SCL-0: Least square approximaton

Note

Prerequisites of this tutorial include MSH-1: Create a 2D mesh from Gmsh

Note

Intended learning outcome:

• general structure of a program developed using MoFEM
• idea of Simple Interface in MoFEM and how to use it
• idea of Domain element in MoFEM and how to use it
• Use default Forms Integrals
• how to push the developed UDOs to the Pipeline
• utilisation of tools to convert outputs (MOAB) and visualise them (Paraview)

/**
 * \file approximation.cpp
 * \example approximation.cpp
 *
 * Using PipelineManager interface calculate the divergence of base functions,
 * and integral of flux on the boundary. Since the h-div space is used, volume
 * integral and boundary integral should give the same result.
 */
 
#include <MoFEM.hpp>
 
using namespace MoFEM;
 
static char help[] = "...\n\n";
 
#include <BasicFiniteElements.hpp>
 
constexpr char FIELD_NAME[] = "U";
constexpr int FIELD_DIM = 1;
constexpr int SPACE_DIM = 2;
 
template <int DIM> struct ElementsAndOps {};
 
template <> struct ElementsAndOps<2> {
  using DomainEle = PipelineManager::FaceEle;
};
 
template <> struct ElementsAndOps<3> {
  using DomainEle = VolumeElementForcesAndSourcesCore;
};
 
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = DomainEle::UserDataOperator;
using EntData = EntitiesFieldData::EntData;
 
using PostProcEle = PostProcBrokenMeshInMoab<DomainEle>;
 
template <int FIELD_DIM> struct ApproxFieldFunction;
 
template <> struct ApproxFieldFunction<1> {
  double operator()(const double x, const double y, const double z) {
    return sin(x * 10.) * cos(y * 10.);
  }
};
 
using OpDomainMass = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::BiLinearForm<GAUSS>::OpMass<1, FIELD_DIM>;
using OpDomainSource = FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpSource<1, FIELD_DIM>;
 
struct Example {
 
  Example(MoFEM::Interface &m_field) : mField(m_field) {}
 
  MoFEMErrorCode runProblem();
 
private:
  MoFEM::Interface &mField;
  Simple *simpleInterface;
 
  static ApproxFieldFunction<FIELD_DIM> approxFunction;
 
  MoFEMErrorCode readMesh();
  MoFEMErrorCode setupProblem();
  MoFEMErrorCode setIntegrationRules();
  MoFEMErrorCode createCommonData();
  MoFEMErrorCode boundaryCondition();
  MoFEMErrorCode assembleSystem();
  MoFEMErrorCode solveSystem();
  MoFEMErrorCode outputResults();
  MoFEMErrorCode checkResults();
 
  struct CommonData {
    boost::shared_ptr<VectorDouble> approxVals;
    SmartPetscObj<Vec> L2Vec;
    SmartPetscObj<Vec> resVec;
  };
  boost::shared_ptr<CommonData> commonDataPtr;
 
  template <int FIELD_DIM> struct OpError;
};
 
ApproxFieldFunction<FIELD_DIM> Example::approxFunction =
    ApproxFieldFunction<FIELD_DIM>();
 
template <> struct Example::OpError<1> : public DomainEleOp {
  boost::shared_ptr<CommonData> commonDataPtr;
  OpError(boost::shared_ptr<CommonData> &common_data_ptr)
      : DomainEleOp(FIELD_NAME, OPROW), commonDataPtr(common_data_ptr) {}
  MoFEMErrorCode doWork(int side, EntityType type, EntData &data) {
    MoFEMFunctionBegin;
 
    if (const size_t nb_dofs = data.getIndices().size()) {
 
      const int nb_integration_pts = getGaussPts().size2();
      auto t_w = getFTensor0IntegrationWeight();
      auto t_val = getFTensor0FromVec(*(commonDataPtr->approxVals));
      auto t_coords = getFTensor1CoordsAtGaussPts();
 
      VectorDouble nf(nb_dofs, false);
      nf.clear();
 
      FTensor::Index<'i', 3> i;
      const double volume = getMeasure();
 
      auto t_row_base = data.getFTensor0N();
      double error = 0;
      for (int gg = 0; gg != nb_integration_pts; ++gg) {
 
        const double alpha = t_w * volume;
        double diff = t_val - Example::approxFunction(t_coords(0), t_coords(1),
                                                      t_coords(2));
        error += alpha * pow(diff, 2);
 
        for (size_t r = 0; r != nb_dofs; ++r) {
          nf[r] += alpha * t_row_base * diff;
          ++t_row_base;
        }
 
        ++t_w;
        ++t_val;
        ++t_coords;
      }
 
      const int index = 0;
      CHKERR VecSetValue(commonDataPtr->L2Vec, index, error, ADD_VALUES);
      CHKERR VecSetValues(commonDataPtr->resVec, data, &nf[0], ADD_VALUES);
    }
 
    MoFEMFunctionReturn(0);
  }
};
 
//! [Run programme]
MoFEMErrorCode Example::runProblem() {
  MoFEMFunctionBegin;
  CHKERR readMesh();
  CHKERR setupProblem();
  CHKERR setIntegrationRules();
  CHKERR createCommonData();
  CHKERR boundaryCondition();
  CHKERR assembleSystem();
  CHKERR solveSystem();
  CHKERR outputResults();
  CHKERR checkResults();
  MoFEMFunctionReturn(0);
}
//! [Run programme]
 
//! [Read mesh]
MoFEMErrorCode Example::readMesh() {
  MoFEMFunctionBegin;
 
  CHKERR mField.getInterface(simpleInterface);
  CHKERR simpleInterface->getOptions();
  CHKERR simpleInterface->loadFile();
 
  MoFEMFunctionReturn(0);
}
//! [Read mesh]
 
//! [Set up problem]
MoFEMErrorCode Example::setupProblem() {
  MoFEMFunctionBegin;
  // Add field
  CHKERR simpleInterface->addDomainField(FIELD_NAME, H1,
                                         AINSWORTH_LEGENDRE_BASE, FIELD_DIM);
  constexpr int order = 4;
  CHKERR simpleInterface->setFieldOrder(FIELD_NAME, order);
  CHKERR simpleInterface->setUp();
  MoFEMFunctionReturn(0);
}
//! [Set up problem]
 
//! [Set integration rule]
MoFEMErrorCode Example::setIntegrationRules() {
  MoFEMFunctionBegin;
 
  auto rule = [](int, int, int p) -> int { return 2 * p; };
 
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  CHKERR pipeline_mng->setDomainLhsIntegrationRule(rule);
  CHKERR pipeline_mng->setDomainRhsIntegrationRule(rule);
 
  MoFEMFunctionReturn(0);
}
//! [Set integration rule]
 
//! [Create common data]
MoFEMErrorCode Example::createCommonData() {
  MoFEMFunctionBegin;
  commonDataPtr = boost::make_shared<CommonData>();
  commonDataPtr->resVec = createDMVector(simpleInterface->getDM());
  commonDataPtr->L2Vec = createVectorMPI(
      mField.get_comm(), (!mField.get_comm_rank()) ? 1 : 0, 1);
  commonDataPtr->approxVals = boost::make_shared<VectorDouble>();
  MoFEMFunctionReturn(0);
}
//! [Create common data]
 
//! [Boundary condition]
MoFEMErrorCode Example::boundaryCondition() { return 0; }
//! [Boundary condition]
 
//! [Push operators to pipeline]
MoFEMErrorCode Example::assembleSystem() {
  MoFEMFunctionBegin;
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  auto beta = [](const double, const double, const double) { return 1; };
  pipeline_mng->getOpDomainLhsPipeline().push_back(
      new OpDomainMass(FIELD_NAME, FIELD_NAME, beta));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpDomainSource(FIELD_NAME, approxFunction));
  MoFEMFunctionReturn(0);
}
//! [Push operators to pipeline]
 
//! [Solve]
MoFEMErrorCode Example::solveSystem() {
  MoFEMFunctionBegin;
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  auto solver = pipeline_mng->createKSP();
  CHKERR KSPSetFromOptions(solver);
  CHKERR KSPSetUp(solver);
 
  auto dm = simpleInterface->getDM();
  auto D = createDMVector(dm);
  auto F = vectorDuplicate(D);
 
  CHKERR KSPSolve(solver, F, D);
  CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
  CHKERR DMoFEMMeshToLocalVector(dm, D, INSERT_VALUES, SCATTER_REVERSE);
  MoFEMFunctionReturn(0);
}
 
//! [Solve]
MoFEMErrorCode Example::outputResults() {
  MoFEMFunctionBegin;
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  pipeline_mng->getDomainLhsFE().reset();
  auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
 
  auto u_ptr = boost::make_shared<VectorDouble>();
  post_proc_fe->getOpPtrVector().push_back(
      new OpCalculateScalarFieldValues(FIELD_NAME, u_ptr));
 
  using OpPPMap = OpPostProcMapInMoab<3, 3>;
 
  post_proc_fe->getOpPtrVector().push_back(
 
      new OpPPMap(
 
          post_proc_fe->getPostProcMesh(), post_proc_fe->getMapGaussPts(),
 
          {{FIELD_NAME, u_ptr}},
 
          {},
 
          {},
 
          {})
 
  );
  
  pipeline_mng->getDomainRhsFE() = post_proc_fe;
  CHKERR pipeline_mng->loopFiniteElements();
  CHKERR post_proc_fe->writeFile("out_approx.h5m");
  MoFEMFunctionReturn(0);
}
//! [Postprocess results]
 
//! [Check results]
MoFEMErrorCode Example::checkResults() {
  MoFEMFunctionBegin;
  PipelineManager *pipeline_mng = mField.getInterface<PipelineManager>();
  pipeline_mng->getDomainLhsFE().reset();
  pipeline_mng->getDomainRhsFE().reset();
  pipeline_mng->getOpDomainRhsPipeline().clear();
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpCalculateScalarFieldValues(FIELD_NAME, commonDataPtr->approxVals));
  pipeline_mng->getOpDomainRhsPipeline().push_back(
      new OpError<FIELD_DIM>(commonDataPtr));
  CHKERR pipeline_mng->loopFiniteElements();
  CHKERR VecAssemblyBegin(commonDataPtr->L2Vec);
  CHKERR VecAssemblyEnd(commonDataPtr->L2Vec);
  CHKERR VecAssemblyBegin(commonDataPtr->resVec);
  CHKERR VecAssemblyEnd(commonDataPtr->resVec);
  double nrm2;
  CHKERR VecNorm(commonDataPtr->resVec, NORM_2, &nrm2);
  const double *array;
  CHKERR VecGetArrayRead(commonDataPtr->L2Vec, &array);
  if (mField.get_comm_rank() == 0)
    PetscPrintf(PETSC_COMM_SELF, "Error %6.4e Vec norm %6.4e\n", std::sqrt(array[0]),
                nrm2);
  CHKERR VecRestoreArrayRead(commonDataPtr->L2Vec, &array);
  constexpr double eps = 1e-8;
  if (nrm2 > eps)
    SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
            "Not converged solution");
  MoFEMFunctionReturn(0);
}
//! [Check 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);
 
  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]
 
    //! [Example]
    Example ex(m_field);
    CHKERR ex.runProblem();
    //! [Example]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
}