ConvectionDiffusionOperator.hpp

#pragma once
 
#include <type_traits>
 
#include <dune/common/hybridutilities.hh>
#include <dune/common/typetree/nodeconcepts.hh>
 
#include <amdis/LocalOperator.hpp>
#include <amdis/VariadicGridFunctionOperator.hpp>
#include <amdis/common/Order.hpp>
#include <amdis/common/Logical.hpp>
#include <amdis/common/StaticSize.hpp>
#include <amdis/common/TypeTraits.hpp>
#include <amdis/typetree/FiniteElementType.hpp>
 
namespace AMDiS
{
  namespace tag{
    template<bool conserving>
    struct convectionDiffusion{};
  }
  template <bool conserving>
  class ConvectionDiffusion
  {
  public:
    ConvectionDiffusion([[maybe_unused]] tag::convectionDiffusion<conserving> )
    {}
 
    template <class CG, class RN, class CN, class Quad, class LocalFctA, class LocalFctB, class LocalFctC, class LocalFctF, class Mat>
    void assemble(CG const& contextGeo, RN const& rowNode, CN const& colNode, Quad const& quad,
                  LocalFctA const& localFctA_, LocalFctB const& localFctB_, LocalFctC const& localFctC_, LocalFctF const& localFctF_,
                  Mat& elementMatrix) const
    {
      using A_range = typename LocalFctA::Range;
      static_assert(static_size_v<A_range> == 1 || (static_num_rows_v<A_range> == CG::dow && static_num_cols_v<A_range> == CG::dow),
        "Expression A(x) must be of scalar or matrix type.");
      using b_range = typename LocalFctB::Range;
      static_assert(static_size_v<b_range> == 1 || static_size_v<b_range> == CG::dow,
        "Expression b(x) must be of scalar or vector type.");
      using c_range = typename LocalFctC::Range;
      static_assert(static_size_v<c_range> == 1,
        "Expression c(x) must be of scalar type.");
      static_assert(Dune::TypeTree::Concept::LeafTreeNode<RN> && Dune::TypeTree::Concept::LeafTreeNode<CN>,
        "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;
 
      std::size_t numLocalFe = rowNode.size();
 
      auto contextGeometry = contextGeo.geometry();
 
      for (std::size_t iq = 0; iq < quad.size(); ++iq) {
        // Position of the current quadrature point in the reference element
        auto&& local = contextGeo.coordinateInElement(quad[iq].position());
 
        // The transposed inverse Jacobian of the map from the reference element to the element
        const auto jacobian = contextGeo.elementGeometry().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<CG::dow>(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);
            multiply(Dune::MatVec::as_scalar(A), gradients[i], gradAi);
            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);
            multiply(Dune::MatVec::as_scalar(A), gradients[i], grad_i);
            grad_i.axpy(shapeValues[i], b);
            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;
            }
          }
        }
      }
    }
 
 
    template <class CG, class Node, class Quad, class LocalFctA, class LocalFctB, class LocalFctC, class LocalFctF, class Vec>
    void assemble(CG const& contextGeo, Node const& node, Quad const& quad,  LocalFctA const& localFctA_, LocalFctB const& localFctB_, LocalFctC const& localFctC_, LocalFctF const& localFctF_, Vec& elementVector) const
    {
      using f_range = typename LocalFctF::Range;
      static_assert( static_size_v<f_range> == 1,
        "Expression f(x) must be of scalar type." );
      static_assert(Dune::TypeTree::Concept::LeafTreeNode<Node>,
        "Operator can be applied to Leaf-Nodes only." );
 
      std::size_t numLocalFe = node.size();
 
      for (std::size_t iq = 0; iq < quad.size(); ++iq) {
        // Position of the current quadrature point in the reference element
        auto&& local = contextGeo.coordinateInElement(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;
        }
      }
    }
 
  private:
 
    template <class T1, int M, int N, class T2, class T3>
    static void multiply(FieldMatrix<T1,M,N> const& A, FieldVector<T2,N> const& x, FieldVector<T3,M>& y)
    {
      A.mv(x, y);
    }
 
    template <class T1, int N, class T2, class T3,
      std::enable_if_t<Dune::IsNumber<T1>::value, int> = 0>
    static void multiply(T1 const& alpha, FieldVector<T2,N> const& x, FieldVector<T3,N>& y)
    {
      y = x;
      y *= alpha;
    }
 
    template <int dow, class T, int N>
    static FieldVector<T,dow> makeB(FieldVector<T,N> const& b) { return b; }
 
    template <int dow, class T>
    static FieldVector<T,dow> makeB(FieldVector<T,1> const& b) { return FieldVector<T,dow>(T(b)); }
 
    template <int dow, class T,
      std::enable_if_t<Dune::IsNumber<T>::value, int> = 0>
    static FieldVector<T,dow> makeB(T b) { return FieldVector<T,dow>(b); }
 
  private:
    int quadOrder_;
  };
 
  template <class LC, bool conserving>
  struct VariadicGridFunctionOperatorRegistry<tag::convectionDiffusion<conserving>, LC>
  {
    static constexpr int degree = 2;
    using type = ConvectionDiffusion<conserving>;
  };
 
  template <bool conserving = true,
            class PreGridFctA, class PreGridFctB, class PreGridFctC, class PreGridFctF>
  auto convectionDiffusion(PreGridFctA const& gridFctA, PreGridFctB const& gridFctB,
                           PreGridFctC const& gridFctC, PreGridFctF const& gridFctF,
                           int gridFctDegree = -1, bool_t<conserving> = {})
  {
    return makeOperator(tag::convectionDiffusion<conserving>{}, gridFctDegree, gridFctA,gridFctB,gridFctC, gridFctF);
  }
 
} // end namespace AMDiS