3#ifndef DUNE_DUAL_Q1_LOCALFINITEELEMENT_HH
4#define DUNE_DUAL_Q1_LOCALFINITEELEMENT_HH
8#include <dune/common/fvector.hh>
9#include <dune/common/fmatrix.hh>
11#include <dune/geometry/type.hh>
12#include <dune/geometry/referenceelements.hh>
13#include <dune/geometry/quadraturerules.hh>
38 template<
class D,
class R,
int dim,
bool faceDual=false>
54 setupFaceDualCoefficients();
56 setupDualCoefficients();
100 void setupFaceDualCoefficients();
103 void setupDualCoefficients();
111 template<
class D,
class R,
int dim,
bool faceDual>
112 void DualQ1LocalFiniteElement<D,R,dim,faceDual>::setupDualCoefficients()
115 const int size = 1 <<dim;
116 std::array<Dune::FieldVector<R, size>, size> coeffs;
120 const auto& quad = Dune::QuadratureRules<D,dim>::rule(gt, 2*dim);
123 Dune::FieldMatrix<R, size, size> massMat;
127 std::vector<Dune::FieldVector<R,1> > integral(size);
128 for (
int i=0; i<size; i++)
132 for(
size_t pt=0; pt<quad.size(); pt++) {
134 const Dune::FieldVector<D ,dim>& pos = quad[pt].position();
135 std::vector<Dune::FieldVector<R,1> > q1Values(size);
138 D weight = quad[pt].weight();
140 for (
int k=0; k<size; k++) {
141 integral[k] += q1Values[k]*weight;
143 for (
int l=0; l<=k; l++)
144 massMat[k][l] += weight*(q1Values[k]*q1Values[l]);
149 for (
int i=0; i<size-1; i++)
150 for (
int j=i+1; j<size; j++)
151 massMat[i][j] = massMat[j][i];
155 for (
int i=0; i<size; i++) {
157 Dune::FieldVector<R, size> rhs(0);
158 rhs[i] = integral[i];
161 massMat.solve(coeffs[i] ,rhs);
165 basis.setCoefficients(coeffs);
166 interpolation.setCoefficients(coeffs);
169 template<
class D,
class R,
int dim,
bool faceDual>
170 void DualQ1LocalFiniteElement<D,R,dim,faceDual>::setupFaceDualCoefficients()
173 const int size = 1 <<dim;
174 std::array<Dune::FieldVector<R, size>, size> coeffs;
179 const auto& refElement = Dune::ReferenceElements<D,dim>::general(gt);
182 for (
size_t i=0; i<refElement.size(1);i++) {
184 const auto& quad = Dune::QuadratureRules<D,dim-1>::rule(refElement.type(i,1),2*dim);
189 Dune::FieldMatrix<R, size/2, size/2> massMat;
193 const auto& geometry = refElement.template geometry<1>(i);
196 std::vector<Dune::FieldVector<R,1> > integral(size/2);
197 for (
int k=0; k<size/2; k++)
200 for(
size_t pt=0; pt<quad.size(); pt++) {
202 const auto& pos = quad[pt].position();
203 const auto& elementPos = geometry.global(pos);
205 std::vector<Dune::FieldVector<R,1> > q1Values(size);
208 D weight = quad[pt].weight();
210 for (
int k=0; k<refElement.size(i,1,dim); k++) {
211 int row = refElement.subEntity(i,1,k,dim);
212 integral[k] += q1Values[row]*weight;
214 for (
int l=0; l<refElement.size(i,1,dim); l++) {
215 int col = refElement.subEntity(i,1,l,dim);
216 massMat[k][l] += weight*(q1Values[row]*q1Values[col]);
224 for (
int l=0; l<refElement.size(i,1,dim); l++) {
226 int row = refElement.subEntity(i,1,l,dim);
227 Dune::FieldVector<R, size/2> rhs(0);
228 rhs[l] = integral[l];
230 Dune::FieldVector<R, size/2> x(0);
231 massMat.solve(x ,rhs);
233 for (
int k=0; k<refElement.size(i,1,dim); k++) {
234 int col = refElement.subEntity(i,1,k,dim);
235 coeffs[row][col]=x[k];
240 basis.setCoefficients(coeffs);
241 interpolation.setCoefficients(coeffs);
Definition brezzidouglasmarini1cube2d.hh:14
traits helper struct
Definition localfiniteelementtraits.hh:11
LB LocalBasisType
Definition localfiniteelementtraits.hh:14
LC LocalCoefficientsType
Definition localfiniteelementtraits.hh:18
LI LocalInterpolationType
Definition localfiniteelementtraits.hh:22
The local dual Q1 finite element on cubes.
Definition dualq1.hh:40
DualQ1LocalFiniteElement * clone() const
Definition dualq1.hh:93
LocalFiniteElementTraits< DualQ1LocalBasis< D, R, dim >, DualQ1LocalCoefficients< dim >, DualQ1LocalInterpolation< dim, DualQ1LocalBasis< D, R, dim > > > Traits
Definition dualq1.hh:45
unsigned int size() const
Number of shape functions in this finite element.
Definition dualq1.hh:81
const Traits::LocalInterpolationType & localInterpolation() const
Definition dualq1.hh:75
const Traits::LocalBasisType & localBasis() const
Definition dualq1.hh:61
const Traits::LocalCoefficientsType & localCoefficients() const
Definition dualq1.hh:68
DualQ1LocalFiniteElement()
Definition dualq1.hh:49
GeometryType type() const
Definition dualq1.hh:88
Dual Lagrange shape functions of order 1 on the reference cube.
Definition dualq1localbasis.hh:27
Layout map for dual Q1 elements.
Definition dualq1localcoefficients.hh:23
Definition dualq1localinterpolation.hh:18
Lagrange shape functions of order 1 on the reference cube.
Definition q1localbasis.hh:27
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition q1localbasis.hh:39