebasis.hh:198
const unsigned int order_
Definition: lagrangebasis.hh:338
size_type vertexOffset_
Definition: lagrangebasis.hh:390
size_type hexahedronOffset_
Definition: lagrangebasis.hh:397
size_type dofsPerCube(std::size_t cubeDim) const
Number of degrees of freedom assigned to a cube (without the ones assigned to its faces!...
Definition: lagrangebasis.hh:347
Impl::DefaultNodeIndexSet< LagrangePreBasis > IndexSet
Type of created tree node index set.
Definition: lagrangebasis.hh:73
size_type quadrilateralOffset_
Definition: lagrangebasis.hh:393
size_type size() const
Same as size(prefix) with empty prefix.
Definition: lagrangebasis.hh:161
LagrangePreBasis(const GridView &gv, unsigned int order)
Constructor for a given grid view object and run-time order.
Definition: lagrangebasis.hh:87
size_type triangleOffset_
Definition: lagrangebasis.hh:392
It indices(const Node &node, It it) const
Definition: lagrangebasis.hh:212
LagrangePreBasis(const GridView &gv)
Constructor for a given grid view object with compile-time order.
Definition: lagrangebasis.hh:82
size_type dofsPerPrism_
Definition: lagrangebasis.hh:387
GV GridView
The grid view that the FE basis is defined on.
Definition: lagrangebasis.hh:64
std::size_t size_type
Type used for indices and size information.
Definition: lagrangebasis.hh:67
size_type dofsPerPrism() const
Definition: lagrangebasis.hh:352
IndexSet makeIndexSet() const
Create tree node index set.
Definition: lagrangebasis.hh:155
GridView gridView_
Definition: lagrangebasis.hh:330
void update(const GridView &gv)
Update the stored grid view, to be called if the grid has changed.
Definition: lagrangebasis.hh:133
size_type pyramidOffset_
Definition: lagrangebasis.hh:395
size_type dofsPerPyramid_
Definition: lagrangebasis.hh:388
MI MultiIndex
Type used for global numbering of the basis vectors.
Definition: lagrangebasis.hh:76
size_type edgeOffset_
Definition: lagrangebasis.hh:391
void initializeIndices()
Initialize the global indices.
Definition: lagrangebasis.hh:103
size_type dofsPerSimplex(std::size_t simplexDim) const
Number of degrees of freedom assigned to a simplex (without the ones assigned to its faces!...
Definition: lagrangebasis.hh:341
size_type computeDofsPerCube(std::size_t cubeDim) const
Number of degrees of freedom assigned to a cube (without the ones assigned to its faces!...
Definition: lagrangebasis.hh:369
size_type tetrahedronOffset_
Definition: lagrangebasis.hh:394
size_type computeDofsPerPyramid() const
Definition: lagrangebasis.hh:379
const GridView & gridView() const
Obtain the grid view that the basis is defined on.
Definition: lagrangebasis.hh:127
unsigned int order() const
Definition: lagrangebasis.hh:332
size_type dofsPerPyramid() const
Definition: lagrangebasis.hh:357
size_type size(const SizePrefix prefix) const
Return number of possible values for next position in multi index.
Definition: lagrangebasis.hh:191
size_type maxNodeSize() const
Get the maximal number of DOFs associated to node for any element.
Definition: lagrangebasis.hh:204
size_type prismOffset_
Definition: lagrangebasis.hh:396
size_type computeDofsPerPrism() const
Definition: lagrangebasis.hh:374
size_type computeDofsPerSimplex(std::size_t simplexDim) const
Number of degrees of freedom assigned to a simplex (without the ones assigned to its faces!...
Definition: lagrangebasis.hh:363
std::array< size_type, dim+1 > dofsPerSimplex_
Definition: lagrangebasis.hh:385
Dune::ReservedVector< size_type, 1 > SizePrefix
Type used for prefixes handed to the size() method.
Definition: lagrangebasis.hh:79
std::array< size_type, dim+1 > dofsPerCube_
Definition: lagrangebasis.hh:386
void setSize(const size_type size)
Definition: nodes.hh:162