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Commit 301640ea authored by Praetorius, Simon's avatar Praetorius, Simon
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some examples modified to make it running

parent 5c70d545
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Showing with 611 additions and 274 deletions
dune/amdis/Assembler.hpp
View file @ 301640ea
......@@ -6,6 +6,7 @@
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
#include <dune/amdis/DirichletBC.hpp>
#include <dune/amdis/LinearAlgebra.hpp>
#include <dune/amdis/Operator.hpp>
#include <dune/amdis/common/Mpl.hpp>
......@@ -23,10 +24,12 @@ namespace AMDiS
/// Constructor, stores a shared-pointer to the feSpaces
Assembler(GlobalBasis& globalBasis,
MatrixOperators<GlobalBasis>& matrixOperators,
VectorOperators<GlobalBasis>& rhsOperators)
VectorOperators<GlobalBasis>& rhsOperators,
Constraints<GlobalBasis>& constraints)
: globalBasis_(globalBasis)
, matrixOperators_(matrixOperators)
, rhsOperators_(rhsOperators)
, constraints_(constraints)
{}
void update(GridView const& gv)
......@@ -88,6 +91,7 @@ namespace AMDiS
GlobalBasis& globalBasis_;
MatrixOperators<GlobalBasis>& matrixOperators_;
VectorOperators<GlobalBasis>& rhsOperators_;
Constraints<GlobalBasis>& constraints_;
};
} // end namespace AMDiS
......
dune/amdis/Assembler.inc.hpp
View file @ 301640ea
#pragma once
#include <dune/functions/functionspacebases/subspacebasis.hh>
#include <dune/typetree/treepath.hh>
#include <dune/amdis/utility/TreePath.hpp>
#include <dune/amdis/utility/Visitor.hpp>
namespace AMDiS {
......@@ -64,15 +64,19 @@ void Assembler<GlobalBasis>::assemble(
for (std::size_t i = 0; i < localView.size(); ++i) {
auto const row = localIndexSet.index(i);
for (std::size_t j = 0; j < localView.size(); ++j) {
auto const col = localIndexSet.index(j);
matrix(row,col) += elementMatrix(i,j);
if (elementMatrix(i,j) != 0.0) {
auto const col = localIndexSet.index(j);
matrix(row,col) += elementMatrix(i,j);
}
}
}
// add element-vector to system-vector
for (std::size_t i = 0; i < localView.size(); ++i) {
auto const idx = localIndexSet.index(i);
rhs[idx] += elementVector[i];
if (elementVector[i] != 0.0) {
auto const idx = localIndexSet.index(i);
rhs[idx] += elementVector[i];
}
}
localIndexSet.unbind();
......@@ -86,43 +90,6 @@ void Assembler<GlobalBasis>::assemble(
}
template <class GlobalBasis>
template <class SystemMatrixType, class SystemVectorType>
void Assembler<GlobalBasis>::initMatrixVector(
SystemMatrixType& matrix,
SystemVectorType& solution,
SystemVectorType& rhs,
bool asmMatrix, bool asmVector) const
{
matrix.init(asmMatrix);
solution.compress();
rhs.compress();
auto localView = globalBasis_.localView();
forEachNode(localView.tree(), [&,this](auto const& rowNode, auto rowTreePath)
{
if (rowNode.isLeaf)
msg(0, " DOFs for Basis[", 1, "]"); // TODO: add right values
auto rowBasis = Dune::Functions::subspaceBasis(globalBasis_, rowTreePath);
if (rhsOperators_[rowNode].assemble(asmVector))
rhsOperators_[rowNode].init(rowBasis);
forEachNode(localView.tree(), [&,this](auto const& colNode, auto colTreePath)
{
auto colBasis = Dune::Functions::subspaceBasis(globalBasis_, colTreePath);
if (matrixOperators_[rowNode][colNode].assemble(asmMatrix))
matrixOperators_[rowNode][colNode].init(rowBasis, colBasis);
// init boundary condition
// for (int c = 0; c < nComponents; ++c)
// for (auto bc : matrixOperators[R][c].dirichlet)
// bc->init(c == C, matrix(_r, _c), solution[_c], rhs[_r]);
});
});
}
template <class GlobalBasis>
template <class ElementContainer, class Container, class Operators, class... LocalViews>
void Assembler<GlobalBasis>::assembleElementOperators(
......@@ -160,6 +127,44 @@ void Assembler<GlobalBasis>::assembleElementOperators(
}
template <class GlobalBasis>
template <class SystemMatrixType, class SystemVectorType>
void Assembler<GlobalBasis>::initMatrixVector(
SystemMatrixType& matrix,
SystemVectorType& solution,
SystemVectorType& rhs,
bool asmMatrix, bool asmVector) const
{
matrix.init(asmMatrix);
solution.compress();
rhs.compress();
auto localView = globalBasis_.localView();
forEachNode(localView.tree(), [&,this](auto const& rowNode, auto rowTreePath)
{
if (rowNode.isLeaf)
msg(0, " DOFs for Basis[", to_string(rowTreePath), "]"); // TODO: add right values
auto rowBasis = Dune::Functions::subspaceBasis(globalBasis_, rowTreePath);
if (rhsOperators_[rowNode].assemble(asmVector))
rhsOperators_[rowNode].init(rowBasis);
forEachNode(localView.tree(), [&,this](auto const& colNode, auto colTreePath)
{
auto colBasis = Dune::Functions::subspaceBasis(globalBasis_, colTreePath);
if (matrixOperators_[rowNode][colNode].assemble(asmMatrix))
matrixOperators_[rowNode][colNode].init(rowBasis, colBasis);
for (auto bc : constraints_[rowNode][colNode].scalar)
bc->init(matrix, solution, rhs, rowBasis, colBasis);
for (auto bc : constraints_[rowNode][colNode].vector)
bc->init(matrix, solution, rhs, rowBasis, colBasis);
});
});
msg(globalBasis_.dimension(), " total DOFs");
}
template <class GlobalBasis>
template <class SystemMatrixType, class SystemVectorType>
std::size_t Assembler<GlobalBasis>::finishMatrixVector(
......@@ -171,27 +176,25 @@ std::size_t Assembler<GlobalBasis>::finishMatrixVector(
matrix.finish();
auto localView = globalBasis_.localView();
forEachNode(localView.tree(), [&,this](auto const& rowNode, auto /*rowTreePath*/)
forEachNode(localView.tree(), [&,this](auto const& rowNode, auto rowTreePath)
{
auto rowBasis = Dune::Functions::subspaceBasis(globalBasis_, rowTreePath);
auto& rhsOp = rhsOperators_[rowNode];
if (rhsOp.assemble(asmVector))
rhsOp.assembled = true;
forEachNode(localView.tree(), [&,this](auto const& colNode, auto /*colTreePath*/)
forEachNode(localView.tree(), [&,this](auto const& colNode, auto colTreePath)
{
auto colBasis = Dune::Functions::subspaceBasis(globalBasis_, colTreePath);
auto& matOp = matrixOperators_[rowNode][colNode];
if (matOp.assemble(asmMatrix))
matOp.assembled = true;
// finish boundary condition
// for (int c = 0; c < nComponents; ++c) {
// for (int r = 0; r < nComponents; ++r) {
// if (r != R && c != C)
// continue;
// for (auto bc : matrixOperators[r][c].dirichlet)
// bc->finish(r == R, c == C, matrix(_r, _c), solution[_c], rhs[_r]);
// }
// }
for (auto bc : constraints_[rowNode][colNode].scalar)
bc->finish(matrix, solution, rhs, rowBasis, colBasis);
for (auto bc : constraints_[rowNode][colNode].vector)
bc->finish(matrix, solution, rhs, rowBasis, colBasis);
});
});
......
dune/amdis/DirichletBC.hpp
View file @ 301640ea
......@@ -4,9 +4,9 @@
#include <type_traits>
#include <vector>
#include <dune/amdis/common/Concepts.hpp>
#include <dune/amdis/Output.hpp>
#include <dune/amdis/common/Concepts.hpp>
#include <dune/amdis/utility/TreeData.hpp>
namespace AMDiS
{
......@@ -25,13 +25,13 @@ namespace AMDiS
* support this symmetric modification. As a result, this method returns a list
* of columns values, that should be subtracted from the rhs.
**/
template <class WorldVector>
template <class Domain, class Range = double>
class DirichletBC
{
public:
template <class Predicate, class Values,
REQUIRES(Concepts::Functor<Predicate, bool(WorldVector)> &&
Concepts::Functor<Values, double(WorldVector)>) >
REQUIRES(Concepts::Functor<Predicate, bool(Domain)> &&
Concepts::Functor<Values, Range(Domain)>) >
DirichletBC(Predicate&& predicate, Values&& values)
: predicate(std::forward<Predicate>(predicate))
, values(std::forward<Values>(values))
......@@ -41,11 +41,15 @@ namespace AMDiS
/// Prepare the matrix, rhs and solution block for assembling dirichlet
/// boundary conditions, e.g. collect the corresponding indices of boundary
/// DOFS for later elimination in \ref finish.
template <class Matrix, class VectorX, class VectorB>
void init(bool apply,
Matrix& matrix,
VectorX& rhs,
VectorB& solution);
template <class Matrix, class VectorX, class VectorB, class RowBasis, class ColBasis>
void init(Matrix& /*matrix*/, VectorX& /*rhs*/, VectorB& /*solution*/,
RowBasis const& rowBasis,
ColBasis const& /*colBasis*/)
{
using RowNode = typename RowBasis::LocalView::Tree;
initImpl(rowBasis, typename RowNode::NodeTag{});
}
/// \brief Apply dirichlet BC to matrix and vector, i.e., add a unit-row
......@@ -55,21 +59,51 @@ namespace AMDiS
* is assembled. The \p matrix, \p rhs, and \p solution correspond to the
* currently visited blocks of system-matrix and system-vector.
**/
template <class Matrix, class VectorX, class VectorB>
void finish(bool apply_row,
bool apply_col,
Matrix& matrix,
template <class Matrix, class VectorX, class VectorB, class RowBasis, class ColBasis>
void finish(Matrix& matrix,
VectorX& rhs,
VectorB& solution);
VectorB& solution,
RowBasis const& rowBasis,
ColBasis const& colBasis);
protected:
template <class RowBasis>
void initImpl(RowBasis const& rowBasis, Dune::TypeTree::LeafNodeTag);
template <class RowBasis>
void initImpl(RowBasis const& rowBasis, Dune::TypeTree::PowerNodeTag);
template <class RB, class RowNodeTag>
void initImpl(RB const&, RowNodeTag) {}
private:
std::function<bool(WorldVector)> predicate;
std::function<double(WorldVector)> values;
std::function<bool(Domain)> predicate;
std::function<Range(Domain)> values;
bool initialized = false;
std::vector<char> dirichletNodes;
};
template <class GlobalBasis>
struct DirichletData
{
using WorldVector = typename GlobalBasis::GridView::template Codim<0>::Geometry::GlobalCoordinate;
template <class Node>
struct type
{
std::list<std::shared_ptr<DirichletBC<WorldVector, double>>> scalar;
std::list<std::shared_ptr<DirichletBC<WorldVector, WorldVector>>> vector;
void push_back(std::shared_ptr<DirichletBC<WorldVector, double>> const& bc) { scalar.push_back(bc); }
void push_back(std::shared_ptr<DirichletBC<WorldVector, WorldVector>> const& bc) { vector.push_back(bc); }
};
};
template <class GlobalBasis>
using Constraints = MatrixData<GlobalBasis, DirichletData<GlobalBasis>::template type>;
} // end namespace AMDiS
#include "DirichletBC.inc.hpp"
dune/amdis/DirichletBC.inc.hpp
View file @ 301640ea
#pragma once
#include <dune/functions/functionspacebases/interpolate.hh>
#include <dune/functions/functionspacebases/subspacebasis.hh>
#include <dune/amdis/LinearAlgebra.hpp>
#include <dune/amdis/linear_algebra/HierarchicWrapper.hpp>
namespace AMDiS
{
template <class WorldVector>
template <class Matrix, class VectorX, class VectorB>
void DirichletBC<WorldVector>::init(bool /*apply*/,
Matrix& matrix,
VectorX& /*solution*/,
VectorB& /*rhs*/)
template <class WorldVector, class Range>
template <class RowBasis>
void DirichletBC<WorldVector, Range>::initImpl(
RowBasis const& rowBasis, Dune::TypeTree::LeafNodeTag)
{
using Dune::Functions::interpolate;
if (!initialized) {
interpolate(matrix.getRowFeSpace(), dirichletNodes, predicate);
interpolate(rowBasis, hierarchicVectorWrapper(dirichletNodes), predicate);
initialized = true;
}
}
template <class WorldVector, class Range>
template <class RowBasis>
void DirichletBC<WorldVector, Range>::initImpl(
RowBasis const& rowBasis, Dune::TypeTree::PowerNodeTag)
{
using Dune::Functions::interpolate;
template <class WorldVector>
template <class Matrix, class VectorX, class VectorB>
void DirichletBC<WorldVector>::finish(bool apply_row,
bool apply_col,
Matrix& matrix,
VectorX& solution,
VectorB& rhs)
if (!initialized) {
auto tp = rowBasis.prefixPath();
auto const& basis = rowBasis.rootBasis();
for (std::size_t i = 0; i < degree(rowBasis.localView().tree()); ++i)
interpolate(Dune::Functions::subspaceBasis(basis, push_back(tp,i)),
hierarchicVectorWrapper(dirichletNodes), predicate);
initialized = true;
}
}
template <class WorldVector, class Range>
template <class Matrix, class VectorX, class VectorB, class RowBasis, class ColBasis>
void DirichletBC<WorldVector, Range>::finish(
Matrix& matrix, VectorX& solution, VectorB& rhs,
RowBasis const& rowBasis, ColBasis const& colBasis)
// Dune::TypeTree::LeafNodeTag, Dune::TypeTree::LeafNodeTag)
{
using Dune::Functions::interpolate;
test_exit_dbg(initialized, "Boundary condition not initialized!");
auto columns = matrix.applyDirichletBC(dirichletNodes, apply_row, apply_col);
auto columns = matrix.applyDirichletBC(dirichletNodes);
if (apply_col) {
interpolate(matrix.getRowFeSpace(), wrapper(rhs.getVector()), values, dirichletNodes);
if (apply_row)
interpolate(matrix.getColFeSpace(), wrapper(solution.getVector()), values, dirichletNodes);
interpolate(rowBasis, hierarchicVectorWrapper(rhs.getVector()), values, hierarchicVectorWrapper(dirichletNodes));
interpolate(colBasis, hierarchicVectorWrapper(solution.getVector()), values, hierarchicVectorWrapper(dirichletNodes));
// subtract columns of dirichlet nodes from rhs
for (auto const& triplet : columns)
rhs[triplet.row] -= triplet.value * solution[triplet.col];
}
// subtract columns of dirichlet nodes from rhs
for (auto const& triplet : columns)
rhs[triplet.row] -= triplet.value * solution[triplet.col];
}
......
dune/amdis/FirstOrderAssembler.hpp
View file @ 301640ea
......@@ -60,19 +60,17 @@ namespace AMDiS
template <class Operator, class RowView, class ColView>
void calculateElementMatrix(Operator& op,
RowView const& rowView,
ColView const& colView,
RowView const& rowView, ColView const& colView,
ElementMatrix& elementMatrix,
double fac,
Dune::TypeTree::LeafNodeTag,
Dune::TypeTree::LeafNodeTag,
Dune::TypeTree::LeafNodeTag, Dune::TypeTree::LeafNodeTag,
FirstOrderType_t<GRD_PHI>)
{
auto geometry = rowView.element().geometry();
auto const& quad_geometry = Super::getGeometry();
auto const& rowLocalBasis = rowView.tree().finiteElement().localBasis();
auto const& colLocalBasis = colView.tree().finiteElement().localBasis();
auto const& rowLocalFE = rowView.tree().finiteElement();
auto const& colLocalFE = colView.tree().finiteElement();
auto const& quad = Super::getQuadrature().getRule();
for (std::size_t iq = 0; iq < quad.size(); ++iq) {
......@@ -86,11 +84,11 @@ namespace AMDiS
const double factor = quad_geometry.integrationElement(quad[iq].position()) * quad[iq].weight() * fac;
std::vector<Dune::FieldVector<double,1> > rowShapeValues;
rowLocalBasis.evaluateFunction(quadPos, rowShapeValues);
rowLocalFE.localBasis().evaluateFunction(quadPos, rowShapeValues);
// The gradients of the shape functions on the reference element
std::vector<Dune::FieldMatrix<double,1,dim> > colReferenceGradients;
colLocalBasis.evaluateJacobian(quadPos, colReferenceGradients);
colLocalFE.localBasis().evaluateJacobian(quadPos, colReferenceGradients);
// Compute the shape function gradients on the real element
std::vector<Dune::FieldVector<double,dow> > colGradients(colReferenceGradients.size());
......@@ -98,8 +96,8 @@ namespace AMDiS
for (std::size_t i = 0; i < colGradients.size(); ++i)
jacobian.mv(colReferenceGradients[i][0], colGradients[i]);
for (std::size_t i = 0; i < num_rows(elementMatrix); ++i) {
for (std::size_t j = 0; j < num_cols(elementMatrix); ++j) {
for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
const int local_i = rowView.tree().localIndex(i);
const int local_j = colView.tree().localIndex(j);
op.evalFot1(elementMatrix[local_i][local_j], iq, factor, rowShapeValues[i], colGradients[j]);
......@@ -110,19 +108,17 @@ namespace AMDiS
template <class Operator, class RowView, class ColView>
void calculateElementMatrix(Operator& op,
RowView const& rowView,
ColView const& colView,
RowView const& rowView, ColView const& colView,
ElementMatrix& elementMatrix,
double fac,
Dune::TypeTree::LeafNodeTag,
Dune::TypeTree::LeafNodeTag,
Dune::TypeTree::LeafNodeTag, Dune::TypeTree::LeafNodeTag,
FirstOrderType_t<GRD_PSI>)
{
auto geometry = rowView.element().geometry();
auto const& quad_geometry = Super::getGeometry();
auto const& rowLocalBasis = rowView.tree().finiteElement().localBasis();
auto const& colLocalBasis = colView.tree().finiteElement().localBasis();
auto const& rowLocalFE = rowView.tree().finiteElement();
auto const& colLocalFE = colView.tree().finiteElement();
auto const& quad = Super::getQuadrature().getRule();
for (std::size_t iq = 0; iq < quad.size(); ++iq) {
......@@ -137,7 +133,7 @@ namespace AMDiS
// The gradients of the shape functions on the reference element
std::vector<Dune::FieldMatrix<double,1,dim> > rowReferenceGradients;
rowLocalBasis.evaluateJacobian(quadPos, rowReferenceGradients);
rowLocalFE.localBasis().evaluateJacobian(quadPos, rowReferenceGradients);
// Compute the shape function gradients on the real element
std::vector<Dune::FieldVector<double,dow> > rowGradients(rowReferenceGradients.size());
......@@ -146,10 +142,10 @@ namespace AMDiS
jacobian.mv(rowReferenceGradients[i][0], rowGradients[i]);
std::vector<Dune::FieldVector<double,1> > colShapeValues;
colLocalBasis.evaluateFunction(quadPos, colShapeValues);
colLocalFE.localBasis().evaluateFunction(quadPos, colShapeValues);
for (std::size_t i = 0; i < num_rows(elementMatrix); ++i) {
for (std::size_t j = 0; j < num_cols(elementMatrix); ++j) {
for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
const int local_i = rowView.tree().localIndex(i);
const int local_j = colView.tree().localIndex(j);
op.evalFot2(elementMatrix[local_i][local_j], iq, factor, rowGradients[i], colShapeValues[j]);
......@@ -158,6 +154,114 @@ namespace AMDiS
}
}
template <class Operator, class RowView, class ColView>
void calculateElementMatrix(Operator& op,
RowView const& rowView, ColView const& colView,
ElementMatrix& elementMatrix,
double fac,
Dune::TypeTree::LeafNodeTag, Dune::TypeTree::PowerNodeTag,
FirstOrderType_t<GRD_PHI>)
{
auto geometry = rowView.element().geometry();
auto const& quad_geometry = Super::getGeometry();
auto const& rowLocalFE = rowView.tree().finiteElement();
auto const& colLocalFE = colView.tree().child(0).finiteElement();
auto const& quad = Super::getQuadrature().getRule();
test_exit( dow == degree(colView.tree()), "Number of childs of Power-Node must be DOW");
for (std::size_t iq = 0; iq < quad.size(); ++iq) {
// Position of the current quadrature point in the reference element
decltype(auto) quadPos = Super::map(quad[iq].position());
// The transposed inverse Jacobian of the map from the reference element to the element
const auto jacobian = geometry.jacobianInverseTransposed(quadPos);
// The multiplicative factor in the integral transformation formula
const double factor = quad_geometry.integrationElement(quad[iq].position()) * quad[iq].weight() * fac;
std::vector<Dune::FieldVector<double,1> > rowShapeValues;
rowLocalFE.localBasis().evaluateFunction(quadPos, rowShapeValues);
// The gradients of the shape functions on the reference element
std::vector<Dune::FieldMatrix<double,1,dim> > colReferenceGradients;
colLocalFE.localBasis().evaluateJacobian(quadPos, colReferenceGradients);
// Compute the shape function gradients on the real element
std::vector<Dune::FieldVector<double,dow> > colGradients(colReferenceGradients.size());
for (std::size_t i = 0; i < colGradients.size(); ++i)
jacobian.mv(colReferenceGradients[i][0], colGradients[i]);
// <div(u), q>
for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
const int local_i = rowView.tree().localIndex(i);
for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
for (std::size_t k = 0; k < degree(colView.tree()); ++k) {
const int local_j = colView.tree().child(k).localIndex(j);
op.evalZot(elementMatrix[local_i][local_j], iq, factor, rowShapeValues[i], colGradients[j][k]);
}
}
}
}
}
template <class Operator, class RowView, class ColView>
void calculateElementMatrix(Operator& op,
RowView const& rowView, ColView const& colView,
ElementMatrix& elementMatrix,
double fac,
Dune::TypeTree::PowerNodeTag, Dune::TypeTree::LeafNodeTag,
FirstOrderType_t<GRD_PSI>)
{
auto geometry = rowView.element().geometry();
auto const& quad_geometry = Super::getGeometry();
auto const& rowLocalFE = rowView.tree().child(0).finiteElement();
auto const& colLocalFE = colView.tree().finiteElement();
auto const& quad = Super::getQuadrature().getRule();
test_exit( dow == degree(rowView.tree()), "Number of childs of Power-Node must be DOW");
for (std::size_t iq = 0; iq < quad.size(); ++iq) {
// Position of the current quadrature point in the reference element
decltype(auto) quadPos = Super::map(quad[iq].position());
// The transposed inverse Jacobian of the map from the reference element to the element
const auto jacobian = geometry.jacobianInverseTransposed(quadPos);
// The multiplicative factor in the integral transformation formula
const double factor = quad_geometry.integrationElement(quad[iq].position()) * quad[iq].weight() * fac;
// The gradients of the shape functions on the reference element
std::vector<Dune::FieldMatrix<double,1,dim> > rowReferenceGradients;
rowLocalFE.localBasis().evaluateJacobian(quadPos, rowReferenceGradients);
// Compute the shape function gradients on the real element
std::vector<Dune::FieldVector<double,dow> > rowGradients(rowReferenceGradients.size());
for (std::size_t i = 0; i < rowGradients.size(); ++i)
jacobian.mv(rowReferenceGradients[i][0], rowGradients[i]);
std::vector<Dune::FieldVector<double,1> > colShapeValues;
colLocalFE.localBasis().evaluateFunction(quadPos, colShapeValues);
// <p, div(v)>
for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
const int local_j = colView.tree().localIndex(j);
for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
for (std::size_t k = 0; k < degree(rowView.tree()); ++k) {
const int local_i = rowView.tree().child(k).localIndex(i);
op.evalZot(elementMatrix[local_i][local_j], iq, factor, rowGradients[i][k], colShapeValues[j]);
}
}
}
}
}
template <class Operator, class RowView, class ColView, class RowNodeTag, class ColNodeTag, class FOT>
void calculateElementMatrix(Operator& op,
RowView const& rowView,
......@@ -178,7 +282,7 @@ namespace AMDiS