nonlinear_elastic.cpp

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/**
 * \file nonlinear_elastic.cpp
 * \example nonlinear_elastic.cpp
 *
 * Plane stress elastic dynamic problem
 *
 */
 
#include <MoFEM.hpp>
#include <MatrixFunction.hpp>
 
using namespace MoFEM;
 
constexpr int SPACE_DIM =
    EXECUTABLE_DIMENSION; //< Space dimension of problem, mesh
 
using EntData = EntitiesFieldData::EntData;
using DomainEle = PipelineManager::ElementsAndOpsByDim<SPACE_DIM>::DomainEle;
using BoundaryEle =
    PipelineManager::ElementsAndOpsByDim<SPACE_DIM>::BoundaryEle;
using DomainEleOp = DomainEle::UserDataOperator;
using BoundaryEleOp = BoundaryEle::UserDataOperator;
 
using DomainNaturalBC =
    NaturalBC<DomainEleOp>::Assembly<PETSC>::LinearForm<GAUSS>;
using OpBodyForce =
    DomainNaturalBC::OpFlux<NaturalMeshsetType<BLOCKSET>, 1, SPACE_DIM>;
 
using BoundaryNaturalBC =
    NaturalBC<BoundaryEleOp>::Assembly<PETSC>::LinearForm<GAUSS>;
using OpForce = BoundaryNaturalBC::OpFlux<NaturalForceMeshsets, 1, SPACE_DIM>;
 
template <int DIM> struct PostProcEleByDim;
 
template <> struct PostProcEleByDim<2> {
  using PostProcEleDomain = PostProcBrokenMeshInMoabBase<DomainEle>;
  using PostProcEleBdy = PostProcBrokenMeshInMoabBase<BoundaryEle>;
  using SideEle = PipelineManager::ElementsAndOpsByDim<2>::FaceSideEle;
};
 
template <> struct PostProcEleByDim<3> {
  using PostProcEleDomain = PostProcBrokenMeshInMoabBase<DomainEle>;
  using PostProcEleBdy = PostProcBrokenMeshInMoabBase<BoundaryEle>;
  using SideEle = PipelineManager::ElementsAndOpsByDim<3>::FaceSideEle;
};
 
using SideEle = PostProcEleByDim<SPACE_DIM>::SideEle;
using PostProcEleBdy = PostProcEleByDim<SPACE_DIM>::PostProcEleBdy;
using PostProcEleDomain = PostProcEleByDim<SPACE_DIM>::PostProcEleDomain;
using PostProcEdges =
    PostProcBrokenMeshInMoabBase<EdgeElementForcesAndSourcesCore>;
 
#include <HenckyOps.hpp>
using namespace HenckyOps;
 
struct Example {
 
  Example(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
private:
  MoFEM::Interface &mField;
  boost::shared_ptr<DomainEle> reactionFe;
 
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode gettingNorms();
  MoFEMErrorCode outputResults();
  MoFEMErrorCode checkResults();
};
 
//! [Run problem]
MoFEMErrorCode Example::runProblem() {
  MoFEMFunctionBegin;
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR boundaryCondition();
  CHKERR assembleSystem();
  CHKERR solveSystem();
  CHKERR gettingNorms();
  CHKERR outputResults();
  CHKERR checkResults();
  MoFEMFunctionReturn(0);
}
//! [Run problem]
 
//! [Read mesh]
MoFEMErrorCode Example::readMesh() {
  MoFEMFunctionBegin;
  auto simple = mField.getInterface<Simple>();
  CHKERR simple->getOptions();
  CHKERR simple->loadFile();
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Set up problem]
MoFEMErrorCode Example::setupProblem() {
  MoFEMFunctionBegin;
  Simple *simple = mField.getInterface<Simple>();
 
  enum bases { AINSWORTH, DEMKOWICZ, LASBASETOPT };
  const char *list_bases[LASBASETOPT] = {"ainsworth", "demkowicz"};
  PetscInt choice_base_value = AINSWORTH;
  CHKERR PetscOptionsGetEList(PETSC_NULLPTR, NULL, "-base", list_bases,
                              LASBASETOPT, &choice_base_value, PETSC_NULLPTR);
 
  FieldApproximationBase base;
  switch (choice_base_value) {
  case AINSWORTH:
    base = AINSWORTH_LEGENDRE_BASE;
    MOFEM_LOG("WORLD", Sev::inform)
        << "Set AINSWORTH_LEGENDRE_BASE for displacements";
    break;
  case DEMKOWICZ:
    base = DEMKOWICZ_JACOBI_BASE;
    MOFEM_LOG("WORLD", Sev::inform)
        << "Set DEMKOWICZ_JACOBI_BASE for displacements";
    break;
  default:
    base = LASTBASE;
    break;
  }
 
  // Add field
  CHKERR simple->addDomainField("U", H1, base, SPACE_DIM);
  CHKERR simple->addBoundaryField("U", H1, base, SPACE_DIM);
  int order = 2;
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-order", &order, PETSC_NULLPTR);
  CHKERR simple->setFieldOrder("U", order);
  CHKERR simple->setUp();
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Boundary condition]
MoFEMErrorCode Example::boundaryCondition() {
  MoFEMFunctionBegin;
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
  auto simple = mField.getInterface<Simple>();
  auto bc_mng = mField.getInterface<BcManager>();
  auto time_scale = boost::make_shared<TimeScale>();
 
  auto integration_rule = [](int, int, int approx_order) {
    return 2 * (approx_order - 1);
  };
 
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(integration_rule);
  CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(integration_rule);
 
  reactionFe = boost::make_shared<DomainEle>(mField);
  reactionFe->getRuleHook = integration_rule;
 
  CHKERR BoundaryNaturalBC::AddFluxToPipeline<OpForce>::add(
      pipeline_mng->getOpBoundaryRhsPipeline(), mField, "U", {time_scale},
      "FORCE", Sev::inform);
 
  //! [Define gravity vector]
  CHKERR DomainNaturalBC::AddFluxToPipeline<OpBodyForce>::add(
      pipeline_mng->getOpDomainRhsPipeline(), mField, "U", {time_scale},
      "BODY_FORCE", Sev::inform);
 
  // Essential BC
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_X",
                                           "U", 0, 0);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_Y",
                                           "U", 1, 1);
  CHKERR bc_mng->removeBlockDOFsOnEntities(simple->getProblemName(), "REMOVE_Z",
                                           "U", 2, 2);
  CHKERR bc_mng->pushMarkDOFsOnEntities<DisplacementCubitBcData>(
      simple->getProblemName(), "U");
 
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode Example::assembleSystem() {
  MoFEMFunctionBegin;
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto add_domain_ops_lhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1});
    CHKERR HenckyOps::opFactoryDomainLhs<SPACE_DIM, PETSC, GAUSS, DomainEleOp>(
        mField, pip, "U", "MAT_ELASTIC", Sev::inform);
    MoFEMFunctionReturn(0);
  };
 
  auto add_domain_ops_rhs = [&](auto &pip) {
    MoFEMFunctionBegin;
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip, {H1});
    CHKERR HenckyOps::opFactoryDomainRhs<SPACE_DIM, PETSC, GAUSS, DomainEleOp>(
        mField, pip, "U", "MAT_ELASTIC", Sev::inform);
    MoFEMFunctionReturn(0);
  };
 
  CHKERR add_domain_ops_lhs(pipeline_mng->getOpDomainLhsPipeline());
  CHKERR add_domain_ops_rhs(pipeline_mng->getOpDomainRhsPipeline());
 
  // push operators to reaction pipeline
  CHKERR add_domain_ops_rhs(reactionFe->getOpPtrVector());
  reactionFe->postProcessHook =
      EssentialPreProcReaction<DisplacementCubitBcData>(mField, reactionFe);
 
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
/**
 * @brief Monitor solution
 *
 * This functions is called by TS solver at the end of each step. It is used
 * to output results to the hard drive.
 */
struct Monitor : public FEMethod {
  Monitor(SmartPetscObj<DM> dm,
          std::pair<boost::shared_ptr<PostProcEleDomain>,
                                boost::shared_ptr<PostProcEleBdy>>
              pair_post_proc,
          boost::shared_ptr<DomainEle> reaction_fe)
      : dM(dm), postProcDomain(pair_post_proc.first), postProcSkin(pair_post_proc.second),
        reactionFe(reaction_fe) {
    CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-save_every", &saveEvery,
                              PETSC_NULLPTR);
  }
  MoFEMErrorCode postProcess() {
    MoFEMFunctionBegin;
 
    auto make_vtk = [&]() {
      MoFEMFunctionBegin;
      if (postProcDomain) {
        CHKERR DMoFEMLoopFiniteElements(dM, "dFE", postProcDomain,
                                        getCacheWeakPtr());
        CHKERR postProcDomain->writeFile(
            "out_step_" + boost::lexical_cast<std::string>(ts_step) + ".h5m");
      }
      if (postProcSkin) {
        CHKERR DMoFEMLoopFiniteElements(dM, "bFE", postProcSkin,
                                        getCacheWeakPtr());
        CHKERR postProcSkin->writeFile(
            "out_skin_" + boost::lexical_cast<std::string>(ts_step) + ".h5m");
      }
      MoFEMFunctionReturn(0);
    };
 
    auto calculate_reaction = [&]() {
      MoFEMFunctionBegin;
      auto r = createDMVector(dM);
      reactionFe->f = r;
      CHKERR VecZeroEntries(r);
      CHKERR DMoFEMLoopFiniteElements(dM, "dFE", reactionFe, getCacheWeakPtr());
      MoFEMFunctionReturn(0);
    };
 
    if (!(ts_step % saveEvery)) {
      CHKERR make_vtk();
    }
    if (reactionFe)
      CHKERR calculate_reaction();
 
    MoFEMFunctionReturn(0);
  }
 
private:
  SmartPetscObj<DM> dM;
  boost::shared_ptr<PostProcEleDomain> postProcDomain;
  boost::shared_ptr<PostProcEleBdy> postProcSkin;
  boost::shared_ptr<DomainEle> reactionFe;
  PetscInt saveEvery = 1;
};
 
//! [Solve]
MoFEMErrorCode Example::solveSystem() {
  MoFEMFunctionBegin;
  auto *simple = mField.getInterface<Simple>();
  auto *pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto dm = simple->getDM();
  auto ts = pipeline_mng->createTSIM();
 
  PetscBool post_proc_vol;
  PetscBool post_proc_skin;
 
  if constexpr (SPACE_DIM == 2) {
    post_proc_vol = PETSC_TRUE;
    post_proc_skin = PETSC_FALSE;
  } else {
    post_proc_vol = PETSC_FALSE;
    post_proc_skin = PETSC_TRUE;
  }
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_vol", &post_proc_vol,
                             PETSC_NULLPTR);
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-post_proc_skin", &post_proc_skin,
                             PETSC_NULLPTR);
 
  // Setup postprocessing
  auto create_post_proc_fe = [dm, this, simple, post_proc_vol,
                              post_proc_skin]() {
    auto post_proc_ele_domain = [dm, this](auto &pip_domain) {
      CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pip_domain, {H1});
      auto common_ptr = commonDataFactory<SPACE_DIM, GAUSS, DomainEleOp>(
          mField, pip_domain, "U", "MAT_ELASTIC", Sev::inform);
      return common_ptr;
    };
 
    auto post_proc_map = [this](auto &pip, auto u_ptr, auto common_ptr) {
      MoFEMFunctionBegin;
 
      using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
 
      pip->getOpPtrVector().push_back(
 
          new OpPPMap(pip->getPostProcMesh(), pip->getMapGaussPts(), {},
                      {{"U", u_ptr}},
                      {{"GRAD", common_ptr->matGradPtr},
                       {"FIRST_PIOLA", common_ptr->getMatFirstPiolaStress()}},
                      {}));
      MoFEMFunctionReturn(0);
    };
 
    auto push_post_proc_bdy = [dm, this, simple, post_proc_skin,
                               &post_proc_ele_domain,
                               &post_proc_map](auto &pip_bdy) {
      if (post_proc_skin == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleBdy>();
 
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_bdy->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      auto op_loop_side =
          new OpLoopSide<SideEle>(mField, simple->getDomainFEName(), SPACE_DIM);
      auto common_ptr = post_proc_ele_domain(op_loop_side->getOpPtrVector());
      pip_bdy->getOpPtrVector().push_back(op_loop_side);
 
      CHKERR post_proc_map(pip_bdy, u_ptr, common_ptr);
 
      return pip_bdy;
    };
 
    auto push_post_proc_domain = [dm, this, simple, post_proc_vol,
                                  &post_proc_ele_domain,
                                  &post_proc_map](auto &pip_domain) {
      if (post_proc_vol == PETSC_FALSE)
        return boost::shared_ptr<PostProcEleDomain>();
 
      auto u_ptr = boost::make_shared<MatrixDouble>();
      pip_domain->getOpPtrVector().push_back(
          new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
      auto common_ptr = post_proc_ele_domain(pip_domain->getOpPtrVector());
 
      CHKERR post_proc_map(pip_domain, u_ptr, common_ptr);
 
      return pip_domain;
    };
 
    auto post_proc_fe_domain = boost::make_shared<PostProcEleDomain>(mField);
    auto post_proc_fe_bdy = boost::make_shared<PostProcEleBdy>(mField);
 
    return std::make_pair(push_post_proc_domain(post_proc_fe_domain),
                          push_post_proc_bdy(post_proc_fe_bdy));
  };
 
  auto add_extra_finite_elements_to_ksp_solver_pipelines = [&]() {
    MoFEMFunctionBegin;
 
    auto pre_proc_ptr = boost::make_shared<FEMethod>();
    auto post_proc_rhs_ptr = boost::make_shared<FEMethod>();
    auto post_proc_lhs_ptr = boost::make_shared<FEMethod>();
 
    auto time_scale = boost::make_shared<TimeScale>();
 
    auto get_bc_hook_rhs = [this, pre_proc_ptr, time_scale]() {
      MoFEMFunctionBeginHot;
      CHKERR EssentialPreProc<DisplacementCubitBcData>(mField, pre_proc_ptr,
                                                       {time_scale}, false)();
      MoFEMFunctionReturnHot(0);
    };
 
    pre_proc_ptr->preProcessHook = get_bc_hook_rhs;
 
    auto get_post_proc_hook_rhs = [this, post_proc_rhs_ptr]() {
      MoFEMFunctionBegin;
      CHKERR EssentialPreProcReaction<DisplacementCubitBcData>(
          mField, post_proc_rhs_ptr, nullptr, Sev::verbose)();
      CHKERR EssentialPostProcRhs<DisplacementCubitBcData>(
          mField, post_proc_rhs_ptr, 1.)();
      MoFEMFunctionReturn(0);
    };
    auto get_post_proc_hook_lhs = [this, post_proc_lhs_ptr]() {
      MoFEMFunctionBegin;
      CHKERR EssentialPostProcLhs<DisplacementCubitBcData>(
          mField, post_proc_lhs_ptr, 1.)();
      MoFEMFunctionReturn(0);
    };
    post_proc_rhs_ptr->postProcessHook = get_post_proc_hook_rhs;
    post_proc_lhs_ptr->postProcessHook = get_post_proc_hook_lhs;
 
    // This is low level pushing finite elements (pipelines) to solver
    auto ts_ctx_ptr = getDMTsCtx(simple->getDM());
    ts_ctx_ptr->getPreProcessIFunction().push_front(pre_proc_ptr);
    ts_ctx_ptr->getPreProcessIJacobian().push_front(pre_proc_ptr);
    ts_ctx_ptr->getPostProcessIFunction().push_back(post_proc_rhs_ptr);
    ts_ctx_ptr->getPostProcessIJacobian().push_back(post_proc_lhs_ptr);
    MoFEMFunctionReturn(0);
  };
 
  // Add extra finite elements to SNES solver pipelines to resolve essential
  // boundary conditions
  CHKERR add_extra_finite_elements_to_ksp_solver_pipelines();
 
  auto create_monitor_fe = [dm](auto &&post_proc_fe, auto &&reactionFe) {
    return boost::make_shared<Monitor>(dm, post_proc_fe, reactionFe);
  };
 
  // Set monitor which postprocessing results and saves them to the hard drive
  boost::shared_ptr<FEMethod> null_fe;
  auto monitor_ptr = create_monitor_fe(create_post_proc_fe(), reactionFe);
  CHKERR DMMoFEMTSSetMonitor(dm, ts, simple->getDomainFEName(), null_fe,
                             null_fe, monitor_ptr);
 
  // Set time solver
  double ftime = 1;
  CHKERR TSSetMaxTime(ts, ftime);
  CHKERR TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
 
  auto B = createDMMatrix(dm);
  CHKERR TSSetI2Jacobian(ts, B, B, PETSC_NULLPTR, PETSC_NULLPTR);
  auto D = createDMVector(simple->getDM());
  CHKERR TSSetSolution(ts, D);
  CHKERR TSSetFromOptions(ts);
 
  CHKERR TSSolve(ts, NULL);
  CHKERR TSGetTime(ts, &ftime);
 
  PetscInt steps, snesfails, rejects, nonlinits, linits;
  CHKERR TSGetStepNumber(ts, &steps);
  CHKERR TSGetSNESFailures(ts, &snesfails);
  CHKERR TSGetStepRejections(ts, &rejects);
  CHKERR TSGetSNESIterations(ts, &nonlinits);
  CHKERR TSGetKSPIterations(ts, &linits);
  MOFEM_LOG_C("EXAMPLE", Sev::inform,
              "steps %d (%d rejected, %d SNES fails), ftime %g, nonlinits "
              "%d, linits %d",
              steps, rejects, snesfails, ftime, nonlinits, linits);
 
  MoFEMFunctionReturn(0);
}
//! [Solve]
 
//! [Getting norms]
MoFEMErrorCode Example::gettingNorms() {
  MoFEMFunctionBegin;
 
  auto simple = mField.getInterface<Simple>();
  auto dm = simple->getDM();
 
  auto T = createDMVector(simple->getDM());
  CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                 SCATTER_FORWARD);
  double nrm2;
  CHKERR VecNorm(T, NORM_2, &nrm2);
  MOFEM_LOG("EXAMPLE", Sev::inform) << "Solution norm " << nrm2;
 
  auto post_proc_norm_fe = boost::make_shared<DomainEle>(mField);
 
  auto post_proc_norm_rule_hook = [](int, int, int p) -> int { return 2 * p; };
  post_proc_norm_fe->getRuleHook = post_proc_norm_rule_hook;
 
  CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(
      post_proc_norm_fe->getOpPtrVector(), {H1});
 
  enum NORMS { U_NORM_L2 = 0, PIOLA_NORM, LAST_NORM };
  auto norms_vec =
      createVectorMPI(mField.get_comm(),
                      (mField.get_comm_rank() == 0) ? LAST_NORM : 0, LAST_NORM);
  CHKERR VecZeroEntries(norms_vec);
 
  auto u_ptr = boost::make_shared<MatrixDouble>();
  post_proc_norm_fe->getOpPtrVector().push_back(
      new OpCalculateVectorFieldValues<SPACE_DIM>("U", u_ptr));
 
  post_proc_norm_fe->getOpPtrVector().push_back(
      new OpCalcNormL2Tensor1<SPACE_DIM>(u_ptr, norms_vec, U_NORM_L2));
 
  auto common_ptr = commonDataFactory<SPACE_DIM, GAUSS, DomainEleOp>(
      mField, post_proc_norm_fe->getOpPtrVector(), "U", "MAT_ELASTIC",
      Sev::inform);
 
  post_proc_norm_fe->getOpPtrVector().push_back(
      new OpCalcNormL2Tensor2<SPACE_DIM, SPACE_DIM>(
          common_ptr->getMatFirstPiolaStress(), norms_vec, PIOLA_NORM));
 
  CHKERR DMoFEMLoopFiniteElements(dm, simple->getDomainFEName(),
                                  post_proc_norm_fe);
 
  CHKERR VecAssemblyBegin(norms_vec);
  CHKERR VecAssemblyEnd(norms_vec);
 
  MOFEM_LOG_CHANNEL("SELF"); // Clear channel from old tags
  if (mField.get_comm_rank() == 0) {
    const double *norms;
    CHKERR VecGetArrayRead(norms_vec, &norms);
    MOFEM_TAG_AND_LOG("SELF", Sev::inform, "example")
        << "norm_u: " << std::scientific << std::sqrt(norms[U_NORM_L2]);
    MOFEM_TAG_AND_LOG("SELF", Sev::inform, "example")
        << "norm_piola: " << std::scientific << std::sqrt(norms[PIOLA_NORM]);
    CHKERR VecRestoreArrayRead(norms_vec, &norms);
  }
 
  MoFEMFunctionReturn(0);
}
//! [Getting norms]
 
//! [Postprocessing results]
MoFEMErrorCode Example::outputResults() {
  MoFEMFunctionBegin;
  PetscInt test_nb = 0;
  PetscBool test_flg = PETSC_FALSE;
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-test", &test_nb, &test_flg);
 
  if (test_flg) {
    auto simple = mField.getInterface<Simple>();
    auto T = createDMVector(simple->getDM());
    CHKERR DMoFEMMeshToLocalVector(simple->getDM(), T, INSERT_VALUES,
                                   SCATTER_FORWARD);
    double nrm2;
    CHKERR VecNorm(T, NORM_2, &nrm2);
    MOFEM_LOG("EXAMPLE", Sev::verbose) << "Regression norm " << nrm2;
    double regression_value = 0;
    switch (test_nb) {
    case 1:
      regression_value = 1.02789;
      break;
    case 2:
      regression_value = 1.8841e+00;
      break;
    case 3:
      regression_value = 1.8841e+00;
      break;
    case 4: // just links
      regression_value = 4.9625e+00;
      break;
    case 5: // link master 
      regression_value = 6.6394e+00;
      break;
    case 6: // link master swap
      regression_value = 4.98764e+00;
      break;
    case 7: // link Y
      regression_value = 4.9473e+00;
      break;
    case 8: // link_3D_repr
      regression_value = 2.5749e-01;
      break;
 
    default:
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID, "Wrong test number.");
      break;
    }
    if (fabs(nrm2 - regression_value) > 1e-2)
      SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
               "Regression test field; wrong norm value. %6.4e != %6.4e", nrm2,
               regression_value);
  }
  MoFEMFunctionReturn(0);
}
//! [Postprocessing results]
 
//! [Check]
MoFEMErrorCode Example::checkResults() {
  MoFEMFunctionBegin;
  MoFEMFunctionReturn(0);
}
//! [Check]
 
static char help[] = "...\n\n";
 
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);
 
  // Add logging channel for example
  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 interface
    //! [Create MoFEM]
 
    //! [Example]
    Example ex(m_field);
    CHKERR ex.runProblem();
    //! [Example]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
}