SecondOrderGradTestGradTrial.hpp

#pragma once
 
#include <type_traits>
 
#include <amdis/GridFunctionOperator.hpp>
#include <amdis/Output.hpp>
#include <amdis/common/StaticSize.hpp>
#include <amdis/common/ValueCategory.hpp>
#include <amdis/typetree/FiniteElementType.hpp>
 
namespace AMDiS
{
  namespace tag
  {
    struct gradtest_gradtrial {};
  }
 
 
  class SecondOrderGradTestGradTrial
  {
  public:
    SecondOrderGradTestGradTrial(tag::gradtest_gradtrial) {}
 
    template <class CG, class RN, class CN, class Quad, class LocalFct, class Mat>
    void assemble(CG const& contextGeo, RN const& rowNode, CN const& colNode,
                  Quad const& quad, LocalFct const& localFct, Mat& elementMatrix) const
    {
      using expr_value_type = typename LocalFct::Range;
      static_assert(static_size_v<expr_value_type> == 1 ||
                      (static_num_rows_v<expr_value_type> == CG::dow &&
                       static_num_cols_v<expr_value_type> == CG::dow),
        "Expression must be of scalar or matrix type.");
      static_assert(RN::isLeaf && CN::isLeaf,
        "Operator can be applied to Leaf-Nodes only.");
 
      const bool sameFE = std::is_same_v<FiniteElementType_t<RN>, FiniteElementType_t<CN>>;
      const bool sameNode = rowNode.treeIndex() == colNode.treeIndex();
      using Category = ValueCategory_t<typename LocalFct::Range>;
 
      if (sameFE && sameNode)
        getElementMatrixOptimized(contextGeo, quad, rowNode, colNode, localFct,  elementMatrix, Category{});
      else if (sameFE)
        getElementMatrixStandard(contextGeo, quad, rowNode, colNode, localFct, elementMatrix);
      else
        error_exit("Not implemented: currently only the implementation for equal fespaces available");
    }
 
  protected:
 
    template <class CG, class QR, class RN, class CN, class LocalFct, class Mat>
    void getElementMatrixStandard(CG const& contextGeo, QR const& quad,
                                  RN const& rowNode, CN const& colNode,
                                  LocalFct const& localFct, Mat& elementMatrix) const
    {
      std::size_t size = rowNode.size();
 
      using RangeFieldType = typename RN::LocalBasis::Traits::RangeFieldType;
      using WorldVector = Dune::FieldVector<RangeFieldType,CG::dow>;
      std::vector<WorldVector> gradients;
 
      for (auto const& qp : quad) {
        // Position of the current quadrature point in the reference element
        auto&& local = contextGeo.coordinateInElement(qp.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(qp.position()) * qp.weight();
        const auto exprValue = localFct(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]);
 
        for (std::size_t i = 0; i < size; ++i) {
          const auto local_i = rowNode.localIndex(i);
          for (std::size_t j = 0; j < size; ++j) {
            const auto local_j = colNode.localIndex(j);
            elementMatrix[local_i][local_j] += eval(exprValue, factor, gradients[i], gradients[j]);
          }
        }
      }
    }
 
    template <class CG, class QR, class RN, class CN, class LocalFct, class Mat>
    void getElementMatrixOptimized(CG const& contextGeo, QR const& quad,
                                   RN const& node, CN const& /*colNode*/,
                                   LocalFct const& localFct, Mat& elementMatrix, tag::scalar) const
    {
      std::size_t size = node.size();
 
      using RangeFieldType = typename RN::LocalBasis::Traits::RangeFieldType;
      using WorldVector = Dune::FieldVector<RangeFieldType,CG::dow>;
      std::vector<WorldVector> gradients;
 
      for (auto const& qp : quad) {
        // Position of the current quadrature point in the reference element
        auto&& local = contextGeo.coordinateInElement(qp.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 = localFct(local) * contextGeo.integrationElement(qp.position()) * qp.weight();
 
        // The gradients of the shape functions on the reference element
        auto const& shapeGradients = node.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]);
 
        for (std::size_t i = 0; i < size; ++i) {
          const auto local_i = node.localIndex(i);
 
          elementMatrix[local_i][local_i] += factor * (gradients[i] * gradients[i]);
 
          for (std::size_t j = i+1; j < size; ++j) {
            const auto local_j = node.localIndex(j);
            const auto value = factor * (gradients[i] * gradients[j]);
 
            elementMatrix[local_i][local_j] += value;
            elementMatrix[local_j][local_i] += value;
          }
        }
      }
    }
 
    template <class CG, class QR, class RN, class CN, class LocalFct, class Mat>
    void getElementMatrixOptimized(CG const& contextGeo, QR const& quad,
                                   RN const& node, CN const& /*colNode*/,
                                   LocalFct const& localFct, Mat& elementMatrix, tag::matrix) const
    {
      std::size_t size = node.size();
 
      using RangeFieldType = typename RN::LocalBasis::Traits::RangeFieldType;
      using WorldVector = Dune::FieldVector<RangeFieldType,CG::dow>;
      std::vector<WorldVector> gradients;
 
      for (auto const& qp : quad) {
        // Position of the current quadrature point in the reference element
        auto&& local = contextGeo.coordinateInElement(qp.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(qp.position()) * qp.weight();
        const auto exprValue = localFct(local);
 
        // The gradients of the shape functions on the reference element
        auto const& shapeGradients = node.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]);
 
        for (std::size_t i = 0; i < size; ++i) {
          const auto local_i = node.localIndex(i);
          for (std::size_t j = 0; j < size; ++j) {
            const auto local_j = node.localIndex(j);
            elementMatrix[local_i][local_j] += eval(exprValue, factor, gradients[i], gradients[j]);
          }
        }
      }
    }
 
  protected:
 
    template <class S, class F, class T, int dow,
      std::enable_if_t<Category::Scalar<S>,int> = 0>
    T eval(S const& scalar, F factor,
           Dune::FieldVector<T,dow> const& grad_test,
           Dune::FieldVector<T,dow> const& grad_trial) const
    {
      return (scalar * factor) * (grad_test * grad_trial);
    }
 
    template <class M, class F, class T, int dow,
      std::enable_if_t<Category::Matrix<M>,int> = 0>
    T eval(M const& mat, F factor,
           Dune::FieldVector<T,dow> const& grad_test,
           Dune::FieldVector<T,dow> const& grad_trial) const
    {
      return factor * (grad_test * (mat * grad_trial));
    }
  };
 
  template <class LC>
  struct GridFunctionOperatorRegistry<tag::gradtest_gradtrial, LC>
  {
    static constexpr int degree = 2;
    using type = SecondOrderGradTestGradTrial;
  };
 
  template <class Expr>
  auto sot(Expr&& expr, int quadOrder = -1)
  {
    return makeOperator(tag::gradtest_gradtrial{}, FWD(expr), quadOrder);
  }
 
} // end namespace AMDiS