FirstOrderAssembler.hpp

#pragma once

#include <vector>

#include <dune/typetree/nodetags.hh>

#include <dune/amdis/LocalAssembler.hpp>
#include <dune/amdis/common/Mpl.hpp>
#include <dune/amdis/common/TypeDefs.hpp>
#include <dune/amdis/utility/GetEntity.hpp>

namespace AMDiS
{
  template <class GridView, class LocalContext, FirstOrderType type>
  class FirstOrderAssembler
      : public LocalAssembler<GridView, LocalContext>
  {
    using Super = LocalAssembler<GridView, LocalContext>;

    static constexpr int dim = GridView::dimension;
    static constexpr int dow = GridView::dimensionworld;

    using ElementMatrix = Impl::ElementMatrix;
    using ElementVector = Impl::ElementVector;

    using OrderTag = std::conditional_t<(type==GRD_PHI), tag::fot_grd_phi, tag::fot_grd_psi>;

  public:
    FirstOrderAssembler()
      : Super(1, type)
    {}

    template <class Operator, class... Args>
    void bind(double factor, Operator& op, LocalContext const& localContext, Args&&... args)
    {
      Super::bind(op, localContext, std::forward<Args>(args)...);

      factor_ = factor;
      op.init(OrderTag{}, localContext, Super::getQuadrature());
    }


    // tag dispatching for FirstOrderType...
    template <class Operator, class RowNode, class ColNode>
    void calculateElementMatrix(Operator& op,
                                ElementMatrix& elementMatrix,
                                RowNode const& rowNode, ColNode const& colNode)
    {
      calculateElementMatrix(op, elementMatrix, rowNode, colNode,
        typename RowNode::NodeTag{}, typename ColNode::NodeTag{}, FirstOrderType_<type>);
    }

    template <class Operator, class Node>
    void calculateElementVector(Operator& op,
                                ElementVector& elementVector,
                                Node const& node)
    {
      calculateElementVector(op, elementVector, node,
        typename Node::NodeTag{}, FirstOrderType_<type>);
    }


    template <class Operator, class RowNode, class ColNode>
    void calculateElementMatrix(Operator& op,
                                ElementMatrix& elementMatrix,
                                RowNode const& rowNode, ColNode const& colNode,
                                Dune::TypeTree::LeafNodeTag, Dune::TypeTree::LeafNodeTag,
                                FirstOrderType_t<GRD_PHI>)
    {
      auto const& rowLocalFE = rowNode.finiteElement();
      auto const& colLocalFE = colNode.finiteElement();
      auto const& quad = Super::getQuadrature().getRule();

      for (std::size_t iq = 0; iq < quad.size(); ++iq) {
        // Position of the current quadrature point in the reference element
        decltype(auto) local = Super::getLocal(quad[iq].position());

        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = Super::getGeometry().jacobianInverseTransposed(local);

        // The multiplicative factor in the integral transformation formula
        const double factor = Super::getLocalGeometry().integrationElement(quad[iq].position()) * quad[iq].weight() * factor_;

        std::vector<Dune::FieldVector<double,1> > rowShapeValues;
        rowLocalFE.localBasis().evaluateFunction(local, rowShapeValues);

        // The gradients of the shape functions on the reference element
        std::vector<Dune::FieldMatrix<double,1,dim> > colReferenceGradients;
        colLocalFE.localBasis().evaluateJacobian(local, 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]);

        for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
          for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
            const int local_i = rowNode.localIndex(i);
            const int local_j = colNode.localIndex(j);
            op.eval(tag::fot_grd_phi{}, elementMatrix[local_i][local_j], iq, factor, rowShapeValues[i], colGradients[j]);
          }
        }
      }
    }


    template <class Operator, class RowNode, class ColNode>
    void calculateElementMatrix(Operator& op,
                                ElementMatrix& elementMatrix,
                                RowNode const& rowNode, ColNode const& colNode,
                                Dune::TypeTree::LeafNodeTag, Dune::TypeTree::LeafNodeTag,
                                FirstOrderType_t<GRD_PSI>)
    {
      auto const& rowLocalFE = rowNode.finiteElement();
      auto const& colLocalFE = colNode.finiteElement();
      auto const& quad = Super::getQuadrature().getRule();

      for (std::size_t iq = 0; iq < quad.size(); ++iq) {
        // Position of the current quadrature point in the reference element
        decltype(auto) local = Super::getLocal(quad[iq].position());

        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = Super::getGeometry().jacobianInverseTransposed(local);

        // The multiplicative factor in the integral transformation formula
        const double factor = Super::getLocalGeometry().integrationElement(quad[iq].position()) * quad[iq].weight() * factor_;

        // The gradients of the shape functions on the reference element
        std::vector<Dune::FieldMatrix<double,1,dim> > rowReferenceGradients;
        rowLocalFE.localBasis().evaluateJacobian(local, 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(local, colShapeValues);

        for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
          for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
            const int local_i = rowNode.localIndex(i);
            const int local_j = colNode.localIndex(j);
            op.eval(tag::fot_grd_psi{}, elementMatrix[local_i][local_j], iq, factor, rowGradients[i], colShapeValues[j]);
          }
        }
      }
    }


    template <class Operator, class RowNode, class ColNode>
    void calculateElementMatrix(Operator& op,
                                ElementMatrix& elementMatrix,
                                RowNode const& rowNode, ColNode const& colNode,
                                Dune::TypeTree::LeafNodeTag, Dune::TypeTree::PowerNodeTag,
                                FirstOrderType_t<GRD_PHI>)
    {
      auto const& rowLocalFE = rowNode.finiteElement();
      auto const& colLocalFE = colNode.child(0).finiteElement();
      auto const& quad = Super::getQuadrature().getRule();

      test_exit( dow == degree(colNode), "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) local = Super::getLocal(quad[iq].position());

        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = Super::getGeometry().jacobianInverseTransposed(local);

        // The multiplicative factor in the integral transformation formula
        const double factor = Super::getLocalGeometry().integrationElement(quad[iq].position()) * quad[iq].weight() * factor_;

        std::vector<Dune::FieldVector<double,1> > rowShapeValues;
        rowLocalFE.localBasis().evaluateFunction(local, rowShapeValues);

        // The gradients of the shape functions on the reference element
        std::vector<Dune::FieldMatrix<double,1,dim> > colReferenceGradients;
        colLocalFE.localBasis().evaluateJacobian(local, 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 = rowNode.localIndex(i);
          for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
            for (std::size_t k = 0; k < degree(colNode); ++k) {
              const int local_j = colNode.child(k).localIndex(j);
              op.eval(tag::fot_grd_phi{}, elementMatrix[local_i][local_j], iq, factor, rowShapeValues[i], colGradients[j][k]);
            }
          }
        }
      }
    }


    template <class Operator, class RowNode, class ColNode>
    void calculateElementMatrix(Operator& op,
                                ElementMatrix& elementMatrix,
                                RowNode const& rowNode, ColNode const& colNode,
                                Dune::TypeTree::PowerNodeTag, Dune::TypeTree::LeafNodeTag,
                                FirstOrderType_t<GRD_PSI>)
    {
      auto const& rowLocalFE = rowNode.child(0).finiteElement();
      auto const& colLocalFE = colNode.finiteElement();
      auto const& quad = Super::getQuadrature().getRule();

      test_exit( dow == degree(rowNode), "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) local = Super::getLocal(quad[iq].position());

        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = Super::getGeometry().jacobianInverseTransposed(local);

        // The multiplicative factor in the integral transformation formula
        const double factor = Super::getLocalGeometry().integrationElement(quad[iq].position()) * quad[iq].weight() * factor_;

        // The gradients of the shape functions on the reference element
        std::vector<Dune::FieldMatrix<double,1,dim> > rowReferenceGradients;
        rowLocalFE.localBasis().evaluateJacobian(local, 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(local, colShapeValues);

        // <p, div(v)>
        for (std::size_t j = 0; j < colLocalFE.size(); ++j) {
          const int local_j = colNode.localIndex(j);
          for (std::size_t i = 0; i < rowLocalFE.size(); ++i) {
            for (std::size_t k = 0; k < degree(rowNode); ++k) {
              const int local_i = rowNode.child(k).localIndex(i);
              op.eval(tag::fot_grd_psi{}, elementMatrix[local_i][local_j], iq, factor, rowGradients[i][k], colShapeValues[j]);
            }
          }
        }
      }
    }


    template <class Operator, class RowNode, class ColNode, class RowNodeTag, class ColNodeTag, class FOT>
    void calculateElementMatrix(Operator&, ElementMatrix&,
                                RowNode const&, ColNode const&,
                                RowNodeTag, ColNodeTag, FOT)
    {
      warning("FirstOrderAssembler::calculateElementMatrix not implemented for RowNode x ColNode");
    }


    template <class Operator, class Node>
    void calculateElementVector(Operator& op,
                                ElementVector& elementVector,
                                Node const& node,
                                Dune::TypeTree::LeafNodeTag,
                                FirstOrderType_t<GRD_PSI>)
    {
      auto const& localFE = node.finiteElement();
      auto const& quad = Super::getQuadrature().getRule();

      for (std::size_t iq = 0; iq < quad.size(); ++iq) {
        // Position of the current quadrature point in the reference element
        decltype(auto) local = Super::getLocal(quad[iq].position());

        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = Super::getGeometry().jacobianInverseTransposed(local);

        // The multiplicative factor in the integral transformation formula
        const double factor = Super::getLocalGeometry().integrationElement(quad[iq].position()) * quad[iq].weight() * factor_;

        // The gradients of the shape functions on the reference element
        std::vector<Dune::FieldMatrix<double,1,dim> > rowReferenceGradients;
        localFE.localBasis().evaluateJacobian(local, 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]);

        for (std::size_t i = 0; i < localFE.size(); ++i) {
          const int local_i = node.localIndex(i);
          op.eval(tag::fot_grd_psi{}, elementVector[local_i], iq, factor, rowGradients[i]);
        }
      }
    }


    template <class Operator, class Node, class NodeTag, class FOT>
    void calculateElementVector(Operator&, ElementVector&,
                                Node const&, NodeTag, FOT)
    {
      warning("FirstOrderAssembler::calculateElementVector not implemented for Node");
    }

  private:
    double factor_;
  };

} // end namespace AMDiS