quad_polynomial_approximation.cpp

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/** \file quad_polynomial_approximation.cpp
  \example mofem/atom_tests/quad_polynomial_approximation.cpp
  \brief Checking approximation functions for quad
 
*/
 
 
 
#include <MoFEM.hpp>
 
using namespace MoFEM;
 
using Ele = FaceElementForcesAndSourcesCore;
using OpEle = FaceElementForcesAndSourcesCore::UserDataOperator;
using EntData = EntitiesFieldData::EntData;
 
static char help[] = "...\n\n";
 
static constexpr int approx_order = 6;
struct ApproxFunction {
  static inline double fun(double x, double y) {
    double r = 1;
    for (int o = 1; o <= approx_order; ++o) {
      for (int i = 0; i <= o; ++i) {
        int j = o - i;
        if (j >= 0)
          r += pow(x, i) * pow(y, j);
      }
    }
    return r;
  }
 
  static inline VectorDouble3 diff_fun(double x, double y) {
    VectorDouble3 r(2);
    r.clear();
    for (int o = 1; o <= approx_order; ++o) {
      for (int i = 0; i <= o; ++i) {
        int j = o - i;
        if (j >= 0) {
          r[0] += i > 0 ? i * pow(x, i - 1) * pow(y, j) : 0;
          r[1] += j > 0 ? j * pow(x, i) * pow(y, j - 1) : 0;
        }
      }
    }
    return r;
  }
};
 
struct QuadOpCheck : public OpEle {
 
  QuadOpCheck(boost::shared_ptr<VectorDouble> &field_vals,
              boost::shared_ptr<MatrixDouble> &diff_field_vals);
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  boost::shared_ptr<VectorDouble> fieldVals;
  boost::shared_ptr<MatrixDouble> diffFieldVals;
};
 
struct QuadOpRhs : public OpEle {
 
  QuadOpRhs(SmartPetscObj<Vec> &f);
  MoFEMErrorCode doWork(int side, EntityType type,
                        EntitiesFieldData::EntData &data);
 
private:
  SmartPetscObj<Vec> F;
};
 
struct QuadOpLhs : public OpEle {
 
  QuadOpLhs(SmartPetscObj<Mat> &a);
  MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
                        EntityType col_type,
                        EntitiesFieldData::EntData &row_data,
                        EntitiesFieldData::EntData &col_data);
 
private:
  SmartPetscObj<Mat> A;
};
 
int main(int argc, char *argv[]) {
 
  MoFEM::Core::Initialize(&argc, &argv, (char *)0, help);
 
  try {
 
    // Declare elements
    enum bases {
      AINSWORTH,
      AINSWORTH_LOBATTO,
      DEMKOWICZ,
      BERNSTEIN,
      LASBASETOP
    };
    const char *list_bases[] = {"ainsworth", "ainsworth_lobatto", "demkowicz",
                                "bernstein"};
    PetscBool flg;
    PetscInt choice_base_value = AINSWORTH;
    CHKERR PetscOptionsGetEList(PETSC_NULLPTR, NULL, "-base", list_bases,
                                LASBASETOP, &choice_base_value, &flg);
 
    if (flg != PETSC_TRUE)
      SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSSIBLE_CASE, "base not set");
    FieldApproximationBase base = AINSWORTH_LEGENDRE_BASE;
    if (choice_base_value == AINSWORTH)
      base = AINSWORTH_LEGENDRE_BASE;
    if (choice_base_value == AINSWORTH_LOBATTO)
      base = AINSWORTH_LOBATTO_BASE;
    else if (choice_base_value == DEMKOWICZ)
      base = DEMKOWICZ_JACOBI_BASE;
    else if (choice_base_value == BERNSTEIN)
      base = AINSWORTH_BERNSTEIN_BEZIER_BASE;
 
    enum spaces { H1SPACE, L2SPACE, LASBASETSPACE };
    const char *list_spaces[] = {"h1", "l2"};
    PetscInt choice_space_value = H1SPACE;
    CHKERR PetscOptionsGetEList(PETSC_NULLPTR, NULL, "-space", list_spaces,
                                LASBASETSPACE, &choice_space_value, &flg);
    if (flg != PETSC_TRUE)
      SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSSIBLE_CASE, "space not set");
    FieldSpace space = H1;
    if (choice_space_value == H1SPACE)
      space = H1;
    else if (choice_space_value == L2SPACE)
      space = L2;
 
    moab::Core mb_instance;
    moab::Interface &moab = mb_instance;
 
    std::array<double, 12> one_quad_coords = {0, 0, 0,
 
                                              2, 0, 0,
 
                                              1, 1, 0,
 
                                              0, 1, 0};
 
    std::array<EntityHandle, 4> one_quad_nodes;
    for (int n = 0; n != 4; ++n)
      CHKERR moab.create_vertex(&one_quad_coords[3 * n], one_quad_nodes[n]);
    EntityHandle one_quad;
    CHKERR moab.create_element(MBQUAD, one_quad_nodes.data(), 4, one_quad);
    Range one_quad_range;
    one_quad_range.insert(one_quad);
    Range one_quad_adj_ents;
    CHKERR moab.get_adjacencies(one_quad_range, 1, true, one_quad_adj_ents,
                                moab::Interface::UNION);
 
    MoFEM::Core core(moab);
    MoFEM::Interface &m_field = core;
 
    BitRefLevel bit_level0 = BitRefLevel().set(0);
    CHKERR m_field.getInterface<BitRefManager>()->setBitRefLevelByDim(
        0, 2, bit_level0);
 
    // Fields
    CHKERR m_field.add_field("FIELD1", space, base, 1);
    CHKERR m_field.add_ents_to_field_by_type(0, MBQUAD, "FIELD1");
 
    CHKERR m_field.set_field_order(0, MBVERTEX, "FIELD1", 1);
    CHKERR m_field.set_field_order(0, MBEDGE, "FIELD1", approx_order + 1);
    CHKERR m_field.set_field_order(0, MBQUAD, "FIELD1", approx_order + 1);
    CHKERR m_field.build_fields();
 
    // FE
    CHKERR m_field.add_finite_element("QUAD");
 
    // Define rows/cols and element data
    CHKERR m_field.modify_finite_element_add_field_row("QUAD", "FIELD1");
    CHKERR m_field.modify_finite_element_add_field_col("QUAD", "FIELD1");
    CHKERR m_field.modify_finite_element_add_field_data("QUAD", "FIELD1");
    CHKERR m_field.add_ents_to_finite_element_by_type(0, MBQUAD, "QUAD");
 
    // build finite elemnts
    CHKERR m_field.build_finite_elements();
    // //build adjacencies
    CHKERR m_field.build_adjacencies(bit_level0);
 
    // Problem
    CHKERR m_field.add_problem("TEST_PROBLEM");
 
    // set finite elements for problem
    CHKERR m_field.modify_problem_add_finite_element("TEST_PROBLEM", "QUAD");
    // set refinement level for problem
    CHKERR m_field.modify_problem_ref_level_add_bit("TEST_PROBLEM", bit_level0);
 
    // build problem
    ProblemsManager *prb_mng_ptr;
    CHKERR m_field.getInterface(prb_mng_ptr);
    CHKERR prb_mng_ptr->buildProblem("TEST_PROBLEM", true);
    // partition
    CHKERR prb_mng_ptr->partitionSimpleProblem("TEST_PROBLEM");
    CHKERR prb_mng_ptr->partitionFiniteElements("TEST_PROBLEM");
    // what are ghost nodes, see Petsc Manual
    CHKERR prb_mng_ptr->partitionGhostDofs("TEST_PROBLEM");
 
    // Create matrices
    SmartPetscObj<Mat> A;
    CHKERR m_field.getInterface<MatrixManager>()
        ->createMPIAIJWithArrays<PetscGlobalIdx_mi_tag>("TEST_PROBLEM", A);
    SmartPetscObj<Vec> F;
    CHKERR m_field.getInterface<VecManager>()->vecCreateGhost("TEST_PROBLEM",
                                                              ROW, F);
    SmartPetscObj<Vec> D;
    CHKERR m_field.getInterface<VecManager>()->vecCreateGhost("TEST_PROBLEM",
                                                              COL, D);
 
    auto rule = [&](int, int, int p) { return 2 * (p + 1); };
 
    auto assemble_matrices_and_vectors = [&]() {
      MoFEMFunctionBegin;
      Ele fe(m_field);
      fe.getRuleHook = rule;
      auto jac_ptr = boost::make_shared<MatrixDouble>();
      auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
      auto det_ptr = boost::make_shared<VectorDouble>();
      fe.getOpPtrVector().push_back(new OpCalculateHOJac<2>(jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpSetHOInvJacToScalarBases<2>(H1, inv_jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpSetHOInvJacToScalarBases<2>(L2, inv_jac_ptr));
      fe.getOpPtrVector().push_back(new OpSetHOWeightsOnFace());
      fe.getOpPtrVector().push_back(new QuadOpRhs(F));
      fe.getOpPtrVector().push_back(new QuadOpLhs(A));
      CHKERR VecZeroEntries(F);
      CHKERR MatZeroEntries(A);
      CHKERR m_field.loop_finite_elements("TEST_PROBLEM", "QUAD", fe);
      CHKERR VecAssemblyBegin(F);
      CHKERR VecAssemblyEnd(F);
      CHKERR MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
      CHKERR MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
      MoFEMFunctionReturn(0);
    };
 
    auto solve_problem = [&] {
      MoFEMFunctionBegin;
      auto solver = createKSP(PETSC_COMM_WORLD);
      CHKERR KSPSetOperators(solver, A, A);
      CHKERR KSPSetFromOptions(solver);
      CHKERR KSPSetUp(solver);
      CHKERR KSPSolve(solver, F, D);
      CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
      CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
      CHKERR m_field.getInterface<VecManager>()->setLocalGhostVector(
          "TEST_PROBLEM", COL, D, INSERT_VALUES, SCATTER_REVERSE);
      MoFEMFunctionReturn(0);
    };
 
    auto check_solution = [&] {
      MoFEMFunctionBegin;
      Ele fe(m_field);
      fe.getRuleHook = rule;
      auto field_vals_ptr = boost::make_shared<VectorDouble>();
      auto diff_field_vals_ptr = boost::make_shared<MatrixDouble>();
      auto jac_ptr = boost::make_shared<MatrixDouble>();
      auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
      auto det_ptr = boost::make_shared<VectorDouble>();
 
      fe.getOpPtrVector().push_back(
          new OpCalculateScalarFieldValues("FIELD1", field_vals_ptr));
      fe.getOpPtrVector().push_back(new OpCalculateHOJac<2>(jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpSetHOInvJacToScalarBases<2>(H1, inv_jac_ptr));
      fe.getOpPtrVector().push_back(
          new OpSetHOInvJacToScalarBases<2>(L2, inv_jac_ptr));
      fe.getOpPtrVector().push_back(new OpSetHOWeightsOnFace());
      fe.getOpPtrVector().push_back(new OpCalculateScalarFieldGradient<2>(
          "FIELD1", diff_field_vals_ptr, space == L2 ? MBQUAD : MBVERTEX));
      fe.getOpPtrVector().push_back(
          new QuadOpCheck(field_vals_ptr, diff_field_vals_ptr));
      CHKERR m_field.loop_finite_elements("TEST_PROBLEM", "QUAD", fe);
      MoFEMFunctionReturn(0);
    };
 
    CHKERR assemble_matrices_and_vectors();
    CHKERR solve_problem();
    CHKERR check_solution();
  }
  CATCH_ERRORS;
 
  MoFEM::Core::Finalize();
  return 0;
}
 
QuadOpCheck::QuadOpCheck(boost::shared_ptr<VectorDouble> &field_vals,
                         boost::shared_ptr<MatrixDouble> &diff_field_vals)
    : OpEle("FIELD1", "FIELD1", ForcesAndSourcesCore::UserDataOperator::OPROW),
      fieldVals(field_vals), diffFieldVals(diff_field_vals) {}
 
MoFEMErrorCode QuadOpCheck::doWork(int side, EntityType type,
                                   EntitiesFieldData::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type == MBQUAD) {
    const int nb_gauss_pts = data.getN().size1();
    auto t_coords = getFTensor1CoordsAtGaussPts();
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      double f = ApproxFunction::fun(t_coords(0), t_coords(1));
      constexpr double eps = 1e-6;
 
      std::cout << f - (*fieldVals)[gg] << std::endl;
 
      if (std::abs(f - (*fieldVals)[gg]) > eps)
        SETERRQ(PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
                 "Wrong value %d : %6.4e != %6.4e", gg, f, (*fieldVals)[gg]);
 
      VectorDouble3 diff_f = ApproxFunction::diff_fun(t_coords(0), t_coords(1));
      for (auto d : {0, 1})
        std::cout << diff_f[d] - (*diffFieldVals)(d, gg) << " ";
      std::cout << std::endl;
      for (auto d : {0, 1})
        if (std::abs(diff_f[d] - (*diffFieldVals)(d, gg)) > eps)
          SETERRQ(PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
                   "Wrong derivative value (%d) %6.4e != %6.4e", diff_f[d],
                   (*diffFieldVals)(d, gg));
 
      ++t_coords;
    }
  }
  MoFEMFunctionReturn(0);
}
 
QuadOpRhs::QuadOpRhs(SmartPetscObj<Vec> &f)
    : OpEle("FIELD1", "FIELD1", ForcesAndSourcesCore::UserDataOperator::OPROW),
      F(f) {}
 
MoFEMErrorCode QuadOpRhs::doWork(int side, EntityType type,
                                 EntitiesFieldData::EntData &data) {
  FTensor::Index<'i', 3> i;
  MoFEMFunctionBegin;
  const int nb_dofs = data.getIndices().size();
  if (nb_dofs) {
    const int nb_gauss_pts = data.getN().size1();
    VectorDouble nf(nb_dofs);
    nf.clear();
    auto t_base = data.getFTensor0N();
    auto t_coords = getFTensor1CoordsAtGaussPts();
    auto t_w = getFTensor0IntegrationWeight();
    auto a = getMeasure();
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      double f = ApproxFunction::fun(t_coords(0), t_coords(1));
      double v = a * t_w * f;
      double *val = &*nf.begin();
      for (int bb = 0; bb != nb_dofs; ++bb) {
        *val += v * t_base;
        ++t_base;
        ++val;
      }
      ++t_coords;
      ++t_w;
      // ++t_normal;
    }
    CHKERR VecSetValues(F, data, &*nf.data().begin(), ADD_VALUES);
  }
  MoFEMFunctionReturn(0);
}
 
QuadOpLhs::QuadOpLhs(SmartPetscObj<Mat> &a)
    : OpEle("FIELD1", "FIELD1",
            ForcesAndSourcesCore::UserDataOperator::OPROWCOL),
      A(a) {
  // FIXME: Can be symmetric, is not for simplicity
  sYmm = false;
}
 
MoFEMErrorCode QuadOpLhs::doWork(int row_side, int col_side,
                                 EntityType row_type, EntityType col_type,
                                 EntitiesFieldData::EntData &row_data,
                                 EntitiesFieldData::EntData &col_data) {
  FTensor::Index<'i', 3> i;
  MoFEMFunctionBegin;
  const int row_nb_dofs = row_data.getIndices().size();
  const int col_nb_dofs = col_data.getIndices().size();
  if (row_nb_dofs && col_nb_dofs) {
    const int nb_gauss_pts = row_data.getN().size1();
    MatrixDouble m(row_nb_dofs, col_nb_dofs);
    m.clear();
    auto t_w = getFTensor0IntegrationWeight();
    auto a = getMeasure();
    double *row_base_ptr = &*row_data.getN().data().begin();
    double *col_base_ptr = &*col_data.getN().data().begin();
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      double v = a * t_w;
      cblas_dger(CblasRowMajor, row_nb_dofs, col_nb_dofs, v, row_base_ptr, 1,
                 col_base_ptr, 1, &*m.data().begin(), col_nb_dofs);
      row_base_ptr += row_nb_dofs;
      col_base_ptr += col_nb_dofs;
      ++t_w;
    }
    CHKERR MatSetValues(A, row_data, col_data, &*m.data().begin(), ADD_VALUES);
  }
  MoFEMFunctionReturn(0);
}