PoissonDiscontinousGalerkin.hpp

Example of implementation for discontinuous Galerkin.

/**
 * \file PoissonDiscontinousGalerkin.hpp
 * \example PoissonDiscontinousGalerkin.hpp
 *
 * Example of implementation for discontinuous Galerkin.
 */
 
 
 
// Define name if it has not been defined yet
#ifndef __POISSON2DISGALERKIN_HPP__
#define __POISSON2DISGALERKIN_HPP__
 
// Namespace that contains necessary UDOs, will be included in the main program
namespace Poisson2DiscontGalerkinOperators {
 
// Declare FTensor index for 2D problem
FTensor::Index<'i', SPACE_DIM> i;
 
enum ElementSide { LEFT_SIDE = 0, RIGHT_SIDE };
// data for skeleton computation
std::array<VectorInt, 2>
    indicesRowSideMap; ///< indices on rows for left hand-side
std::array<VectorInt, 2>
    indicesColSideMap; ///< indices on columns for left hand-side
std::array<MatrixDouble, 2> rowBaseSideMap; // base functions on rows
std::array<MatrixDouble, 2> colBaseSideMap; // base function  on columns
std::array<MatrixDouble, 2> rowDiffBaseSideMap; // derivative of base functions
std::array<MatrixDouble, 2> colDiffBaseSideMap; // derivative of base functions
std::array<double, 2> areaMap; // area/volume of elements on the side
std::array<int, 2> senseMap; // orientaton of local element edge/face in respect
                             // to global orientation of edge/face
 
/**
 * @brief Operator tp collect data from elements on the side of Edge/Face
 * 
 */
struct OpCalculateSideData : public FaceSideOp {
 
  OpCalculateSideData(std::string field_name, std::string col_field_name)
      : FaceSideOp(field_name, col_field_name, FaceSideOp::OPROWCOL) {
 
    std::fill(&doEntities[MBVERTEX], &doEntities[MBMAXTYPE], false);
 
    for (auto t = moab::CN::TypeDimensionMap[SPACE_DIM].first;
         t <= moab::CN::TypeDimensionMap[SPACE_DIM].second; ++t)
      doEntities[t] = true;
  }
 
  MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
                        EntityType col_type, EntData &row_data,
                        EntData &col_data) {
    MoFEMFunctionBeginHot;
 
    // Note: THat for L2 base data rows, and columns are the same, so operator
    // above can be simpler operator for the right hand side, and data can be
    // stored only for rows, since for columns data are the same. However for
    // complex multi-physics problems that not necessary would be a case. For
    // generality, we keep generic case.
 
    if ((CN::Dimension(row_type) == SPACE_DIM) &&
        (CN::Dimension(col_type) == SPACE_DIM)) {
      const auto nb_in_loop = getFEMethod()->nInTheLoop;
      indicesRowSideMap[nb_in_loop] = row_data.getIndices();
      indicesColSideMap[nb_in_loop] = col_data.getIndices();
      rowBaseSideMap[nb_in_loop] = row_data.getN();
      colBaseSideMap[nb_in_loop] = col_data.getN();
      rowDiffBaseSideMap[nb_in_loop] = row_data.getDiffN();
      colDiffBaseSideMap[nb_in_loop] = col_data.getDiffN();
      areaMap[nb_in_loop] = getMeasure();
      senseMap[nb_in_loop] = getSkeletonSense();
      if (!nb_in_loop) {
        indicesRowSideMap[1].clear();
        indicesColSideMap[1].clear();
        rowBaseSideMap[1].clear();
        colBaseSideMap[1].clear();
        rowDiffBaseSideMap[1].clear();
        colDiffBaseSideMap[1].clear();
        areaMap[1] = 0;
        senseMap[1] = 0;
      }
    } else {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "Should not happen");
    }
 
    MoFEMFunctionReturnHot(0);
  }
};
 
template <typename T> inline auto get_ntensor(T &base_mat) {
  return FTensor::Tensor0<FTensor::PackPtr<double *, 1>>(
      &*base_mat.data().begin());
};
 
template <typename T> inline auto get_ntensor(T &base_mat, int gg, int bb) {
  double *ptr = &base_mat(gg, bb);
  return FTensor::Tensor0<FTensor::PackPtr<double *, 1>>(ptr);
};
 
template <typename T> inline auto get_diff_ntensor(T &base_mat) {
  double *ptr = &*base_mat.data().begin();
  return getFTensor1FromPtr<2>(ptr);
};
 
template <typename T>
inline auto get_diff_ntensor(T &base_mat, int gg, int bb) {
  double *ptr = &base_mat(gg, 2 * bb);
  return getFTensor1FromPtr<2>(ptr);
};
 
/**
 * @brief Operator the left hand side matrix 
 * 
 */
struct OpL2LhsPenalty : public BoundaryEleOp {
public:
 
  /**
   * @brief Construct a new OpL2LhsPenalty 
   * 
   * @param side_fe_ptr pointer to FE to evaluate side elements
   */
  OpL2LhsPenalty(boost::shared_ptr<FaceSideEle> side_fe_ptr)
      : BoundaryEleOp(NOSPACE, BoundaryEleOp::OPSPACE), sideFEPtr(side_fe_ptr) {}
 
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    // Collect data from side domian elements
    CHKERR loopSideFaces("dFE", *sideFEPtr);
    const auto in_the_loop =
        sideFEPtr->nInTheLoop; // return number of elements on the side
 
#ifndef NDEBUG
    const std::array<std::string, 2> ele_type_name = {"BOUNDARY", "SKELETON"};
    MOFEM_LOG("SELF", Sev::noisy)
        << "OpL2LhsPenalty inTheLoop " << ele_type_name[in_the_loop];
    MOFEM_LOG("SELF", Sev::noisy)
        << "OpL2LhsPenalty sense " << senseMap[0] << " " << senseMap[1];
#endif
 
    // calculate  penalty
    const double s = getMeasure() / (areaMap[0] + areaMap[1]);
    const double p = penalty * s;
 
    // get normal of the face or edge
    auto t_normal = getFTensor1Normal();
    t_normal.normalize();
 
    // get number of integration points on face
    const size_t nb_integration_pts = getGaussPts().size2();
 
    // beta paramter is zero, when penalty method is used, also, takes value 1,
    // when boundary edge/face is evaluated, and 2 when is skeleton edge/face.
    const double beta = static_cast<double>(nitsche) / (in_the_loop + 1);
 
    // iterate the sides rows
    for (auto s0 : {LEFT_SIDE, RIGHT_SIDE}) {
 
      // gent number of DOFs on the right side. 
      const auto nb_rows = indicesRowSideMap[s0].size();
 
      if (nb_rows) {
 
        // get orientation of the local element edge
        const auto sense_row = senseMap[s0];
 
        // iterate the side cols
        const auto nb_row_base_functions = rowBaseSideMap[s0].size2();
        for (auto s1 : {LEFT_SIDE, RIGHT_SIDE}) {
 
          // get orientation of the edge
          const auto sense_col = senseMap[s1];
 
          // number of dofs, for homogenous approximation this value is
          // constant.
          const auto nb_cols = indicesColSideMap[s1].size();
 
          // resize local element matrix
          locMat.resize(nb_rows, nb_cols, false);
          locMat.clear();
 
          // get base functions, and integration weights
          auto t_row_base = get_ntensor(rowBaseSideMap[s0]);
          auto t_diff_row_base = get_diff_ntensor(rowDiffBaseSideMap[s0]);
          auto t_w = getFTensor0IntegrationWeight();
 
          // iterate integration points on face/edge
          for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
 
            // t_w is integration weight, and measure is element area, or
            // volume, depending if problem is in 2d/3d.
            const double alpha = getMeasure() * t_w;
            auto t_mat = locMat.data().begin();
            
            // iterate rows
            size_t rr = 0;
            for (; rr != nb_rows; ++rr) {
 
              // calculate tetting function 
              FTensor::Tensor1<double, SPACE_DIM> t_vn_plus;
              t_vn_plus(i) = beta * (phi * t_diff_row_base(i) / p);
              FTensor::Tensor1<double, SPACE_DIM> t_vn;
              t_vn(i) = t_row_base * t_normal(i) * sense_row - t_vn_plus(i);
 
              // get base functions on columns
              auto t_col_base = get_ntensor(colBaseSideMap[s1], gg, 0);
              auto t_diff_col_base =
                  get_diff_ntensor(colDiffBaseSideMap[s1], gg, 0);
 
              // iterate columns
              for (size_t cc = 0; cc != nb_cols; ++cc) {
 
                // calculate variance of tested function 
                FTensor::Tensor1<double, SPACE_DIM> t_un;
                t_un(i) = -p * (t_col_base * t_normal(i) * sense_col -
                                beta * t_diff_col_base(i) / p);
 
                // assemble matrix
                *t_mat -= alpha * (t_vn(i) * t_un(i));
                *t_mat -= alpha * (t_vn_plus(i) * (beta * t_diff_col_base(i)));
 
                // move to next column base and element of matrix
                ++t_col_base;
                ++t_diff_col_base;
                ++t_mat;
              }
 
              // move to next row base
              ++t_row_base;
              ++t_diff_row_base;
            }
 
            // this is obsolete for this particular example, we keep it for
            // generality. in case of multi-physics problems different fields can
            // chare hierarchical base but use different approx. order, so is
            // possible to have more base functions than DOFs on element.
            for (; rr < nb_row_base_functions; ++rr) {
              ++t_row_base;
              ++t_diff_row_base;
            }
 
            ++t_w;
          }
 
          // assemble system
          CHKERR ::MatSetValues(getKSPB(), indicesRowSideMap[s0].size(),
                                &*indicesRowSideMap[s0].begin(),
                                indicesColSideMap[s1].size(),
                                &*indicesColSideMap[s1].begin(),
                                &*locMat.data().begin(), ADD_VALUES);
 
          // stop of boundary element
          if (!in_the_loop)
            MoFEMFunctionReturnHot(0);
        }
      }
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<FaceSideEle>
      sideFEPtr; ///< pointer to element to get data on edge/face sides
  MatrixDouble locMat; ///< local operator matrix
};
 
/**
 * @brief Operator to evaluate Dirichlet boundary conditions using DG
 *
 */
struct OpL2BoundaryRhs : public BoundaryEleOp {
public:
  OpL2BoundaryRhs(boost::shared_ptr<FaceSideEle> side_fe_ptr, ScalarFun fun)
      : BoundaryEleOp(NOSPACE, BoundaryEleOp::OPSPACE), sideFEPtr(side_fe_ptr),
        sourceFun(fun) {}
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    // get normal of the face or edge
    CHKERR loopSideFaces("dFE", *sideFEPtr);
    const auto in_the_loop =
        sideFEPtr->nInTheLoop; // return number of elements on the side
 
    // calculate  penalty
    const double s = getMeasure() / (areaMap[0]);
    const double p = penalty * s;
 
    // get normal of the face or edge
    auto t_normal = getFTensor1Normal();
    t_normal.normalize();
 
    auto t_w = getFTensor0IntegrationWeight();
 
    const size_t nb_rows = indicesRowSideMap[0].size();
 
    if (!nb_rows)
      MoFEMFunctionReturnHot(0);
 
    // resize local operator vector
    rhsF.resize(nb_rows, false);
    rhsF.clear();
 
    const size_t nb_integration_pts = getGaussPts().size2();
    const size_t nb_row_base_functions = rowBaseSideMap[0].size2();
 
    // shape funcs
    auto t_row_base = get_ntensor(rowBaseSideMap[0]);
    auto t_diff_row_base = get_diff_ntensor(rowDiffBaseSideMap[0]);
    auto t_coords = getFTensor1CoordsAtGaussPts();
 
    const auto sense_row = senseMap[0];
    const double beta = static_cast<double>(nitsche) / (in_the_loop + 1);
 
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
      const double alpha = getMeasure() * t_w;
 
      const double source_val =
          -p * sourceFun(t_coords(0), t_coords(1), t_coords(2));
 
      auto t_f = rhsF.data().begin();
 
      size_t rr = 0;
      for (; rr != nb_rows; ++rr) {
 
        FTensor::Tensor1<double, SPACE_DIM> t_vn_plus;
        t_vn_plus(i) = beta * (phi * t_diff_row_base(i) / p);
        FTensor::Tensor1<double, SPACE_DIM> t_vn;
        t_vn(i) = t_row_base * t_normal(i) * sense_row - t_vn_plus(i);
 
        // assemble operator local vactor
        *t_f -= alpha * t_vn(i) * (source_val * t_normal(i));
 
        ++t_row_base;
        ++t_diff_row_base;
        ++t_f;
      }
 
      for (; rr < nb_row_base_functions; ++rr) {
        ++t_row_base;
        ++t_diff_row_base;
      }
 
      ++t_w;
      ++t_coords;
    }
 
    // assemble local operator vector to global vector
    CHKERR ::VecSetValues(getKSPf(), indicesRowSideMap[0].size(),
                          &*indicesRowSideMap[0].begin(), &*rhsF.data().begin(),
                          ADD_VALUES);
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<FaceSideEle>
      sideFEPtr;       ///< pointer to element to get data on edge/face sides
  ScalarFun sourceFun; ///< pointer to function to evaluate value of function on boundary
  VectorDouble rhsF;   ///< vector to store local operator right hand side
};
 
}; // namespace Poisson2DiscontGalerkinOperators
 
#endif //__POISSON2DISGALERKIN_HPP__