electrostatics.cpp

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/**
 * @file Electrostatics.cpp
 * \example mofem/tutorials/scl-12_electrostatics/electrostatics.cpp
 *  */
 
#ifndef EXECUTABLE_DIMENSION
#define EXECUTABLE_DIMENSION 3
#endif
 
#include <electrostatics.hpp>
static char help[] = "...\n\n";
struct Electrostatics {
public:
  Electrostatics(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 setIntegrationRules();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode outputResults();
  MoFEMErrorCode getTotalEnergy();
  MoFEMErrorCode getElectrodeCharge();
 
  int oRder = 2;      // default order
  int geomOrder = 1; // default gemoetric order
  MoFEM::Interface &mField;
  Simple *simpleInterface;
  std::string domainField;
  boost::shared_ptr<std::map<int, BlockData>> permBlockSetsPtr;
  boost::shared_ptr<std::map<int, BlockData>> intBlockSetsPtr;
  boost::shared_ptr<std::map<int, BlockData>> electrodeBlockSetsPtr;
  boost::shared_ptr<DataAtIntegrationPts> commonDataPtr;
 
  boost::shared_ptr<ForcesAndSourcesCore> interFaceRhsFe;
  boost::shared_ptr<ForcesAndSourcesCore> electrodeRhsFe;
 
  double aLpha = 0.0; // declaration for total charge on first electrode
  double bEta = 0.0;  // declaration for total charge on second electrode
  SmartPetscObj<Vec> petscVec;       // petsc vector for the charge solution
  SmartPetscObj<Vec> petscVecEnergy; // petsc vector for the energy solution
  PetscBool out_skin = PETSC_FALSE;  //
  PetscBool is_partitioned = PETSC_FALSE;
  enum VecElements { ZERO = 0, ONE = 1, LAST_ELEMENT };
  int atomTest = 0;
};
 
Electrostatics::Electrostatics(MoFEM::Interface &m_field)
    : domainField("POTENTIAL"), mField(m_field) {}
 
//! [Read mesh]
MoFEMErrorCode Electrostatics::readMesh() {
  MoFEMFunctionBegin;
  CHKERR mField.getInterface(simpleInterface);
  CHKERR simpleInterface->getOptions();
 
  simpleInterface->getAddSkeletonFE() =
      true; // create lower dimensional element to ensure sharing of partitioed
            // entities at the boundaries.
  CHKERR JsonConfigManager::addCanonicalAttributeNames(
      {"permittivity", "charge_density"});
  CHKERR simpleInterface->loadFile();
  CHKERR mField.getInterface<MeshsetsManager>()->setMeshsetFromFile();
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Setup problem]
MoFEMErrorCode Electrostatics::setupProblem() {
  MoFEMFunctionBegin;
 
  Range domain_ents;
  CHKERR mField.get_moab().get_entities_by_dimension(0, SPACE_DIM, domain_ents,
                                                     true);
  auto get_ents_by_dim = [&](const auto dim) {
    if (dim == SPACE_DIM) {
      return domain_ents;
    } else {
      Range ents;
      if (dim == 0)
        CHKERR mField.get_moab().get_connectivity(domain_ents, ents, true);
      else
        CHKERR mField.get_moab().get_entities_by_dimension(0, dim, ents, true);
      return ents;
    }
  };
 
  // Select base for the field based on the element type
  auto get_base = [&]() {
    auto domain_ents = get_ents_by_dim(SPACE_DIM);
    if (domain_ents.empty())
      CHK_THROW_MESSAGE(MOFEM_NOT_FOUND, "Empty mesh");
    const auto type = type_from_handle(domain_ents[0]);
    switch (type) {
    case MBQUAD:
      return DEMKOWICZ_JACOBI_BASE;
    case MBHEX:
      return DEMKOWICZ_JACOBI_BASE;
    case MBTRI:
      return AINSWORTH_LEGENDRE_BASE;
    case MBTET:
      return AINSWORTH_LEGENDRE_BASE;
    default:
      CHK_THROW_MESSAGE(MOFEM_NOT_FOUND, "Element type is not handled");
    }
    return NOBASE;
  };
 
  auto base = get_base();
  CHKERR simpleInterface->addDomainField(domainField, H1, base, 1);
  CHKERR simpleInterface->addBoundaryField(domainField, H1, base, 1);
 
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-order", &oRder, PETSC_NULLPTR);
 
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-geom_order", &geomOrder,
                            PETSC_NULLPTR);
 
  CHKERR PetscOptionsGetInt(PETSC_NULLPTR, "", "-atom_test", &atomTest,
                            PETSC_NULLPTR);
  CHKERR simpleInterface->setFieldOrder(domainField, oRder);
  CHKERR simpleInterface->addDataField("GEOMETRY", H1, base, SPACE_DIM);
  CHKERR simpleInterface->setFieldOrder("GEOMETRY", geomOrder);
 
  auto project_ho_geometry = [&]() {
    Projection10NodeCoordsOnField ent_method(mField, "GEOMETRY");
    return mField.loop_dofs("GEOMETRY", ent_method);
  };
 
  CHKERR simpleInterface->setUp();
  CHKERR project_ho_geometry();
 
  commonDataPtr = boost::make_shared<DataAtIntegrationPts>(mField);
 
  // gets the map of the permittivity attributes and the block sets
  permBlockSetsPtr = boost::make_shared<std::map<int, BlockData>>();
  Range mat_electr_ents; // range of entities with the permittivity
  for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, bit)) {
    if (bit->getName().compare(0, 12, "MAT_ELECTRIC") == 0) {
      const int id = bit->getMeshsetId();
      auto &block_data = (*permBlockSetsPtr)[id];
 
      CHKERR mField.get_moab().get_entities_by_dimension(
          bit->getMeshset(), SPACE_DIM, block_data.domainEnts, true);
      mat_electr_ents.merge(block_data.domainEnts);
 
      std::vector<double> attributes;
      bit->getAttributes(attributes);
      if (attributes.size() < 1) {
        SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
                " At least one permittivity attributes should be given but "
                "found %zu",
                attributes.size());
      }
      block_data.epsPermit = attributes[0];
      block_data.iD = id;                   // id of the block
    }
  }
 
  // gets the map of the charge attributes and the block sets
  intBlockSetsPtr = boost::make_shared<std::map<int, BlockData>>();
  Range int_electr_ents; // range of entities with the charge
  for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, bit)) {
    if (bit->getName().compare(0, 12, "INT_ELECTRIC") == 0) {
      const int id = bit->getMeshsetId();
      auto &block_data = (*intBlockSetsPtr)[id];
 
      CHKERR mField.get_moab().get_entities_by_dimension(
          bit->getMeshset(), SPACE_DIM - 1, block_data.interfaceEnts, true);
      int_electr_ents.merge(block_data.interfaceEnts);
 
      std::vector<double> attributes;
      bit->getAttributes(attributes);
      if (attributes.size() < 1) {
        SETERRQ(PETSC_COMM_WORLD, MOFEM_DATA_INCONSISTENCY,
                "At least one charge attributes should be given but found %zu",
                attributes.size());
      }
      block_data.chargeDensity = attributes[0];
 
      block_data.iD = id;                       // id-> block ID
    }
  }
  // gets the map of the electrode entity range in the  block sets
  electrodeBlockSetsPtr = boost::make_shared<std::map<int, BlockData>>();
  Range electrode_ents; // range of entities with the electrode
  int electrodeCount = 0;
  for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, bit)) {
    if (bit->getName().compare(0, 9, "ELECTRODE") == 0) {
      const int id = bit->getMeshsetId();
      auto &block_data = (*electrodeBlockSetsPtr)[id];
      ++electrodeCount;
 
      CHKERR mField.get_moab().get_entities_by_dimension(
          bit->getMeshset(), SPACE_DIM - 1, block_data.electrodeEnts, true);
      electrode_ents.merge(block_data.electrodeEnts);
     
 
      if (electrodeCount > 2) {
        SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA,
                "Three or more electrode blocksets found");
        ;
      }
    }
  }
 
  // sync entities
  CHKERR mField.getInterface<CommInterface>()->synchroniseEntities(
      mat_electr_ents);
  CHKERR mField.getInterface<CommInterface>()->synchroniseEntities(
      int_electr_ents);
  CHKERR mField.getInterface<CommInterface>()->synchroniseEntities(
      electrode_ents);
 
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-out_skin", &out_skin,
                             PETSC_NULLPTR);
  CHKERR PetscOptionsGetBool(PETSC_NULLPTR, "", "-is_partitioned", &is_partitioned,
                             PETSC_NULLPTR);
  // get the skin entities
  Skinner skinner(&mField.get_moab());
  Range skin_tris;
  CHKERR skinner.find_skin(0, mat_electr_ents, false, skin_tris);
  Range proc_skin;
  ParallelComm *pcomm =
      ParallelComm::get_pcomm(&mField.get_moab(), MYPCOMM_INDEX);
  if (is_partitioned) {
    CHKERR pcomm->filter_pstatus(skin_tris,
                                 PSTATUS_SHARED | PSTATUS_MULTISHARED,
                                 PSTATUS_NOT, -1, &proc_skin);
  } else {
    proc_skin = skin_tris;
  }
  // add the skin entities to the field
  CHKERR mField.add_finite_element("SKIN", MF_ZERO);
  CHKERR mField.add_ents_to_finite_element_by_dim(proc_skin, SPACE_DIM - 1,
                                                  "SKIN");
  CHKERR mField.modify_finite_element_add_field_row("SKIN", domainField);
  CHKERR mField.modify_finite_element_add_field_col("SKIN", domainField);
  CHKERR mField.modify_finite_element_add_field_data("SKIN", domainField);
  // add the interface entities to the field
  CHKERR mField.add_finite_element("INTERFACE");
  CHKERR mField.modify_finite_element_add_field_row("INTERFACE", domainField);
  CHKERR mField.modify_finite_element_add_field_col("INTERFACE", domainField);
  CHKERR mField.modify_finite_element_add_field_data("INTERFACE", domainField);
  CHKERR mField.modify_finite_element_add_field_data("INTERFACE", "GEOMETRY");
 
  CHKERR mField.add_ents_to_finite_element_by_dim(int_electr_ents,
                                                  SPACE_DIM - 1, "INTERFACE");
  // add the electrode entities to the field
  CHKERR mField.add_finite_element("ELECTRODE");
  CHKERR mField.modify_finite_element_add_field_row("ELECTRODE", domainField);
  CHKERR mField.modify_finite_element_add_field_col("ELECTRODE", domainField);
  CHKERR mField.modify_finite_element_add_field_data("ELECTRODE", domainField);
  CHKERR mField.modify_finite_element_add_field_data("ELECTRODE", "GEOMETRY");
 
  CHKERR mField.add_ents_to_finite_element_by_dim(electrode_ents, SPACE_DIM - 1,
                                                  "ELECTRODE");
 
  // sync field entities
  mField.getInterface<CommInterface>()->synchroniseFieldEntities(domainField);
  mField.getInterface<CommInterface>()->synchroniseFieldEntities("GEOMETRY");
  CHKERR simpleInterface->defineFiniteElements();
  CHKERR simpleInterface->defineProblem(PETSC_TRUE);
  CHKERR simpleInterface->buildFields();
  CHKERR simpleInterface->buildFiniteElements();
  CHKERR simpleInterface->buildProblem();
  CHKERR mField.build_finite_elements("SKIN");
  CHKERR mField.build_finite_elements("INTERFACE");
  CHKERR mField.build_finite_elements("ELECTRODE");
 
  CHKERR DMMoFEMAddElement(simpleInterface->getDM(), "SKIN");
  CHKERR DMMoFEMAddElement(simpleInterface->getDM(), "INTERFACE");
  CHKERR DMMoFEMAddElement(simpleInterface->getDM(), "ELECTRODE");
 
  DMType dm_name = "DMMOFEM";
  CHKERR DMRegister_MoFEM(dm_name);
 
  SmartPetscObj<DM> dm;
  dm = createDM(mField.get_comm(), dm_name);
 
  // create dm instance
  CHKERR DMSetType(dm, dm_name);
 
  CHKERR simpleInterface->buildProblem();
 
  // initialise petsc vector for required processor
  int local_size;
  if (mField.get_comm_rank() == 0) // get_comm_rank() gets processor number
 
    local_size = LAST_ELEMENT; // last element gives size of vector
 
  else
    // other processors (e.g. 1, 2, 3, etc.)
    local_size = 0; // local size of vector is zero on other processors
 
  petscVec = createVectorMPI(mField.get_comm(), local_size, LAST_ELEMENT);
  petscVecEnergy = createVectorMPI(mField.get_comm(), local_size, LAST_ELEMENT);
  MoFEMFunctionReturn(0);
}
//! [Setup problem]
 
//! [Boundary condition]
MoFEMErrorCode Electrostatics::boundaryCondition() {
  MoFEMFunctionBegin;
 
  auto bc_mng = mField.getInterface<BcManager>();
 
  // Remove_BCs_from_blockset name "BOUNDARY_CONDITION";
  CHKERR bc_mng->removeBlockDOFsOnEntities<BcScalarMeshsetType<BLOCKSET>>(
      simpleInterface->getProblemName(), "BOUNDARY_CONDITION",
      std::string(domainField), true);
 
  MoFEMFunctionReturn(0);
}
//! [Boundary condition]
 
//! [Set integration rules]
MoFEMErrorCode Electrostatics::setIntegrationRules() {
  MoFEMFunctionBegin;
 
  auto rule_lhs = [this](int, int, int p) -> int { return 2 * p + geomOrder -1; };
  auto rule_rhs = [this](int, int, int p) -> int { return 2 * p + geomOrder -1; };
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(rule_lhs);
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(rule_rhs);
 
  MoFEMFunctionReturn(0);
}
//! [Set integration rules]
 
//! [Assemble system]
MoFEMErrorCode Electrostatics::assembleSystem() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  commonDataPtr = boost::make_shared<DataAtIntegrationPts>(mField);
 
  auto add_domain_base_ops = [&](auto &pipeline) {
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pipeline, {H1},
                                                          "GEOMETRY");
 
    pipeline.push_back(
        new OpBlockPermittivity(commonDataPtr, permBlockSetsPtr, domainField));
  };
 
  add_domain_base_ops(pipeline_mng->getOpDomainLhsPipeline());
  auto epsilon = [&](const double, const double, const double) {
    return commonDataPtr->blockPermittivity;
  };
 
  { // Push operators to the Pipeline that is responsible for calculating LHS
    pipeline_mng->getOpDomainLhsPipeline().push_back(
        new OpDomainLhsMatrixK(domainField, domainField, epsilon));
  }
 
  { // Push operators to the Pipeline that is responsible for calculating RHS
    auto set_values_to_bc_dofs = [&](auto &fe) {
      auto get_bc_hook = [&]() {
        EssentialPreProc<TemperatureCubitBcData> hook(mField, fe, {});
        return hook;
      };
      fe->preProcessHook = get_bc_hook();
    };
    // Set essential BC
    auto calculate_residual_from_set_values_on_bc = [&](auto &pipeline) {
      using OpInternal =
          FormsIntegrators<DomainEleOp>::Assembly<PETSC>::LinearForm<
              GAUSS>::OpGradTimesTensor<BASE_DIM, FIELD_DIM, SPACE_DIM>;
 
      add_domain_base_ops(pipeline_mng->getOpDomainRhsPipeline());
 
      auto grad_u_ptr = boost::make_shared<MatrixDouble>();
      pipeline_mng->getOpDomainRhsPipeline().push_back(
          new OpCalculateScalarFieldGradient<SPACE_DIM>(domainField,
                                                        grad_u_ptr));
      auto minus_epsilon = [&](double, double, double) constexpr {
        return -commonDataPtr->blockPermittivity;
      };
      pipeline_mng->getOpDomainRhsPipeline().push_back(
          new OpInternal(domainField, grad_u_ptr, minus_epsilon));
    };
 
    set_values_to_bc_dofs(pipeline_mng->getDomainRhsFE());
    calculate_residual_from_set_values_on_bc(
        pipeline_mng->getOpDomainRhsPipeline());
 
    auto bodySourceTerm = [&](const double, const double, const double) {
      return bodySource;
    };
    pipeline_mng->getOpDomainRhsPipeline().push_back(
        new OpBodySourceVectorb(domainField, bodySourceTerm));
  }
 
  interFaceRhsFe = boost::shared_ptr<ForcesAndSourcesCore>(
      new IntElementForcesAndSourcesCore(mField));
  interFaceRhsFe->getRuleHook = [this](int, int, int p) {
    return 2 * p + geomOrder -1;
  };
 
  {
 
    CHKERR AddHOOps<SPACE_DIM - 1, SPACE_DIM, SPACE_DIM>::add(
        interFaceRhsFe->getOpPtrVector(), {NOSPACE}, "GEOMETRY");
 
    interFaceRhsFe->getOpPtrVector().push_back(
        new OpBlockChargeDensity(commonDataPtr, intBlockSetsPtr, domainField));
 
    auto sIgma = [&](const double, const double, const double) {
      return commonDataPtr->blockChrgDens;
    };
 
    interFaceRhsFe->getOpPtrVector().push_back(
        new OpInterfaceRhsVectorF(domainField, sIgma));
  }
 
  MoFEMFunctionReturn(0);
}
//! [Assemble system]
 
//! [Solve system]
MoFEMErrorCode Electrostatics::solveSystem() {
  MoFEMFunctionBegin;
 
  auto pipeline_mng = mField.getInterface<PipelineManager>();
 
  auto ksp_solver = pipeline_mng->createKSP();
 
  boost::shared_ptr<ForcesAndSourcesCore> null; ///< Null element does
  DM dm;
  CHKERR simpleInterface->getDM(&dm);
 
  CHKERR DMMoFEMKSPSetComputeRHS(dm, "INTERFACE", interFaceRhsFe, null, null);
 
  CHKERR KSPSetFromOptions(ksp_solver);
 
  // Create RHS and solution vectors
  auto F = createDMVector(dm);
  auto D = vectorDuplicate(F);
  // Solve the system
  CHKERR KSPSetUp(ksp_solver);
  CHKERR KSPSolve(ksp_solver, F, D);
 
  CHKERR VecGhostUpdateBegin(F, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR VecGhostUpdateEnd(F, INSERT_VALUES, SCATTER_FORWARD);
 
  double fnorm;
  CHKERR VecNorm(F, NORM_2, &fnorm);
  CHKERR PetscPrintf(PETSC_COMM_WORLD, "F norm  = %9.8e\n", fnorm);
 
  // Scatter result data on the mesh
  CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
 
  double dnorm;
  CHKERR VecNorm(D, NORM_2, &dnorm);
  CHKERR PetscPrintf(PETSC_COMM_WORLD, "D norm  = %9.8e\n", dnorm);
 
  CHKERR DMoFEMMeshToLocalVector(dm, D, INSERT_VALUES, SCATTER_REVERSE);
 
  MoFEMFunctionReturn(0);
}
//! [Solve system]
 
//! [Output results]
MoFEMErrorCode Electrostatics::outputResults() {
  MoFEMFunctionBegin;
  auto pipeline_mng = mField.getInterface<PipelineManager>();
  auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
 
  // lamda function to calculate electric field
  auto calculate_e_field = [&](auto &pipeline) {
    auto u_ptr = boost::make_shared<VectorDouble>();
    auto x_ptr = boost::make_shared<MatrixDouble>();
    auto grad_u_ptr = boost::make_shared<MatrixDouble>();
    auto e_field_ptr = boost::make_shared<MatrixDouble>();
    // add higher order operator
    CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(pipeline, {H1},
                                                          "GEOMETRY");
    // calculate field values
    pipeline.push_back(new OpCalculateScalarFieldValues(domainField, u_ptr));
    pipeline.push_back(
        new OpCalculateVectorFieldValues<SPACE_DIM>("GEOMETRY", x_ptr));
 
    // calculate gradient
    pipeline.push_back(
        new OpCalculateScalarFieldGradient<SPACE_DIM>(domainField, grad_u_ptr));
    // calculate electric field
    pipeline.push_back(new OpElectricField(e_field_ptr, grad_u_ptr));
    return boost::make_tuple(u_ptr, e_field_ptr, x_ptr);
  };
 
  auto [u_ptr, e_field_ptr, x_ptr] =
      calculate_e_field(post_proc_fe->getOpPtrVector());
 
  auto e_field_times_perm_ptr = boost::make_shared<MatrixDouble>();
  auto energy_density_ptr = boost::make_shared<VectorDouble>();
 
  post_proc_fe->getOpPtrVector().push_back(
      new OpGradTimesPerm(domainField, e_field_ptr, e_field_times_perm_ptr,
                          permBlockSetsPtr, commonDataPtr));
  post_proc_fe->getOpPtrVector().push_back(
      new OpEnergyDensity(domainField, e_field_ptr, energy_density_ptr,
                          permBlockSetsPtr, commonDataPtr));
 
  using OpPPMap = OpPostProcMapInMoab<SPACE_DIM, SPACE_DIM>;
  post_proc_fe->getOpPtrVector().push_back(new OpPPMap(
      post_proc_fe->getPostProcMesh(), post_proc_fe->getMapGaussPts(),
 
      OpPPMap::DataMapVec{{"POTENTIAL", u_ptr},
                          {"ENERGY_DENSITY", energy_density_ptr}},
      OpPPMap::DataMapMat{
          {"GEOMETRY", x_ptr},
          {"ELECTRIC_FIELD", e_field_ptr},
          {"ELECTRIC_DISPLACEMENT", e_field_times_perm_ptr},
      },
      OpPPMap::DataMapMat{},
 
      OpPPMap::DataMapMat{})
 
  );
 
  pipeline_mng->getDomainPostProcFE() = post_proc_fe;
  CHKERR pipeline_mng->loopFiniteElementsPostProc();
  CHKERR post_proc_fe->writeFile("out.h5m");
 
  if (out_skin && SPACE_DIM == 3) {
 
    auto post_proc_skin = boost::make_shared<PostProcFaceEle>(mField);
    auto op_loop_skin = new OpLoopSide<SideEle>(
        mField, simpleInterface->getDomainFEName(), SPACE_DIM);
 
    auto [u_ptr, e_field_ptr, x_ptr] =
        calculate_e_field(op_loop_skin->getOpPtrVector());
 
    op_loop_skin->getOpPtrVector().push_back(
        new OpGradTimesPerm(domainField, e_field_ptr, e_field_times_perm_ptr,
                            permBlockSetsPtr, commonDataPtr));
    op_loop_skin->getOpPtrVector().push_back(
        new OpEnergyDensity(domainField, e_field_ptr, energy_density_ptr,
                            permBlockSetsPtr, commonDataPtr));
 
    // push op to boundary element
    post_proc_skin->getOpPtrVector().push_back(op_loop_skin);
 
    post_proc_skin->getOpPtrVector().push_back(new OpPPMap(
        post_proc_skin->getPostProcMesh(), post_proc_skin->getMapGaussPts(),
        OpPPMap::DataMapVec{{"POTENTIAL", u_ptr},
                            {"ENERGY_DENSITY", energy_density_ptr}},
        OpPPMap::DataMapMat{{"ELECTRIC_FIELD", e_field_ptr},
                            {"GEOMETRY", x_ptr},
                            {"ELECTRIC_DISPLACEMENT", e_field_times_perm_ptr}},
        OpPPMap::DataMapMat{}, OpPPMap::DataMapMat{}));
 
    CHKERR DMoFEMLoopFiniteElements(simpleInterface->getDM(), "SKIN",
                                    post_proc_skin);
    CHKERR post_proc_skin->writeFile("out_skin.h5m");
  }
  MoFEMFunctionReturn(0);
}
//! [Output results]
 
//! [Get Total Energy]
MoFEMErrorCode Electrostatics::getTotalEnergy() {
  MoFEMFunctionBegin;
  auto pip_energy = mField.getInterface<PipelineManager>();
 
  auto rule = [this](int, int, int p) { return 2 * p + geomOrder - 1; };
  CHKERR pip_energy->setEvaluationIntegrationRule(rule);
  auto &evaluation_pipeline = pip_energy->getOpEvaluationPipeline();
 
  // gets the map of the internal domain entity range to get the total energy
 
  boost::shared_ptr<std::map<int, BlockData>> intrnlDomnBlckSetPtr =
      boost::make_shared<std::map<int, BlockData>>();
  Range internal_domain; // range of entities marked the internal domain
  for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, bit)) {
    if (bit->getName().compare(0, 10, "DOMAIN_INT") == 0) {
      const int id = bit->getMeshsetId();
      auto &block_data = (*intrnlDomnBlckSetPtr)[id];
 
      CHKERR mField.get_moab().get_entities_by_dimension(
          bit->getMeshset(), SPACE_DIM, block_data.internalDomainEnts, true);
      internal_domain.merge(block_data.internalDomainEnts);
      block_data.iD = id;
    }
  }
  CHKERR mField.getInterface<CommInterface>()->synchroniseEntities(
      internal_domain);
 
  CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(evaluation_pipeline,
                                                        {H1}, "GEOMETRY");
 
  auto grad_u_ptr = boost::make_shared<MatrixDouble>();
  auto e_field_ptr = boost::make_shared<MatrixDouble>();
 
  evaluation_pipeline.push_back(
      new OpCalculateScalarFieldGradient<SPACE_DIM>(domainField, grad_u_ptr));
  evaluation_pipeline.push_back(new OpElectricField(e_field_ptr, grad_u_ptr));
 
  commonDataPtr = boost::make_shared<DataAtIntegrationPts>(mField);
 
  evaluation_pipeline.push_back(
      new OpTotalEnergy(domainField, grad_u_ptr, permBlockSetsPtr,
                        intrnlDomnBlckSetPtr, commonDataPtr, petscVecEnergy));
 
  CHKERR pip_energy->loopFiniteElementsEvaluation();
  CHKERR VecAssemblyBegin(petscVecEnergy);
  CHKERR VecAssemblyEnd(petscVecEnergy);
 
  double total_energy = 0.0; // declaration for total energy
  if (!mField.get_comm_rank()) {
    const double *array;
 
    CHKERR VecGetArrayRead(petscVecEnergy, &array);
    total_energy = array[ZERO];
    MOFEM_LOG_CHANNEL("SELF");
    MOFEM_LOG_C("SELF", Sev::inform, "Total Energy: %6.15f", total_energy);
    CHKERR VecRestoreArrayRead(petscVecEnergy, &array);
  }
 
  MoFEMFunctionReturn(0);
}
//! [Get Total Energy]
 
//! [Get Charges]
MoFEMErrorCode Electrostatics::getElectrodeCharge() {
  MoFEMFunctionBegin;
  auto op_loop_side = new OpLoopSide<SideEle>(
      mField, simpleInterface->getDomainFEName(), SPACE_DIM);
 
  CHKERR AddHOOps<SPACE_DIM, SPACE_DIM, SPACE_DIM>::add(
      op_loop_side->getOpPtrVector(), {H1}, "GEOMETRY");
 
  auto grad_u_ptr_charge = boost::make_shared<MatrixDouble>();
  auto e_ptr_charge = boost::make_shared<MatrixDouble>();
 
  op_loop_side->getOpPtrVector().push_back(
      new OpCalculateScalarFieldGradient<SPACE_DIM>(domainField,
                                                    grad_u_ptr_charge));
 
  op_loop_side->getOpPtrVector().push_back(
      new OpElectricField(e_ptr_charge, grad_u_ptr_charge));
  auto d_jump = boost::make_shared<MatrixDouble>();
  op_loop_side->getOpPtrVector().push_back(new OpElectricDispJump<SPACE_DIM>(
      domainField, e_ptr_charge, d_jump, commonDataPtr, permBlockSetsPtr));
 
  electrodeRhsFe = boost::shared_ptr<ForcesAndSourcesCore>(
      new IntElementForcesAndSourcesCore(mField));
  electrodeRhsFe->getRuleHook = [this](int, int, int p) {
    return 2 * p + geomOrder -1;
  };
 
  // push all the operators in on the side to the electrodeRhsFe
  electrodeRhsFe->getOpPtrVector().push_back(op_loop_side);
 
  electrodeRhsFe->getOpPtrVector().push_back(new OpElectrodeCharge<SPACE_DIM>(
      domainField, d_jump, petscVec, electrodeBlockSetsPtr));
  CHKERR VecZeroEntries(petscVec);
  CHKERR DMoFEMLoopFiniteElementsUpAndLowRank(simpleInterface->getDM(),
                                              "ELECTRODE", electrodeRhsFe, 0,
                                              mField.get_comm_size());
  CHKERR VecAssemblyBegin(petscVec);
  CHKERR VecAssemblyEnd(petscVec);
 
  if (!mField.get_comm_rank()) {
    const double *array;
 
    CHKERR(VecGetArrayRead(petscVec, &array));
    double aLpha = array[0]; // Use explicit index instead of ZERO
    double bEta = array[1];  // Use explicit index instead of ONE
    MOFEM_LOG_CHANNEL("SELF");
    MOFEM_LOG_C("SELF", Sev::inform,
                "CHARGE_ELEC_1: %6.15f , CHARGE_ELEC_2: %6.15f", aLpha, bEta);
 
    CHKERR(VecRestoreArrayRead(petscVec, &array));
  }
  if (atomTest && !mField.get_comm_rank()) {
    double cal_charge_elec1;
    double cal_charge_elec2;
    double cal_total_energy;
    const double *c_ptr, *te_ptr;
 
    // Get a pointer to the PETSc vector data
    CHKERR(VecGetArrayRead(petscVec, &c_ptr));
    CHKERR(VecGetArrayRead(petscVecEnergy, &te_ptr));
 
    // Expected charges at the electrodes
    double ref_charge_elec1;
    double ref_charge_elec2;
    // Expected total energy of the system
    double ref_tot_energy;
    double tol;
    cal_charge_elec1 = c_ptr[0];  // Read charge at the first electrode
    cal_charge_elec2 = c_ptr[1];  // Read charge at the second electrode
    cal_total_energy = te_ptr[0]; // Read total energy of the system
    if (std::isnan(cal_charge_elec1) || std::isnan(cal_charge_elec2) ||
        std::isnan(cal_total_energy)) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
              "Atom test failed! NaN detected in calculated values.");
    }
    switch (atomTest) {
    case 1: // 2D & 3D test
    case 3: // JSON clear-block 2D test
      // Expected charges at the electrodes
      ref_charge_elec1 = 50.0;
      ref_charge_elec2 = -50.0;
      // Expected total energy of the system
      ref_tot_energy = 500.0;
      tol = 1e-10;
      break;
    case 2: // wavy 3D test
      ref_charge_elec1 = 10.00968352472943;
      ref_charge_elec2 = 0.0; // no electrode
      ref_tot_energy = 50.5978;
      tol = 1e-4;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA,
               "atom test %d does not exist", atomTest);
    }
 
    // Validate the results
    if (std::abs(ref_charge_elec1 - cal_charge_elec1) > tol ||
        std::abs(ref_charge_elec2 - cal_charge_elec2) > tol ||
        std::abs(ref_tot_energy - cal_total_energy) > tol) {
      SETERRQ(
          PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
          "atom test %d failed! Calculated values do not match expected values",
          atomTest);
    }
 
    CHKERR(VecRestoreArrayRead(petscVec,
                               &c_ptr)); // Restore the PETSc vector array
    CHKERR(VecRestoreArrayRead(petscVecEnergy, &te_ptr));
  }
 
  MoFEMFunctionReturn(0);
}
//! [Get Charges]
 
//! [Run program]
MoFEMErrorCode Electrostatics::runProgram() {
  MoFEMFunctionBegin;
 
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR boundaryCondition();
  CHKERR setIntegrationRules();
  CHKERR assembleSystem();
  CHKERR solveSystem();
  CHKERR outputResults();
  CHKERR getTotalEnergy();
  CHKERR getElectrodeCharge();
  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
    Electrostatics Electrostatics_problem(m_field);
    CHKERR Electrostatics_problem.runProgram();
  }
  CATCH_ERRORS;
 
  // Finish work: cleaning memory, getting statistics, etc.
  MoFEM::Core::Finalize();
 
  return 0;
}
//! [Main]