SCL-4: Nonlinear Poisson's equation

Table of Contents

• Introduction
• Plain program
  • Implementation of User Data Operators (*.hpp)
  • Implementation of the main program (*.cpp)

Note

Prerequisite of this tutorial is SCL-3: Poisson's equation (Lagrange multiplier)

Note

Intended learning outcome:

• solving a nonlinear problem in MoFEM
• usage of PETSc SNES solver to solve nonlinear equations

Introduction

Plain program

The plain program for both the implementation of the UDOs (*.hpp) and the main program (*.cpp) are as follows

Implementation of User Data Operators (*.hpp)

#ifndef __NONLINEARPOISSON2D_HPP__
#define __NONLINEARPOISSON2D_HPP__
 
#include <stdlib.h>
#include <BasicFiniteElements.hpp>
 
using FaceEle = MoFEM::FaceElementForcesAndSourcesCore;
using EdgeEle = MoFEM::EdgeElementForcesAndSourcesCore;
 
using OpFaceEle = MoFEM::FaceElementForcesAndSourcesCore::UserDataOperator;
using OpEdgeEle = MoFEM::EdgeElementForcesAndSourcesCore::UserDataOperator;
 
using EntData = EntitiesFieldData::EntData;
 
namespace NonlinearPoissonOps {
 
FTensor::Index<'i', 2> i;
 
typedef boost::function<double(const double, const double, const double)>
    ScalarFunc;
 
struct DataAtGaussPoints {
  // This struct is for data required for the update of Newton's iteration
 
  VectorDouble fieldValue;
  MatrixDouble fieldGrad;
};
 
struct OpDomainTangentMatrix : public OpFaceEle {
public:
  OpDomainTangentMatrix(
      std::string row_field_name, std::string col_field_name,
      boost::shared_ptr<DataAtGaussPoints> &common_data,
      boost::shared_ptr<std::vector<unsigned char>> boundary_marker = nullptr)
      : OpFaceEle(row_field_name, col_field_name, OpFaceEle::OPROWCOL),
        commonData(common_data), boundaryMarker(boundary_marker) {
    sYmm = false;
  }
 
  MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
                        EntityType col_type, EntData &row_data,
                        EntData &col_data) {
    MoFEMFunctionBegin;
 
    const int nb_row_dofs = row_data.getIndices().size();
    const int nb_col_dofs = col_data.getIndices().size();
 
    if (nb_row_dofs && nb_col_dofs) {
 
      locLhs.resize(nb_row_dofs, nb_col_dofs, false);
      locLhs.clear();
 
      // get element area
      const double area = getMeasure();
 
      // get number of integration points
      const int nb_integration_points = getGaussPts().size2();
      // get integration weights
      auto t_w = getFTensor0IntegrationWeight();
      // get solution (field value) at integration points
      auto t_field = getFTensor0FromVec(commonData->fieldValue);
      // get gradient of field at integration points
      auto t_field_grad = getFTensor1FromMat<2>(commonData->fieldGrad);
 
      // get base functions on row
      auto t_row_base = row_data.getFTensor0N();
      // get derivatives of base functions on row
      auto t_row_diff_base = row_data.getFTensor1DiffN<2>();
 
      // START THE LOOP OVER INTEGRATION POINTS TO CALCULATE LOCAL MATRIX
      for (int gg = 0; gg != nb_integration_points; gg++) {
        const double a = t_w * area;
 
        for (int rr = 0; rr != nb_row_dofs; ++rr) {
          // get base functions on column
          auto t_col_base = col_data.getFTensor0N(gg, 0);
          // get derivatives of base functions on column
          auto t_col_diff_base = col_data.getFTensor1DiffN<2>(gg, 0);
 
          for (int cc = 0; cc != nb_col_dofs; cc++) {
            locLhs(rr, cc) += (((1 + t_field * t_field) * t_row_diff_base(i) *
                                t_col_diff_base(i)) +
                               (2.0 * t_field * t_field_grad(i) *
                                t_row_diff_base(i) * t_col_base)) *
                              a;
 
            // move to the next base functions on column
            ++t_col_base;
            // move to the derivatives of the next base function on column
            ++t_col_diff_base;
          }
 
          // move to the next base function on row
          ++t_row_base;
          // move to the derivatives of the next base function on row
          ++t_row_diff_base;
        }
 
        // move to the weight of the next integration point
        ++t_w;
        // move to the solution (field value) at the next integration point
        ++t_field;
        // move to the gradient of field value at the next integration point
        ++t_field_grad;
      }
 
      // FILL VALUES OF LOCAL MATRIX ENTRIES TO THE GLOBAL MATRIX
 
      // store original row indices
      auto row_indices = row_data.getIndices();
      // mark the boundary DOFs (as -1) and fill only domain DOFs
      if (boundaryMarker) {
        for (int r = 0; r != row_data.getIndices().size(); ++r) {
          if ((*boundaryMarker)[row_data.getLocalIndices()[r]]) {
            row_data.getIndices()[r] = -1;
          }
        }
      }
      // fill value to local stiffness matrix ignoring boundary DOFs
      CHKERR MatSetValues(getSNESB(), row_data, col_data, &locLhs(0, 0),
                          ADD_VALUES);
      // revert back row indices to the original
      row_data.getIndices().swap(row_indices);
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  boost::shared_ptr<DataAtGaussPoints> commonData;
  boost::shared_ptr<std::vector<unsigned char>> boundaryMarker;
  MatrixDouble locLhs;
};
 
struct OpDomainResidualVector : public OpFaceEle {
public:
  OpDomainResidualVector(
      std::string field_name, ScalarFunc source_term_function,
      boost::shared_ptr<DataAtGaussPoints> &common_data,
      boost::shared_ptr<std::vector<unsigned char>> boundary_marker = nullptr)
      : OpFaceEle(field_name, OpFaceEle::OPROW),
        sourceTermFunc(source_term_function), commonData(common_data),
        boundaryMarker(boundary_marker) {}
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    const int nb_dofs = data.getIndices().size();
 
    if (nb_dofs) {
      locRhs.resize(nb_dofs, false);
      locRhs.clear();
 
      // get element area
      const double area = getMeasure();
 
      // get number of integration points
      const int nb_integration_points = getGaussPts().size2();
      // get integration weights
      auto t_w = getFTensor0IntegrationWeight();
      // get coordinates of the integration point
      auto t_coords = getFTensor1CoordsAtGaussPts();
      // get solution (field value) at integration point
      auto t_field = getFTensor0FromVec(commonData->fieldValue);
      // get gradient of field value of integration point
      auto t_field_grad = getFTensor1FromMat<2>(commonData->fieldGrad);
 
      // get base function
      auto t_base = data.getFTensor0N();
      // get derivatives of base function
      auto t_grad_base = data.getFTensor1DiffN<2>();
 
      // START THE LOOP OVER INTEGRATION POINTS TO CALCULATE LOCAL VECTOR
      for (int gg = 0; gg != nb_integration_points; gg++) {
        const double a = t_w * area;
        double body_source =
            sourceTermFunc(t_coords(0), t_coords(1), t_coords(2));
 
        // calculate the local vector
        for (int rr = 0; rr != nb_dofs; rr++) {
          locRhs[rr] -=
              (t_base * body_source -
               t_grad_base(i) * t_field_grad(i) * (1 + t_field * t_field)) *
              a;
 
          // move to the next base function
          ++t_base;
          // move to the derivatives of the next base function
          ++t_grad_base;
        }
 
        // move to the weight of the next integration point
        ++t_w;
        // move to the coordinates of the next integration point
        ++t_coords;
        // move to the solution (field value) at the next integration point
        ++t_field;
        // move to the gradient of field value at the next integration point
        ++t_field_grad;
      }
 
      // FILL VALUES OF LOCAL VECTOR ENTRIES TO THE GLOBAL VECTOR
 
      // store original row indices
      auto row_indices = data.getIndices();
      // mark the boundary DOFs (as -1) and fill only domain DOFs
      if (boundaryMarker) {
        for (int r = 0; r != data.getIndices().size(); ++r) {
          if ((*boundaryMarker)[data.getLocalIndices()[r]]) {
            data.getIndices()[r] = -1;
          }
        }
      }
      // fill value to local vector ignoring boundary DOFs
      CHKERR VecSetOption(getSNESf(), VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE);
      CHKERR VecSetValues(getSNESf(), data, &*locRhs.begin(), ADD_VALUES);
      // revert back the indices
      data.getIndices().swap(row_indices);
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  ScalarFunc sourceTermFunc;
  boost::shared_ptr<DataAtGaussPoints> commonData;
  boost::shared_ptr<std::vector<unsigned char>> boundaryMarker;
  VectorDouble locRhs;
};
 
struct OpBoundaryTangentMatrix : public OpEdgeEle {
public:
  OpBoundaryTangentMatrix(std::string row_field_name,
                          std::string col_field_name)
      : OpEdgeEle(row_field_name, col_field_name, OpEdgeEle::OPROWCOL) {
    sYmm = true;
  }
 
  MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
                        EntityType col_type, EntData &row_data,
                        EntData &col_data) {
    MoFEMFunctionBegin;
 
    const int nb_row_dofs = row_data.getIndices().size();
    const int nb_col_dofs = col_data.getIndices().size();
    // cerr << nb_row_dofs;
 
    if (nb_row_dofs && nb_col_dofs) {
      locBoundaryLhs.resize(nb_row_dofs, nb_col_dofs, false);
      locBoundaryLhs.clear();
 
      // get (boundary) element length
      const double edge = getMeasure();
 
      // get number of integration points
      const int nb_integration_points = getGaussPts().size2();
      // get integration weights
      auto t_w = getFTensor0IntegrationWeight();
 
      // get base function on row
      auto t_row_base = row_data.getFTensor0N();
 
      // START THE LOOP OVER INTEGRATION POINTS TO CALCULATE LOCAL MATRIX
      for (int gg = 0; gg != nb_integration_points; gg++) {
        const double a = t_w * edge;
 
        for (int rr = 0; rr != nb_row_dofs; ++rr) {
          // get base function on column
          auto t_col_base = col_data.getFTensor0N(gg, 0);
 
          for (int cc = 0; cc != nb_col_dofs; cc++) {
            locBoundaryLhs(rr, cc) += t_row_base * t_col_base * a;
 
            // move to the next base function on column
            ++t_col_base;
          }
 
          // move to the next base function on row
          ++t_row_base;
        }
 
        // move to the weight of the next integration point
        ++t_w;
      }
 
      // FILL VALUES OF LOCAL MATRIX ENTRIES TO THE GLOBAL MATRIX
      CHKERR MatSetValues(getSNESB(), row_data, col_data, &locBoundaryLhs(0, 0),
                          ADD_VALUES);
 
      if (row_side != col_side || row_type != col_type) {
        transLocBoundaryLhs.resize(nb_col_dofs, nb_row_dofs, false);
        noalias(transLocBoundaryLhs) = trans(locBoundaryLhs);
        CHKERR MatSetValues(getSNESB(), col_data, row_data,
                            &transLocBoundaryLhs(0, 0), ADD_VALUES);
      }
      // cerr << locBoundaryLhs << endl;
      // cerr << transLocBoundaryLhs << endl;
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  MatrixDouble locBoundaryLhs, transLocBoundaryLhs;
};
 
struct OpBoundaryResidualVector : public OpEdgeEle {
public:
  OpBoundaryResidualVector(std::string field_name, ScalarFunc boundary_function,
                           boost::shared_ptr<DataAtGaussPoints> &common_data)
      : OpEdgeEle(field_name, OpEdgeEle::OPROW),
        boundaryFunc(boundary_function), commonData(common_data) {}
 
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    const int nb_dofs = data.getIndices().size();
 
    if (nb_dofs) {
 
      locBoundaryRhs.resize(nb_dofs, false);
      locBoundaryRhs.clear();
 
      // get (boundary) element length
      const double edge = getMeasure();
 
      // get number of integration points
      const int nb_integration_points = getGaussPts().size2();
      // get integration weights
      auto t_w = getFTensor0IntegrationWeight();
      // get coordinates at integration point
      auto t_coords = getFTensor1CoordsAtGaussPts();
      // get solution (field value) at integration point
      auto t_field = getFTensor0FromVec(commonData->fieldValue);
 
      // get base function
      auto t_base = data.getFTensor0N();
 
      // START THE LOOP OVER INTEGRATION POINTS TO CALCULATE LOCAL VECTOR
      for (int gg = 0; gg != nb_integration_points; gg++) {
        const double a = t_w * edge;
        double boundary_term =
            boundaryFunc(t_coords(0), t_coords(1), t_coords(2));
 
        // calculate the local vector
        for (int rr = 0; rr != nb_dofs; rr++) {
          locBoundaryRhs[rr] -= t_base * (boundary_term - t_field) * a;
 
          // move to the next base function
          ++t_base;
        }
 
        // move to the weight of the next integration point
        ++t_w;
        // move to the coordinates of the next integration point
        ++t_coords;
        // move to the solution (field value) at the next integration point
        ++t_field;
      }
 
      // FILL VALUES OF LOCAL VECTOR ENTRIES TO THE GLOBAL VECTOR
      CHKERR VecSetValues(getSNESf(), data, &*locBoundaryRhs.begin(),
                          ADD_VALUES);
    }
 
    MoFEMFunctionReturn(0);
  }
 
private:
  ScalarFunc boundaryFunc;
  boost::shared_ptr<DataAtGaussPoints> commonData;
  VectorDouble locBoundaryRhs;
};
 
}; // namespace NonlinearPoissonOps
 
#endif //__NONLINEARPOISSON2D_HPP__

Implementation of the main program (*.cpp)

#include <stdlib.h>
#include <BasicFiniteElements.hpp>
#include <nonlinear_poisson_2d.hpp>
 
using namespace MoFEM;
using namespace NonlinearPoissonOps;
 
static char help[] = "...\n\n";
 
struct NonlinearPoisson {
public:
  NonlinearPoisson(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 setIntegrationRules();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode outputResults();
 
  // Function to calculate the Source term
  static double sourceTermFunction(const double x, const double y,
                                   const double z) {
    return 200 * sin(x * 10.) * cos(y * 10.);
    // return 1;
  }
 
  // Function to calculate the Boundary term
  static double boundaryFunction(const double x, const double y,
                                 const double z) {
    return sin(x * 10.) * cos(y * 10.);
    // return 0;
  }
 
  // Main interfaces
  MoFEM::Interface &mField;
  Simple *simpleInterface;
 
  // mpi parallel communicator
  MPI_Comm mpiComm;
  // Number of processors
  const int mpiRank;
 
  // Discrete Manager and nonliner SNES solver using SmartPetscObj
  SmartPetscObj<DM> dM;
  SmartPetscObj<SNES> snesSolver;
 
  // Field name and approximation order
  std::string domainField;
  int order;
 
  // Object to mark boundary entities for the assembling of domain elements
  boost::shared_ptr<std::vector<unsigned char>> boundaryMarker;
 
  // MoFEM working Pipelines for LHS and RHS of domain and boundary
  boost::shared_ptr<FaceEle> domainTangentMatrixPipeline;
  boost::shared_ptr<FaceEle> domainResidualVectorPipeline;
  boost::shared_ptr<EdgeEle> boundaryTangentMatrixPipeline;
  boost::shared_ptr<EdgeEle> boundaryResidualVectorPipeline;
 
  // Objects needed for solution updates in Newton's method
  boost::shared_ptr<DataAtGaussPoints> previousUpdate;
  boost::shared_ptr<VectorDouble> fieldValuePtr;
  boost::shared_ptr<MatrixDouble> fieldGradPtr;
 
  using PostProcEle = PostProcBrokenMeshInMoab<FaceEle>;
 
  // Object needed for postprocessing
  boost::shared_ptr<PostProcEle> postProc;
 
  // Boundary entities marked for fieldsplit (block) solver - optional
  Range boundaryEntitiesForFieldsplit;
};
 
NonlinearPoisson::NonlinearPoisson(MoFEM::Interface &m_field)
    : domainField("U"), mField(m_field), mpiComm(mField.get_comm()),
      mpiRank(mField.get_comm_rank()) {
  domainTangentMatrixPipeline = boost::shared_ptr<FaceEle>(new FaceEle(mField));
  domainResidualVectorPipeline =
      boost::shared_ptr<FaceEle>(new FaceEle(mField));
  boundaryTangentMatrixPipeline =
      boost::shared_ptr<EdgeEle>(new EdgeEle(mField));
  boundaryResidualVectorPipeline =
      boost::shared_ptr<EdgeEle>(new EdgeEle(mField));
 
  previousUpdate =
      boost::shared_ptr<DataAtGaussPoints>(new DataAtGaussPoints());
  fieldValuePtr = boost::shared_ptr<VectorDouble>(previousUpdate,
                                                  &previousUpdate->fieldValue);
  fieldGradPtr = boost::shared_ptr<MatrixDouble>(previousUpdate,
                                                 &previousUpdate->fieldGrad);
}
 
MoFEMErrorCode NonlinearPoisson::runProgram() {
  MoFEMFunctionBegin;
 
  readMesh();
  setupProblem();
  setIntegrationRules();
  boundaryCondition();
  assembleSystem();
  solveSystem();
  outputResults();
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::readMesh() {
  MoFEMFunctionBegin;
 
  CHKERR mField.getInterface(simpleInterface);
  CHKERR simpleInterface->getOptions();
  CHKERR simpleInterface->loadFile();
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::setupProblem() {
  MoFEMFunctionBegin;
 
  CHKERR simpleInterface->addDomainField(domainField, H1,
                                         AINSWORTH_BERNSTEIN_BEZIER_BASE, 1);
  CHKERR simpleInterface->addBoundaryField(domainField, H1,
                                           AINSWORTH_BERNSTEIN_BEZIER_BASE, 1);
 
  int order = 3;
  CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &order, PETSC_NULL);
  CHKERR simpleInterface->setFieldOrder(domainField, order);
 
  CHKERR simpleInterface->setUp();
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::setIntegrationRules() {
  MoFEMFunctionBegin;
 
  auto domain_rule_lhs = [](int, int, int p) -> int { return 2 * (p + 1); };
  auto domain_rule_rhs = [](int, int, int p) -> int { return 2 * (p + 1); };
  domainTangentMatrixPipeline->getRuleHook = domain_rule_lhs;
  domainResidualVectorPipeline->getRuleHook = domain_rule_rhs;
 
  auto boundary_rule_lhs = [](int, int, int p) -> int { return 2 * p + 1; };
  auto boundary_rule_rhs = [](int, int, int p) -> int { return 2 * p + 1; };
  boundaryTangentMatrixPipeline->getRuleHook = boundary_rule_lhs;
  boundaryResidualVectorPipeline->getRuleHook = boundary_rule_rhs;
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::boundaryCondition() {
  MoFEMFunctionBegin;
 
  // Get boundary edges marked in block named "BOUNDARY_CONDITION"
  auto get_ents_on_mesh_skin = [&]() {
    Range boundary_entities;
    for (_IT_CUBITMESHSETS_BY_SET_TYPE_FOR_LOOP_(mField, BLOCKSET, it)) {
      std::string entity_name = it->getName();
      if (entity_name.compare(0, 18, "BOUNDARY_CONDITION") == 0) {
        CHKERR it->getMeshsetIdEntitiesByDimension(mField.get_moab(), 1,
                                                   boundary_entities, true);
      }
    }
    // Add vertices to boundary entities
    Range boundary_vertices;
    CHKERR mField.get_moab().get_connectivity(boundary_entities,
                                              boundary_vertices, true);
    boundary_entities.merge(boundary_vertices);
 
    // Store entities for fieldsplit (block) solver
    boundaryEntitiesForFieldsplit = boundary_entities;
 
    return boundary_entities;
  };
 
  auto mark_boundary_dofs = [&](Range &&skin_edges) {
    auto problem_manager = mField.getInterface<ProblemsManager>();
    auto marker_ptr = boost::make_shared<std::vector<unsigned char>>();
    problem_manager->markDofs(simpleInterface->getProblemName(), ROW,
                              skin_edges, *marker_ptr);
    return marker_ptr;
  };
 
  // Get global local vector of marked DOFs. Is global, since is set for all
  // DOFs on processor. Is local since only DOFs on processor are in the
  // vector. To access DOFs use local indices.
  boundaryMarker = mark_boundary_dofs(get_ents_on_mesh_skin());
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::assembleSystem() {
  MoFEMFunctionBegin;
 
  auto det_ptr = boost::make_shared<VectorDouble>();
  auto jac_ptr = boost::make_shared<MatrixDouble>();
  auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
 
  { // Push operators to the Pipeline that is responsible for calculating the
    // domain tangent matrix (LHS)
 
    // Add default operators to calculate inverse of Jacobian (needed for
    // implementation of 2D problem but not 3D ones)
 
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpCalculateHOJac<2>(jac_ptr));
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpSetHOInvJacToScalarBases<2>(H1, inv_jac_ptr));
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpSetHOWeightsOnFace());
 
    // Add default operator to calculate field values at integration points
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpCalculateScalarFieldValues(domainField, fieldValuePtr));
    // Add default operator to calculate field gradient at integration points
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpCalculateScalarFieldGradient<2>(domainField, fieldGradPtr));
 
    // Push operators for domain tangent matrix (LHS)
    domainTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpDomainTangentMatrix(domainField, domainField, previousUpdate,
                                  boundaryMarker));
  }
 
  { // Push operators to the Pipeline that is responsible for calculating the
    // domain residual vector (RHS)
 
    // Add default operators to calculate inverse of Jacobian (needed for
    // implementation of 2D problem but not 3D ones)
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpCalculateHOJac<2>(jac_ptr));
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpInvertMatrix<2>(jac_ptr, det_ptr, inv_jac_ptr));
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpSetHOInvJacToScalarBases<2>(H1, inv_jac_ptr));
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpSetHOWeightsOnFace());
 
    // Add default operator to calculate field values at integration points
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpCalculateScalarFieldValues(domainField, fieldValuePtr));
    // Add default operator to calculate field gradient at integration points
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpCalculateScalarFieldGradient<2>(domainField, fieldGradPtr));
 
    domainResidualVectorPipeline->getOpPtrVector().push_back(
        new OpDomainResidualVector(domainField, sourceTermFunction,
                                   previousUpdate, boundaryMarker));
  }
 
  { // Push operators to the Pipeline that is responsible for calculating the
    // boundary tangent matrix (LHS)
 
    boundaryTangentMatrixPipeline->getOpPtrVector().push_back(
        new OpBoundaryTangentMatrix(domainField, domainField));
  }
 
  { // Push operators to the Pipeline that is responsible for calculating
    // boundary residual vector (RHS)
 
    // Add default operator to calculate field values at integration points
    boundaryResidualVectorPipeline->getOpPtrVector().push_back(
        new OpCalculateScalarFieldValues(domainField, fieldValuePtr));
 
    boundaryResidualVectorPipeline->getOpPtrVector().push_back(
        new OpBoundaryResidualVector(domainField, boundaryFunction,
                                     previousUpdate));
  }
 
  // get Discrete Manager (SmartPetscObj)
  dM = simpleInterface->getDM();
 
  { // Set operators for nonlinear equations solver (SNES) from MoFEM Pipelines
 
    // Set operators for calculation of LHS and RHS of domain elements
    boost::shared_ptr<FaceEle> null_face;
    CHKERR DMMoFEMSNESSetJacobian(dM, simpleInterface->getDomainFEName(),
                                  domainTangentMatrixPipeline, null_face,
                                  null_face);
    CHKERR DMMoFEMSNESSetFunction(dM, simpleInterface->getDomainFEName(),
                                  domainResidualVectorPipeline, null_face,
                                  null_face);
 
    // Set operators for calculation of LHS and RHS of boundary elements
    boost::shared_ptr<EdgeEle> null_edge;
    CHKERR DMMoFEMSNESSetJacobian(dM, simpleInterface->getBoundaryFEName(),
                                  boundaryTangentMatrixPipeline, null_edge,
                                  null_edge);
    CHKERR DMMoFEMSNESSetFunction(dM, simpleInterface->getBoundaryFEName(),
                                  boundaryResidualVectorPipeline, null_edge,
                                  null_edge);
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::solveSystem() {
  MoFEMFunctionBegin;
 
  // Create RHS and solution vectors
  SmartPetscObj<Vec> global_rhs, global_solution;
  CHKERR DMCreateGlobalVector_MoFEM(dM, global_rhs);
  global_solution = vectorDuplicate(global_rhs);
 
  // Create nonlinear solver (SNES)
  snesSolver = createSNES(mField.get_comm());
  CHKERR SNESSetFromOptions(snesSolver);
 
  // Fieldsplit block solver: yes/no
  if (1) {
    KSP ksp_solver;
    CHKERR SNESGetKSP(snesSolver, &ksp_solver);
    PC pc;
    CHKERR KSPGetPC(ksp_solver, &pc);
 
    PetscBool is_pcfs = PETSC_FALSE;
    PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &is_pcfs);
 
    // Set up FIELDSPLIT, only when option used -pc_type fieldsplit
    if (is_pcfs == PETSC_TRUE) {
      IS is_boundary;
      const MoFEM::Problem *problem_ptr;
      CHKERR DMMoFEMGetProblemPtr(dM, &problem_ptr);
      CHKERR mField.getInterface<ISManager>()->isCreateProblemFieldAndRank(
          problem_ptr->getName(), ROW, domainField, 0, 1, &is_boundary,
          &boundaryEntitiesForFieldsplit);
      // CHKERR ISView(is_boundary, PETSC_VIEWER_STDOUT_SELF);
 
      CHKERR PCFieldSplitSetIS(pc, NULL, is_boundary);
 
      CHKERR ISDestroy(&is_boundary);
    }
  }
 
  CHKERR SNESSetDM(snesSolver, dM);
  CHKERR SNESSetUp(snesSolver);
 
  // Solve the system
  CHKERR SNESSolve(snesSolver, global_rhs, global_solution);
  // VecView(global_rhs, PETSC_VIEWER_STDOUT_SELF);
 
  // Scatter result data on the mesh
  CHKERR DMoFEMMeshToGlobalVector(dM, global_solution, INSERT_VALUES,
                                  SCATTER_REVERSE);
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode NonlinearPoisson::outputResults() {
  MoFEMFunctionBegin;
 
  postProc = boost::make_shared<PostProcEle>(mField);
 
  auto u_ptr = boost::make_shared<VectorDouble>();
  postProc->getOpPtrVector().push_back(
      new OpCalculateScalarFieldValues(domainField, u_ptr));
 
  using OpPPMap = OpPostProcMapInMoab<2, 2>;
 
  postProc->getOpPtrVector().push_back(
 
      new OpPPMap(postProc->getPostProcMesh(), postProc->getMapGaussPts(),
 
                  {{"U", u_ptr}},
 
                  {}, {}, {}
 
                  )
 
  );
 
  CHKERR DMoFEMLoopFiniteElements(
      dM, simpleInterface->getDomainFEName(),
      boost::dynamic_pointer_cast<FEMethod>(postProc));
 
  CHKERR postProc->writeFile("out_result.h5m");
 
  MoFEMFunctionReturn(0);
}
 
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
    NonlinearPoisson poisson_problem(m_field);
    CHKERR poisson_problem.runProgram();
  }
  CATCH_ERRORS;
 
  // Finish work: cleaning memory, getting statistics, etc.
  MoFEM::Core::Finalize();
 
  return 0;
}