ConvectionDiffusionOperator.hpp

#pragma once

#include <type_traits>

#include <dune/common/hybridutilities.hh>

#include <amdis/LocalOperator.hpp>
#include <amdis/Output.hpp>
#include <amdis/common/TypeTraits.hpp>
#include <amdis/common/StaticSize.hpp>

namespace AMDiS
{
  template <class LC, class GridFctA, class GridFctB, class GridFctC, class GridFctF, bool conserving = true>
  class ConvectionDiffusionOperator
      : public LocalOperator<ConvectionDiffusionOperator<LC, GridFctA, GridFctB, GridFctC, GridFctF, conserving>, LC>
  {
    static const int dow = ContextGeometry<LC>::dow;

    using A_range = typename GridFctA::Range;
    static_assert( static_size_v<A_range> == 1 || (static_num_rows_v<A_range> == dow && static_num_cols_v<A_range> == dow),
      "Expression A(x) must be of scalar or matrix type." );
    using b_range = typename GridFctB::Range;
    static_assert( static_size_v<b_range> == 1 || static_size_v<b_range> == dow,
      "Expression b(x) must be of scalar or vector type." );
    using c_range = typename GridFctC::Range;
    static_assert( static_size_v<c_range> == 1,
      "Expression c(x) must be of scalar type." );
    using f_range = typename GridFctF::Range;
    static_assert( static_size_v<f_range> == 1,
      "Expression f(x) must be of scalar type." );

  public:
    ConvectionDiffusionOperator(GridFctA const& gridFctA, GridFctB const& gridFctB,
                                GridFctC const& gridFctC, GridFctF const& gridFctF)
      : gridFctA_(gridFctA)
      , gridFctB_(gridFctB)
      , gridFctC_(gridFctC)
      , gridFctF_(gridFctF)
    {}

    template <class CG, class RN, class CN, class Mat>
    void getElementMatrix(CG const& contextGeo, RN const& rowNode, CN const& colNode, Mat& elementMatrix)
    {
      static_assert(RN::isLeaf && CN::isLeaf,
        "Operator can be applied to Leaf-Nodes only." );

      static_assert(std::is_same_v<FiniteElementType_t<RN>, FiniteElementType_t<CN>>,
        "Galerkin operator requires equal finite elements for test and trial space." );

      using RangeFieldType = typename RN::LocalBasis::Traits::RangeFieldType;
      using WorldVector = FieldVector<RangeFieldType,CG::dow>;
      std::vector<WorldVector> gradients;

      auto localFctA = localFunction(gridFctA_); localFctA.bind(contextGeo.element());
      auto localFctB = localFunction(gridFctB_); localFctB.bind(contextGeo.element());
      auto localFctC = localFunction(gridFctC_); localFctC.bind(contextGeo.element());

      std::size_t numLocalFe = rowNode.size();

      int quadDeg = std::max({this->getDegree(2,coeffOrder(localFctA),rowNode,colNode),
                              this->getDegree(1,coeffOrder(localFctB),rowNode,colNode),
                              this->getDegree(0,coeffOrder(localFctC),rowNode,colNode)});

      using QuadratureRules = Dune::QuadratureRules<typename CG::Geometry::ctype, CG::LocalContext::mydimension>;
      auto const& quad = QuadratureRules::rule(contextGeo.type(), quadDeg);

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

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

        // The multiplicative factor in the integral transformation formula
        const auto factor = contextGeo.integrationElement(quad[iq].position()) * quad[iq].weight();

        // the values of the shape functions on the reference element at the quadrature point
        auto const& shapeValues = rowNode.localBasisValuesAt(local);

        // The gradients of the shape functions on the reference element
        auto const& shapeGradients = rowNode.localBasisJacobiansAt(local);

        // Compute the shape function gradients on the real element
        gradients.resize(shapeGradients.size());

        for (std::size_t i = 0; i < gradients.size(); ++i)
          jacobian.mv(shapeGradients[i][0], gradients[i]);

        const auto A = localFctA(local);
        WorldVector b = makeB(localFctB(local));
        const auto c = localFctC(local);

        if (conserving) {
          WorldVector gradAi;
          for (std::size_t i = 0; i < numLocalFe; ++i) {
            const auto local_i = rowNode.localIndex(i);
            gradAi = A * gradients[i];
            auto gradBi = b * gradients[i];
            for (std::size_t j = 0; j < numLocalFe; ++j) {
              const auto local_j = colNode.localIndex(j);
              elementMatrix[local_i][local_j] += (dot(gradAi, gradients[j]) + (c * shapeValues[i] - gradBi) * shapeValues[j]) * factor;
            }
          }
        } else {
          WorldVector grad_i;
          for (std::size_t i = 0; i < numLocalFe; ++i) {
            const auto local_i = rowNode.localIndex(i);
            grad_i = A * gradients[i];
            grad_i+= b * shapeValues[i];
            for (std::size_t j = 0; j < numLocalFe; ++j) {
              const auto local_j = colNode.localIndex(j);
              elementMatrix[local_i][local_j] += (dot(grad_i, gradients[j]) + c * shapeValues[i] * shapeValues[j]) * factor;
            }
          }
        }
      }

      localFctA.unbind();
      localFctB.unbind();
      localFctC.unbind();
    }


    template <class CG, class Node, class Vec>
    void getElementVector(CG const& contextGeo, Node const& node, Vec& elementVector)
    {
      static_assert(Node::isLeaf,
        "Operator can be applied to Leaf-Nodes only." );

      auto localFctF = localFunction(gridFctF_); localFctF.bind(contextGeo.element());

      std::size_t numLocalFe = node.size();

      int quad_order = this->getDegree(0,coeffOrder(localFctF),node);

      using QuadratureRules = Dune::QuadratureRules<typename CG::Geometry::ctype, CG::LocalContext::dimension>;
      auto const& quad = QuadratureRules::rule(contextGeo.type(), quad_order);

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

        // the values of the shape functions on the reference element at the quadrature point
        auto const& shapeValues = node.localBasisValuesAt(local);

        // The multiplicative factor in the integral transformation formula
        const auto factor = localFctF(local) * contextGeo.integrationElement(quad[iq].position()) * quad[iq].weight();

        for (std::size_t i = 0; i < numLocalFe; ++i) {
          const auto local_i = node.localIndex(i);
          elementVector[local_i] += shapeValues[i] * factor;
        }
      }

      localFctF.unbind();
    }

  private:

    template <class LocalFct>
    int coeffOrder(LocalFct const& localFct)
    {
      if constexpr (Concepts::Polynomial<LocalFct>)
        return order(localFct);
      else
        return 0;
    }

    template <class T, int N>
    static FieldVector<T,dow> makeB(FieldVector<T,N> const& b) { return b; }

    template <class T, int N>
    static FieldVector<T,dow> makeB(FieldVector<T,N>&& b) { return std::move(b); }

    template <class T>
    static FieldVector<T,dow> makeB(FieldVector<T,1> const& b) { return FieldVector<T,dow>(T(b)); }

    template <class T>
    static FieldVector<T,dow> makeB(FieldVector<T,1>&& b) { return FieldVector<T,dow>(T(b)); }

    template <class T, std::enable_if_t<std::is_arithmetic_v<T>, int> = 0>
    static FieldVector<T,dow> makeB(T b) { return FieldVector<T,dow>(b); }

  private:
    GridFctA gridFctA_;
    GridFctB gridFctB_;
    GridFctC gridFctC_;
    GridFctF gridFctF_;
  };

#ifndef DOXYGEN
  template <class PreGridFctA, class PreGridFctB, class PreGridFctC, class PreGridFctF, class c>
  struct PreConvectionDiffusionOperator
  {
    static constexpr bool conserving = c::value;
    PreGridFctA gridFctA;
    PreGridFctB gridFctB;
    PreGridFctC gridFctC;
    PreGridFctF gridFctF;
  };
#endif


  template <class PreGridFctA, class PreGridFctB, class PreGridFctC, class PreGridFctF, bool conserving = true>
  auto convectionDiffusion(PreGridFctA const& gridFctA, PreGridFctB const& gridFctB,
                           PreGridFctC const& gridFctC, PreGridFctF const& gridFctF,
                           bool_t<conserving> = {})
  {
    using Pre = PreConvectionDiffusionOperator<PreGridFctA, PreGridFctB, PreGridFctC, PreGridFctF, bool_t<conserving>>;
    return Pre{gridFctA, gridFctB, gridFctC, gridFctF};
  }


#ifndef DOXYGEN
  template <class Context, class... T, class GridView>
  auto makeLocalOperator(PreConvectionDiffusionOperator<T...> pre, GridView const& gridView)
  {
    using Pre = PreConvectionDiffusionOperator<T...>;
    auto gridFctA = makeGridFunction(std::move(pre.gridFctA), gridView);
    auto gridFctB = makeGridFunction(std::move(pre.gridFctB), gridView);
    auto gridFctC = makeGridFunction(std::move(pre.gridFctC), gridView);
    auto gridFctF = makeGridFunction(std::move(pre.gridFctF), gridView);

    using GridFctOp = ConvectionDiffusionOperator<Context,
      decltype(gridFctA), decltype(gridFctB), decltype(gridFctC), decltype(gridFctF), Pre::conserving>;

    GridFctOp localOperator{std::move(gridFctA), std::move(gridFctB), std::move(gridFctC), std::move(gridFctF)};
    return localOperator;
  }
#endif

} // end namespace AMDiS