StokesOperator.hpp

#pragma once
 
#include <type_traits>
#include <vector>
 
#include <amdis/GridFunctionOperator.hpp>
#include <amdis/common/StaticSize.hpp>
 
namespace AMDiS
{
  namespace tag
  {
    struct stokes
    {
      bool constViscosity = false;
    };
  }
 
 
  class StokesOperator
  {
    bool constViscosity_;
 
  public:
    StokesOperator(tag::stokes t)
      : constViscosity_(t.constViscosity)
    {}
 
    template <class CG, class Node, class Quad, class LocalFct, class Mat>
    void assemble(CG const& contextGeo, Node const& tree, Node const& /*colNode*/,
                  Quad const& quad, LocalFct const& localFct, Mat& elementMatrix) const
    {
      static_assert(static_size_v<typename LocalFct::Range> == 1,
        "Viscosity must be of scalar type.");
 
      using VelocityNode = Dune::TypeTree::Child<Node,0>;
      using VelocityCompNode = Dune::TypeTree::Child<Node,0,0>;
      using PressureNode = Dune::TypeTree::Child<Node,1>;
 
      static_assert(VelocityNode::isPower && PressureNode::isLeaf, "");
 
      using namespace Dune::Indices;
 
      std::size_t numVelocityLocalFE = tree.child(_0,0).size();
      std::size_t numPressureLocalFE = tree.child(_1).size();
 
      using RangeFieldType = typename VelocityNode::ChildType::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 vel_factor = localFct(local) * factor;
 
        auto const& shapeGradients = tree.child(_0,0).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]);
 
        auto const& pressureValues = tree.child(_1).localBasisValuesAt(local);
 
        // <viscosity * grad(u), grad(v)>
        for (std::size_t i = 0; i < numVelocityLocalFE; ++i) {
          const auto value_ii = vel_factor * (gradients[i] * gradients[i]);
          for (std::size_t k = 0; k < CG::dow; ++k) {
            const auto local_ki = tree.child(_0,k).localIndex(i);
            elementMatrix[local_ki][local_ki] += value_ii;
          }
 
          for (std::size_t j = i+1; j < numVelocityLocalFE; ++j) {
            const auto value = vel_factor * (gradients[i] * gradients[j]);
            for (std::size_t k = 0; k < CG::dow; ++k) {
              const auto local_ki = tree.child(_0,k).localIndex(i);
              const auto local_kj = tree.child(_0,k).localIndex(j);
              elementMatrix[local_ki][local_kj] += value;
              elementMatrix[local_kj][local_ki] += value;
            }
          }
        }
 
        if (!constViscosity_) {
          // <viscosity * d_i u_j, d_j v_i>
          for (std::size_t i = 0; i < numVelocityLocalFE; ++i) {
          for (std::size_t kj = 0; kj < CG::dow; ++kj) {
            const auto value_i_kj = vel_factor * gradients[i][kj];
            for (std::size_t j = 0; j < numVelocityLocalFE; ++j) {
            for (std::size_t ki = 0; ki < CG::dow; ++ki) {
              const auto local_ki = tree.child(_0,ki).localIndex(i);
              const auto local_kj = tree.child(_0,kj).localIndex(j);
              elementMatrix[local_ki][local_kj] += value_i_kj * gradients[j][ki];
            }
            }
          }
          }
        }
 
        // <p, div(v)> + <div(u), q>
        for (std::size_t i = 0; i < numVelocityLocalFE; ++i) {
          for (std::size_t j = 0; j < numPressureLocalFE; ++j) {
            const auto value = factor * pressureValues[j];
            for (std::size_t k = 0; k < CG::dow; ++k) {
              const auto local_v = tree.child(_0,k).localIndex(i);
              const auto local_p = tree.child(_1).localIndex(j);
 
              elementMatrix[local_v][local_p] += gradients[i][k] * value;
              elementMatrix[local_p][local_v] += gradients[i][k] * value;
            }
          }
        }
      }
 
    } // end assemble
  };
 
  template <class LC>
  struct GridFunctionOperatorRegistry<tag::stokes, LC>
  {
    static constexpr int degree = 2;
    using type = StokesOperator;
  };
 
} // end namespace AMDiS