approx_sphere.cpp

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/**
 * \file approx_sphere.cpp
 * \example approx_sphere.cpp
 *
 */
 
#include <MoFEM.hpp>
 
using namespace MoFEM;
 
static char help[] = "...\n\n";
 
#include <BasicFiniteElements.hpp>
 
constexpr int FM_DIM = 2;
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = MoFEM::FaceElementForcesAndSourcesCore;
};
 
using DomainEle = ElementsAndOps<FM_DIM>::DomainEle;
using DomainEleOp = DomainEle::UserDataOperator;
using EntData = EntitiesFieldData::EntData;
 
using AssemblyDomainEleOp =
    FormsIntegrators<DomainEleOp>::Assembly<PETSC>::OpBase;
 
constexpr double a = 1;
constexpr double a2 = a * a;
constexpr double a4 = a2 * a2;
 
constexpr double A = 6371220;
 
FTensor::Index<'i', 3> i;
FTensor::Index<'j', 3> j;
FTensor::Index<'k', 3> k;
 
auto res_J = [](const double x, const double y, const double z) {
  const double res = (x * x + y * y + z * z - a2);
  return res;
};
 
auto res_J_dx = [](const double x, const double y, const double z) {
  const double res = res_J(x, y, z);
  return FTensor::Tensor1<double, 3>{res * (2 * x), res * (2 * y),
                                     res * (2 * z)};
};
 
auto lhs_J_dx2 = [](const double x, const double y, const double z) {
  const double res = res_J(x, y, z);
  return FTensor::Tensor2<double, 3, 3>{
 
      (res * 2 + (4 * x * x)),
      (4 * y * x),
      (4 * z * x),
 
      (4 * x * y),
      (2 * res + (4 * y * y)),
      (4 * z * y),
 
      (4 * x * z),
      (4 * y * z),
      (2 * res + (4 * z * z))};
};
 
struct OpRhs : public AssemblyDomainEleOp {
 
  OpRhs(const std::string field_name, boost::shared_ptr<MatrixDouble> x_ptr,
        boost::shared_ptr<MatrixDouble> dot_x_ptr)
      : AssemblyDomainEleOp(field_name, field_name, AssemblyDomainEleOp::OPROW),
        xPtr(x_ptr), xDotPtr(dot_x_ptr) {}
 
  MoFEMErrorCode iNtegrate(EntitiesFieldData::EntData &row_data) {
    MoFEMFunctionBegin;
 
    auto t_w = getFTensor0IntegrationWeight();
    auto t_row_base = row_data.getFTensor0N();
 
    auto t_x0 = getFTensor1CoordsAtGaussPts();
    auto t_x = getFTensor1FromMat<3>(*xPtr);
    auto t_dot_x = getFTensor1FromMat<3>(*xDotPtr);
    auto t_normal = getFTensor1NormalsAtGaussPts();
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<double>();
 
    for (int gg = 0; gg != nbIntegrationPts; gg++) {
 
      constexpr auto t_kd = FTensor::Kronecker_Delta<double>();
      FTensor::Tensor1<double, 3> t_n{t_x0(0), t_x0(1), t_x0(2)};
      t_n.normalize();
      FTensor::Tensor2<double, 3, 3> t_P, t_Q;
      t_P(i, j) = t_n(i) * t_n(j);
      t_Q(i, j) = t_kd(i, j) - t_P(i, j);
 
      auto t_J_res = res_J_dx(t_x(0), t_x(1), t_x(2));
 
      const double alpha = t_w;
      auto t_nf = getFTensor1FromArray<3, 3>(locF);
      double l = std::sqrt(t_normal(i) * t_normal(i));
 
      FTensor::Tensor1<double, 3> t_res;
      t_res(i) =
          alpha * l * ((t_P(i, k) * t_J_res(k) + t_Q(i, k) * t_dot_x(k)));
 
      int rr = 0;
      for (; rr != nbRows / 3; ++rr) {
 
        t_nf(j) += t_row_base * t_res(j);
 
        ++t_row_base;
        ++t_nf;
      }
      for (; rr < nbRowBaseFunctions; ++rr) {
        ++t_row_base;
      }
 
      ++t_w;
      ++t_x;
      ++t_dot_x;
      ++t_x0;
      ++t_normal;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> xPtr;
  boost::shared_ptr<MatrixDouble> xDotPtr;
};
 
struct OpLhs : public AssemblyDomainEleOp {
 
  OpLhs(const std::string field_name, boost::shared_ptr<MatrixDouble> x_ptr,
        boost::shared_ptr<MatrixDouble> dot_x_ptr)
      : AssemblyDomainEleOp(field_name, field_name,
                            AssemblyDomainEleOp::OPROWCOL),
        xPtr(x_ptr), xDotPtr(dot_x_ptr) {
    this->sYmm = false;
  }
 
  MoFEMErrorCode iNtegrate(EntitiesFieldData::EntData &row_data,
                           EntitiesFieldData::EntData &col_data) {
    MoFEMFunctionBegin;
 
    auto t_w = getFTensor0IntegrationWeight();
    auto t_row_base = row_data.getFTensor0N();
 
    auto t_x0 = getFTensor1CoordsAtGaussPts();
    auto t_x = getFTensor1FromMat<3>(*xPtr);
    auto t_dot_x = getFTensor1FromMat<3>(*xDotPtr);
    auto t_normal = getFTensor1NormalsAtGaussPts();
 
    auto get_t_mat = [&](const int rr) {
      return FTensor::Tensor2<FTensor::PackPtr<double *, 3>, 3, 3>{
          &locMat(rr + 0, 0), &locMat(rr + 0, 1), &locMat(rr + 0, 2),
 
          &locMat(rr + 1, 0), &locMat(rr + 1, 1), &locMat(rr + 1, 2),
 
          &locMat(rr + 2, 0), &locMat(rr + 2, 1), &locMat(rr + 2, 2)};
    };
 
    constexpr auto t_kd = FTensor::Kronecker_Delta<double>();
    const double ts_a = getTSa();
 
    for (int gg = 0; gg != nbIntegrationPts; gg++) {
 
      constexpr auto t_kd = FTensor::Kronecker_Delta<double>();
      FTensor::Tensor1<double, 3> t_n{t_x0(0), t_x0(1), t_x0(2)};
      t_n.normalize();
      FTensor::Tensor2<double, 3, 3> t_P, t_Q;
      t_P(i, j) = t_n(i) * t_n(j);
      t_Q(i, j) = t_kd(i, j) - t_P(i, j);
 
      auto t_J_lhs = lhs_J_dx2(t_x(0), t_x(1), t_x(2));
      double l = std::sqrt(t_normal(i) * t_normal(i));
 
      const double alpha = t_w;
      FTensor::Tensor2<double, 3, 3> t_lhs;
      t_lhs(i, j) =
          (alpha * l) * (t_P(i, k) * t_J_lhs(k, j) + t_Q(i, j) * ts_a);
 
      int rr = 0;
      for (; rr != nbRows / 3; rr++) {
 
        auto t_col_base = col_data.getFTensor0N(gg, 0);
        auto t_mat = get_t_mat(3 * rr);
 
        for (int cc = 0; cc != nbCols / 3; cc++) {
 
          const double rc = t_row_base * t_col_base;
          t_mat(i, j) += rc * t_lhs(i, j);
 
          ++t_col_base;
          ++t_mat;
        }
        ++t_row_base;
      }
 
      for (; rr < nbRowBaseFunctions; ++rr)
        ++t_row_base;
 
      ++t_w;
      ++t_x;
      ++t_x0;
      ++t_normal;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<MatrixDouble> xPtr;
  boost::shared_ptr<MatrixDouble> xDotPtr;
};
 
struct OpError : public DomainEleOp {
 
  OpError(const std::string field_name, boost::shared_ptr<MatrixDouble> x_ptr)
      : DomainEleOp(field_name, field_name, AssemblyDomainEleOp::OPROW),
        xPtr(x_ptr) {
 
    std::fill(&doEntities[MBEDGE], &doEntities[MBMAXTYPE], false);
  }
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
 
    MoFEMFunctionBegin;
 
    auto t_w = getFTensor0IntegrationWeight();
    auto t_x = getFTensor1FromMat<3>(*xPtr);
    auto t_normal = getFTensor1NormalsAtGaussPts();
    auto nb_integration_pts = getGaussPts().size2();
 
    double error = 0;
 
    for (int gg = 0; gg != nb_integration_pts; gg++) {
 
      double l = std::sqrt(t_normal(i) * t_normal(i));
      error += t_w * l * std::abs((t_x(i) * t_x(i) - A * A));
 
      ++t_w;
      ++t_x;
      ++t_normal;
    }
 
    CHKERR VecSetValue(errorVec, 0, error, ADD_VALUES);
 
    MoFEMFunctionReturn(0);
  }
 
  static SmartPetscObj<Vec> errorVec;
 
private:
  boost::shared_ptr<MatrixDouble> xPtr;
};
 
SmartPetscObj<Vec> OpError::errorVec;
 
struct ApproxSphere {
 
  ApproxSphere(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
private:
  MoFEM::Interface &mField;
 
  MoFEMErrorCode getOptions();
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode setOPs();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode outputResults();
};
 
//! [Run programme]
MoFEMErrorCode ApproxSphere::runProblem() {
  MoFEMFunctionBegin;
  CHKERR getOptions();
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR setOPs();
  CHKERR solveSystem();
  CHKERR outputResults();
  MoFEMFunctionReturn(0);
}
//! [Run programme]
 
MoFEMErrorCode ApproxSphere::getOptions() {
  MoFEMFunctionBeginHot;
  MoFEMFunctionReturnHot(0);
}
 
//! [Read mesh]
MoFEMErrorCode ApproxSphere::readMesh() {
  MoFEMFunctionBegin;
  auto simple = mField.getInterface<Simple>();
  CHKERR simple->getOptions();
  CHKERR simple->loadFile();
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Set up problem]
MoFEMErrorCode ApproxSphere::setupProblem() {
  MoFEMFunctionBegin;
 
  auto simple = mField.getInterface<Simple>();
  CHKERR simple->addDomainField("HO_POSITIONS", H1, AINSWORTH_LEGENDRE_BASE, 3);
  CHKERR simple->addDataField("HO_POSITIONS", H1, AINSWORTH_LEGENDRE_BASE, 3);
 
  int order = 3;
  CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &order, PETSC_NULL);
  CHKERR simple->setFieldOrder("HO_POSITIONS", order);
  CHKERR simple->setUp();
 
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Push operators to pipeline]
MoFEMErrorCode ApproxSphere::setOPs() {
  MoFEMFunctionBegin;
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto integration_rule = [](int, int, int approx_order) {
    return 3 * approx_order;
  };
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
 
  auto x_ptr = boost::make_shared<MatrixDouble>();
  auto dot_x_ptr = boost::make_shared<MatrixDouble>();
  auto det_ptr = boost::make_shared<VectorDouble>();
  auto jac_ptr = boost::make_shared<MatrixDouble>();
  auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
 
  auto def_ops = [&](auto &pipeline) {
    pipeline.push_back(
        new OpCalculateVectorFieldValues<3>("HO_POSITIONS", x_ptr));
    pipeline.push_back(
        new OpCalculateVectorFieldValuesDot<3>("HO_POSITIONS", dot_x_ptr));
  };
 
  def_ops(pipeline_mng->getOpDomainRhsPipeline());
  def_ops(pipeline_mng->getOpDomainLhsPipeline());
 
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpRhs("HO_POSITIONS", x_ptr, dot_x_ptr));
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpLhs("HO_POSITIONS", x_ptr, dot_x_ptr));
 
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
//! [Solve]
MoFEMErrorCode ApproxSphere::solveSystem() {
  MoFEMFunctionBegin;
 
  // Project HO geometry from mesh
  Projection10NodeCoordsOnField ent_method_material(mField, "HO_POSITIONS");
  CHKERR mField.loop_dofs("HO_POSITIONS", ent_method_material);
 
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto dm = simple->getDM();
  MoFEM::SmartPetscObj<TS> ts;
  ts = pipeline_mng->createTSIM();
 
  double ftime = 1;
  CHKERR TSSetMaxSteps(ts, 1);
  CHKERR TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
 
  auto T = smartCreateDMVector(simple->getDM());
  CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                 SCATTER_FORWARD);
  CHKERR TSSetSolution(ts, T);
  CHKERR TSSetFromOptions(ts);
 
  CHKERR TSSolve(ts, NULL);
  CHKERR TSGetTime(ts, &ftime);
 
  CHKERR mField.getInterface<FieldBlas>()->fieldScale(A, "HO_POSITIONS");
 
  MoFEMFunctionReturn(0);
}
 
//! [Solve]
MoFEMErrorCode ApproxSphere::outputResults() {
  MoFEMFunctionBegin;
 
  auto x_ptr = boost::make_shared<MatrixDouble>();
  auto det_ptr = boost::make_shared<VectorDouble>();
  auto jac_ptr = boost::make_shared<MatrixDouble>();
  auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
 
  auto simple = mField.getInterface<Simple>();
  auto dm = simple->getDM();
 
  auto post_proc_fe =
      boost::make_shared<PostProcBrokenMeshInMoab<DomainEle>>(mField);
 
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldValues<3>("HO_POSITIONS", x_ptr));
 
  using OpPPMap = OpPostProcMapInMoab<3, 3>;
 
  post_proc_fe->getOpPtrVector().push_back(
 
      new OpPPMap(post_proc_fe->getPostProcMesh(),
                  post_proc_fe->getMapGaussPts(),
 
                  {},
 
                  {{"HO_POSITIONS", x_ptr}},
 
                  {}, {}
 
                  )
 
  );
 
  CHKERR DMoFEMLoopFiniteElements(dm, "dFE", post_proc_fe);
  CHKERR post_proc_fe->writeFile("out_approx.h5m");
 
  auto error_fe = boost::make_shared<DomainEle>(mField);
 
  error_fe->getOpPtrVector().push_back(
      new OpGetHONormalsOnFace("HO_POSITIONS"));
  error_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldValues<3>("HO_POSITIONS", x_ptr));
  error_fe->getOpPtrVector().push_back(new OpError("HO_POSITIONS", x_ptr));
 
  error_fe->preProcessHook = [&]() {
    MoFEMFunctionBegin;
    MOFEM_LOG("EXAMPLE", Sev::inform) << "Create vec ";
    OpError::errorVec = createSmartVectorMPI(
        mField.get_comm(), (!mField.get_comm_rank()) ? 1 : 0, 1);
    VecZeroEntries(OpError::errorVec);
    MoFEMFunctionReturn(0);
  };
 
  error_fe->postProcessHook = [&]() {
    MoFEMFunctionBegin;
    CHKERR VecAssemblyBegin(OpError::errorVec);
    CHKERR VecAssemblyEnd(OpError::errorVec);
    double error2;
    CHKERR VecSum(OpError::errorVec, &error2);
    MOFEM_LOG("EXAMPLE", Sev::inform)
        << "Error " << std::sqrt(error2 / (4 * M_PI * A * A));
    OpError::errorVec.reset();
    MoFEMFunctionReturn(0);
  };
 
  CHKERR DMoFEMLoopFiniteElements(dm, "dFE", error_fe);
 
  CHKERR simple->deleteDM();
  CHKERR simple->deleteFiniteElements();
  if (mField.get_comm_size() > 1)
    CHKERR mField.get_moab().write_file("out_ho_mesh.h5m", "MOAB",
                                        "PARALLEL=WRITE_PART");
  else
    CHKERR mField.get_moab().write_file("out_ho_mesh.h5m");
  MoFEMFunctionReturn(0);
}
//! [Postprocess results]
 
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);
 
  auto core_log = logging::core::get();
  core_log->add_sink(
      LogManager::createSink(LogManager::getStrmWorld(), "EXAMPLE"));
  LogManager::setLog("EXAMPLE");
  MOFEM_LOG_TAG("EXAMPLE", "example");
 
  try {
 
    //! [Register MoFEM discrete manager in PETSc]
    DMType dm_name = "DMMOFEM";
    CHKERR DMRegister_MoFEM(dm_name);
    //! [Register MoFEM discrete manager in PETSc
 
    //! [Create MoAB]
    moab::Core mb_instance;              ///< mesh database
    moab::Interface &moab = mb_instance; ///< mesh database interface
    //! [Create MoAB]
 
    //! [Create MoFEM]
    MoFEM::Core core(moab);           ///< finite element database
    MoFEM::Interface &m_field = core; ///< finite element database insterface
    //! [Create MoFEM]
 
    //! [ApproxSphere]
    ApproxSphere ex(m_field);
    CHKERR ex.runProblem();
    //! [ApproxSphere]
  }
  CATCH_ERRORS;
 
  MoFEM::Core::Finalize();
}