poisson_2d_dis_galerkin.cpp

Example of implementation for discontinuous Galerkin.

/**
 * \file poisson_2d_dis_galerkin.cpp
 * \example poisson_2d_dis_galerkin.cpp
 *
 * Example of implementation for discontinuous Galerkin.
 */
 
/* This file is part of MoFEM.
 * MoFEM is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 *
 * MoFEM is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
 
#include <BasicFiniteElements.hpp>
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = PipelineManager::FaceEle;
  using DomainEleOp = DomainEle::UserDataOperator;
  using BoundaryEle = PipelineManager::EdgeEle;
  using BoundaryEleOp = BoundaryEle::UserDataOperator;
  using PostProcEle = PostProcFaceOnRefinedMesh;
 
  using FaceSideEle = MoFEM::FaceElementForcesAndSourcesCoreOnSide;
  using FaceSideOp = FaceSideEle::UserDataOperator;
};
 
constexpr int BASE_DIM = 1;
constexpr int FIELD_DIM = 1;
constexpr int SPACE_DIM = 2;
 
using EntData = EntitiesFieldData::EntData;
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = ElementsAndOps<SPACE_DIM>::DomainEleOp;
using BoundaryEle = ElementsAndOps<SPACE_DIM>::BoundaryEle;
using BoundaryEleOp = ElementsAndOps<SPACE_DIM>::BoundaryEleOp;
using FaceSideEle = ElementsAndOps<SPACE_DIM>::FaceSideEle;
using FaceSideOp = ElementsAndOps<SPACE_DIM>::FaceSideOp;
using PostProcEle = ElementsAndOps<SPACE_DIM>::PostProcEle;
 
static double penalty = 1e6;
static double phi =
    -1; // 1 - symmetric Nitsche, 0 - nonsymmetric, -1 antisymmetrica
static double nitsche = 1;
 
#include <PoissonDiscontinousGalerkin.hpp>
 
using OpDomainGradGrad = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::BiLinearForm<GAUSS>::OpGradGrad<BASE_DIM, FIELD_DIM, SPACE_DIM>;
using OpDomainSource = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpSource<BASE_DIM, FIELD_DIM>;
 
PetscBool is_test = PETSC_FALSE;
 
auto u_exact = [](const double x, const double y, const double) {
  if (is_test)
    return x * x * y * y;
  else
    return cos(2 * x * M_PI) * cos(2 * y * M_PI);
};
 
auto u_grad_exact = [](const double x, const double y, const double) {
  if (is_test)
    return FTensor::Tensor1<double, 2>{2 * x * y * y, 2 * x * x * y};
  else
    return FTensor::Tensor1<double, 2>{
 
        -2 * M_PI * cos(2 * M_PI * y) * sin(2 * M_PI * x),
        -2 * M_PI * cos(2 * M_PI * x) * sin(2 * M_PI * y)
 
    };
};
 
auto source = [](const double x, const double y, const double) {
  if (is_test)
    return -(2 * x * x + 2 * y * y);
  else
    return 8 * M_PI * M_PI * cos(2 * x * M_PI) * cos(2 * y * M_PI);
};
 
using namespace MoFEM;
using namespace Poisson2DiscontGalerkinOperators;
 
static char help[] = "...\n\n";
 
struct Poisson2DiscontGalerkin {
public:
  Poisson2DiscontGalerkin(MoFEM::Interface &m_field);
 
  // Declaration of the main function to run analysis
  MoFEMErrorCode runProgram();
 
private:
  // Declaration of other main functions called in runProgram()
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode setIntegrationRules();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode checkResults();
  MoFEMErrorCode outputResults();
 
  // MoFEM interfaces
  MoFEM::Interface &mField;
  Simple *simpleInterface;
 
  // Field name and approximation order
  std::string domainField;
  int oRder;
};
 
Poisson2DiscontGalerkin::Poisson2DiscontGalerkin(MoFEM::Interface &m_field)
    : domainField("U"), mField(m_field), oRder(4) {}
 
//! [Read mesh]
MoFEMErrorCode Poisson2DiscontGalerkin::readMesh() {
  MoFEMFunctionBegin;
 
  CHKERR mField.getInterface(simpleInterface);
  CHKERR simpleInterface->getOptions();
 
  // Only L2 field is set in this example. Two lines bellow forces simple
  // interface to creat lower diminesion (edge) elements, despite that fact that
  // there is no field spanning on such elements. We need them for DF method.
  simpleInterface->getAddSkeletonFE() = true;
  simpleInterface->getAddBoundaryFE() = true;
 
  CHKERR simpleInterface->loadFile();
 
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Setup problem]
MoFEMErrorCode Poisson2DiscontGalerkin::setupProblem() {
  MoFEMFunctionBegin;
 
  CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &oRder, PETSC_NULL);
  CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-penalty", &penalty,
                               PETSC_NULL);
  CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-phi", &phi, PETSC_NULL);
  CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-nitsche", &nitsche,
                               PETSC_NULL);
  PetscOptionsGetBool(PETSC_NULL, "", "-is_test", &is_test, PETSC_NULL);
 
  MOFEM_LOG("WORLD", Sev::inform) << "Set order: " << oRder;
  MOFEM_LOG("WORLD", Sev::inform) << "Set penalty: " << penalty;
  MOFEM_LOG("WORLD", Sev::inform) << "Set phi: " << phi;
  MOFEM_LOG("WORLD", Sev::inform) << "Set nitche: " << nitsche;
  MOFEM_LOG("WORLD", Sev::inform) << "Set test: " << (is_test == PETSC_TRUE);
 
  CHKERR simpleInterface->addDomainField(domainField, L2,
                                         AINSWORTH_LOBATTO_BASE, 1);
  CHKERR simpleInterface->setFieldOrder(domainField, oRder);
  CHKERR simpleInterface->setUp();
 
  // This is only for debigging and experimentation, to see boundary and edge
  // elements.
  auto save_shared = [&](auto meshset, std::string prefix) {
    MoFEMFunctionBegin;
    auto file_name =
        prefix + "_" +
        boost::lexical_cast<std::string>(mField.get_comm_rank()) + ".vtk";
    CHKERR mField.get_moab().write_file(file_name.c_str(), "VTK", "", &meshset,
                                        1);
    MoFEMFunctionReturn(0);
  };
 
  // CHKERR save_shared(simpleInterface->getBoundaryMeshSet(), "bdy");
  // CHKERR save_shared(simpleInterface->getSkeletonMeshSet(), "skel");
 
  MoFEMFunctionReturn(0);
}
//! [Setup problem]
 
//! [Boundary condition]
MoFEMErrorCode Poisson2DiscontGalerkin::boundaryCondition() {
  MoFEMFunctionBegin;
  MoFEMFunctionReturn(0);
}
 
//! [Boundary condition]
 
//! [Assemble system]
MoFEMErrorCode Poisson2DiscontGalerkin::assembleSystem() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto add_base_ops = [&](auto &pipeline) {
    auto det_ptr = boost::make_shared<VectorDouble>();
    auto jac_ptr = boost::make_shared<MatrixDouble>();
    auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
    pipeline.push_back(new OpCalculateHOJacForFace(jac_ptr));
    pipeline.push_back(new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
    pipeline.push_back(new OpSetInvJacL2ForFace(inv_jac_ptr));
  };
 
  add_base_ops(pipeline_mng->getOpDomainLhsPipeline());
  pipeline_mng->getOpDomainLhsPipeline().push_back(new OpDomainGradGrad(
      domainField, domainField,
      [](const double, const double, const double) { return 1; }));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpDomainSource(domainField, source));
 
  // Push operators to the Pipeline for Skeleton
  auto side_fe_ptr = boost::make_shared<FaceSideEle>(mField);
  add_base_ops(side_fe_ptr->getOpPtrVector());
  side_fe_ptr->getOpPtrVector().push_back(
      new OpCalculateSideData(domainField, domainField));
 
  // Push operators to the Pipeline for Skeleton
  pipeline_mng->getOpSkeletonLhsPipeline().push_back(
      new OpL2LhsPenalty(side_fe_ptr));
 
  // Push operators to the Pipeline for Boundary
  pipeline_mng->getOpBoundaryLhsPipeline().push_back(
      new OpL2LhsPenalty(side_fe_ptr));
  pipeline_mng->getOpBoundaryRhsPipeline().push_back(
      new OpL2BoundaryRhs(side_fe_ptr, u_exact));
 
  MoFEMFunctionReturn(0);
}
//! [Assemble system]
 
//! [Set integration rules]
MoFEMErrorCode Poisson2DiscontGalerkin::setIntegrationRules() {
  MoFEMFunctionBegin;
 
  auto rule_lhs = [](int, int, int p) -> int { return 2 * p; };
  auto rule_rhs = [](int, int, int p) -> int { return 2 * p; };
  auto rule_2 = [this](int, int, int) { return 2 * oRder; };
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(rule_lhs);
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(rule_rhs);
 
  CHKERR pipeline_mng->setSkeletonLhsIntegrationRule(rule_2);
  CHKERR pipeline_mng->setSkeletonRhsIntegrationRule(rule_2);
  CHKERR pipeline_mng->setBoundaryLhsIntegrationRule(rule_2);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(rule_2);
 
  MoFEMFunctionReturn(0);
}
//! [Set integration rules]
 
//! [Solve system]
MoFEMErrorCode Poisson2DiscontGalerkin::solveSystem() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto ksp_solver = pipeline_mng->createKSP();
  CHKERR KSPSetFromOptions(ksp_solver);
  CHKERR KSPSetUp(ksp_solver);
 
  // Create RHS and solution vectors
  auto dm = simpleInterface->getDM();
  auto F = smartCreateDMVector(dm);
  auto D = smartVectorDuplicate(F);
 
  CHKERR KSPSolve(ksp_solver, F, D);
 
  // Scatter result data on the mesh
  CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR DMoFEMMeshToLocalVector(dm, D, INSERT_VALUES, SCATTER_REVERSE);
 
  MoFEMFunctionReturn(0);
}
//! [Solve system]
 
MoFEMErrorCode Poisson2DiscontGalerkin::checkResults() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  pipeline_mng->getDomainRhsFE().reset();
  pipeline_mng->getDomainLhsFE().reset();
  pipeline_mng->getSkeletonRhsFE().reset();
  pipeline_mng->getSkeletonLhsFE().reset();
  pipeline_mng->getBoundaryRhsFE().reset();
  pipeline_mng->getBoundaryLhsFE().reset();
 
  auto rule = [](int, int, int p) -> int { return 2 * p; };
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(rule);
  auto rule_2 = [this](int, int, int) { return 2 * oRder; };
  CHKERR pipeline_mng->setSkeletonRhsIntegrationRule(rule_2);
 
  auto add_base_ops = [&](auto &pipeline) {
    auto det_ptr = boost::make_shared<VectorDouble>();
    auto jac_ptr = boost::make_shared<MatrixDouble>();
    auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
    pipeline.push_back(new OpCalculateHOJacForFace(jac_ptr));
    pipeline.push_back(new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
    pipeline.push_back(new OpSetInvJacL2ForFace(inv_jac_ptr));
  };
 
  auto u_vals_ptr = boost::make_shared<VectorDouble>();
  auto u_grad_ptr = boost::make_shared<MatrixDouble>();
 
  add_base_ops(pipeline_mng->getOpDomainRhsPipeline());
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateScalarFieldValues(domainField, u_vals_ptr));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateScalarFieldGradient<2>(domainField, u_grad_ptr));
 
  enum NORMS { L2 = 0, SEMI_NORM, H1, LAST_NORM };
  std::array<int, LAST_NORM> error_indices;
  for (int i = 0; i != LAST_NORM; ++i)
    error_indices[i] = i;
  auto l2_vec = createSmartVectorMPI(
      mField.get_comm(), (!mField.get_comm_rank()) ? LAST_NORM : 0, LAST_NORM);
 
  auto error_op = new DomainEleOp(domainField, DomainEleOp::OPROW);
  error_op->doWorkRhsHook = [&](DataOperator *op_ptr, int side, EntityType type,
                                EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    auto o = static_cast<DomainEleOp *>(op_ptr);
 
    FTensor::Index<'i', 2> i;
 
    if (const size_t nb_dofs = data.getIndices().size()) {
 
      const int nb_integration_pts = o->getGaussPts().size2();
      auto t_w = o->getFTensor0IntegrationWeight();
      auto t_val = getFTensor0FromVec(*u_vals_ptr);
      auto t_grad = getFTensor1FromMat<2>(*u_grad_ptr);
      auto t_coords = o->getFTensor1CoordsAtGaussPts();
 
      std::array<double, LAST_NORM> error;
      std::fill(error.begin(), error.end(), 0);
 
      for (int gg = 0; gg != nb_integration_pts; ++gg) {
 
        const double alpha = t_w * o->getMeasure();
        const double diff =
            t_val - u_exact(t_coords(0), t_coords(1), t_coords(2));
 
        auto t_exact_grad = u_grad_exact(t_coords(0), t_coords(1), t_coords(2));
 
        const double diff_grad =
            (t_grad(i) - t_exact_grad(i)) * (t_grad(i) - t_exact_grad(i));
 
        error[L2] += alpha * pow(diff, 2);
        error[SEMI_NORM] += alpha * diff_grad;
 
        ++t_w;
        ++t_val;
        ++t_grad;
        ++t_coords;
      }
 
      error[H1] = error[L2] + error[SEMI_NORM];
 
      CHKERR VecSetValues(l2_vec, LAST_NORM, error_indices.data(), error.data(),
                          ADD_VALUES);
    }
 
    MoFEMFunctionReturn(0);
  };
 
  auto side_fe_ptr = boost::make_shared<FaceSideEle>(mField);
  add_base_ops(side_fe_ptr->getOpPtrVector());
  side_fe_ptr->getOpPtrVector().push_back(
      new OpCalculateScalarFieldValues(domainField, u_vals_ptr));
  std::array<VectorDouble, 2> side_vals;
  std::array<double, 2> area_map;
 
  auto side_vals_op = new DomainEleOp(domainField, DomainEleOp::OPROW);
  side_vals_op->doWorkRhsHook = [&](DataOperator *op_ptr, int side,
                                    EntityType type,
                                    EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    auto o = static_cast<FaceSideOp *>(op_ptr);
 
    const auto nb_in_loop = o->getFEMethod()->nInTheLoop;
    area_map[nb_in_loop] = o->getMeasure();
    side_vals[nb_in_loop] = *u_vals_ptr;
    if (!nb_in_loop) {
      area_map[1] = 0;
      side_vals[1].clear();
    }
 
    MoFEMFunctionReturn(0);
  };
  side_fe_ptr->getOpPtrVector().push_back(side_vals_op);
 
  auto do_work_rhs_error = [&](DataOperator *op_ptr, int side, EntityType type,
                               EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
    auto o = static_cast<BoundaryEleOp *>(op_ptr);
 
    CHKERR o->loopSideFaces("dFE", *side_fe_ptr);
    const auto in_the_loop = side_fe_ptr->nInTheLoop;
 
#ifndef NDEBUG
    const std::array<std::string, 2> ele_type_name = {"BOUNDARY", "SKELETON"};
    MOFEM_LOG("SELF", Sev::noisy)
        << "do_work_rhs_error in_the_loop " << ele_type_name[in_the_loop];
#endif
 
    const double s = o->getMeasure() / (area_map[0] + area_map[1]);
    const double p = penalty * s;
 
    constexpr std::array<int, 2> sign_array{1, -1};
 
    std::array<double, LAST_NORM> error;
    std::fill(error.begin(), error.end(), 0);
 
    const int nb_integration_pts = o->getGaussPts().size2();
 
    if (!in_the_loop) {
      side_vals[1].resize(nb_integration_pts, false);
      auto t_coords = o->getFTensor1CoordsAtGaussPts();
      auto t_val_m = getFTensor0FromVec(side_vals[1]);
      for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
        t_val_m = u_exact(t_coords(0), t_coords(1), t_coords(2));
        ++t_coords;
        ++t_val_m;
      }
    }
 
    auto t_val_p = getFTensor0FromVec(side_vals[0]);
    auto t_val_m = getFTensor0FromVec(side_vals[1]);
    auto t_w = o->getFTensor0IntegrationWeight();
 
    for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
 
      const double alpha = o->getMeasure() * t_w;
      const auto diff = t_val_p - t_val_m;
      error[SEMI_NORM] += alpha * p * diff * diff;
 
      ++t_w;
      ++t_val_p;
      ++t_val_m;
    }
 
 
    error[H1] = error[SEMI_NORM];
    CHKERR VecSetValues(l2_vec, LAST_NORM, error_indices.data(), error.data(),
                        ADD_VALUES);
 
    MoFEMFunctionReturn(0);
  };
 
  auto skeleton_error_op = new BoundaryEleOp(NOSPACE, BoundaryEleOp::OPSPACE);
  skeleton_error_op->doWorkRhsHook = do_work_rhs_error;
  auto boundary_error_op = new BoundaryEleOp(NOSPACE, BoundaryEleOp::OPSPACE);
  boundary_error_op->doWorkRhsHook = do_work_rhs_error;
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(error_op);
  pipeline_mng->getOpSkeletonLhsPipeline().push_back(skeleton_error_op);
  pipeline_mng->getOpBoundaryRhsPipeline().push_back(boundary_error_op);
 
  CHKERR pipeline_mng->loopFiniteElements();
 
  CHKERR VecAssemblyBegin(l2_vec);
  CHKERR VecAssemblyEnd(l2_vec);
 
  if (mField.get_comm_rank() == 0) {
    const double *array;
    CHKERR VecGetArrayRead(l2_vec, &array);
    MOFEM_LOG_C("SELF", Sev::inform, "Error Norm L2 %6.4e",
                std::sqrt(array[L2]));
    MOFEM_LOG_C("SELF", Sev::inform, "Error Norm Energetic %6.4e",
                std::sqrt(array[SEMI_NORM]));
    MOFEM_LOG_C("SELF", Sev::inform, "Error Norm H1 %6.4e",
                std::sqrt(array[H1]));
 
    if(is_test) {
      constexpr double eps = 1e-12;
      if (std::sqrt(array[H1]) > eps)
        SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID, "Error is too big");
    }
                
    CHKERR VecRestoreArrayRead(l2_vec, &array);
    const MoFEM::Problem *problem_ptr;
    CHKERR DMMoFEMGetProblemPtr(simpleInterface->getDM(), &problem_ptr);
    MOFEM_LOG_C("SELF", Sev::inform, "Nb. DOFs %d",
                problem_ptr->getNbDofsRow());
  }
 
 
 
  MoFEMFunctionReturn(0);
}
 
//! [Output results]
MoFEMErrorCode Poisson2DiscontGalerkin::outputResults() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  pipeline_mng->getDomainLhsFE().reset();
  pipeline_mng->getSkeletonRhsFE().reset();
  pipeline_mng->getSkeletonLhsFE().reset();
  pipeline_mng->getBoundaryRhsFE().reset();
  pipeline_mng->getBoundaryLhsFE().reset();
 
  auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
  post_proc_fe->generateReferenceElementMesh();
  post_proc_fe->addFieldValuesPostProc(domainField);
  pipeline_mng->getDomainRhsFE() = post_proc_fe;
  CHKERR pipeline_mng->loopFiniteElements();
  CHKERR post_proc_fe->writeFile("out_result.h5m");
 
  MoFEMFunctionReturn(0);
}
//! [Output results]
 
//! [Run program]
MoFEMErrorCode Poisson2DiscontGalerkin::runProgram() {
  MoFEMFunctionBegin;
 
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR boundaryCondition();
  CHKERR assembleSystem();
  CHKERR setIntegrationRules();
  CHKERR solveSystem();
  CHKERR outputResults();
  CHKERR checkResults();
 
  MoFEMFunctionReturn(0);
}
//! [Run program]
 
//! [Main]
int main(int argc, char *argv[]) {
 
  // Initialisation of MoFEM/PETSc and MOAB data structures
  const char param_file[] = "param_file.petsc";
  MoFEM::Core::Initialize(&argc, &argv, param_file, help);
 
  // Error handling
  try {
    // Register MoFEM discrete manager in PETSc
    DMType dm_name = "DMMOFEM";
    CHKERR DMRegister_MoFEM(dm_name);
 
    // Create MOAB instance
    moab::Core mb_instance;              // mesh database
    moab::Interface &moab = mb_instance; // mesh database interface
 
    // Create MoFEM instance
    MoFEM::Core core(moab);           // finite element database
    MoFEM::Interface &m_field = core; // finite element interface
 
    // Run the main analysis
    Poisson2DiscontGalerkin poisson_problem(m_field);
    CHKERR poisson_problem.runProgram();
  }
  CATCH_ERRORS;
 
  // Finish work: cleaning memory, getting statistics, etc.
  MoFEM::Core::Finalize();
 
  return 0;
}
//! [Main]