poisson_2d_homogeneous.hpp

Solution of poisson equation. Direct implementation of User Data Operators for teaching proposes.

Note

In practical application we suggest use form integrators to generalise and simplify code. However, here we like to expose user to ways how to implement data operator from scratch.

/**
 * \file poisson_2d_homogeneous.hpp
 * \example poisson_2d_homogeneous.hpp
 *
 * Solution of poisson equation. Direct implementation of User Data Operators
 * for teaching proposes.
 *
 * \note In practical application we suggest use form integrators to generalise
 * and simplify code. However, here we like to expose user to ways how to
 * implement data operator from scratch.
 */
 
// Define name if it has not been defined yet
#ifndef __POISSON_2D_HOMOGENEOUS_HPP__
#define __POISSON_2D_HOMOGENEOUS_HPP__
 
// Use of alias for some specific functions
// We are solving Poisson's equation in 2D so Face element is used
using EntData = EntitiesFieldData::EntData;
 
template <int DIM>
using ElementsAndOps = PipelineManager::ElementsAndOpsByDim<SPACE_DIM>;
using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle;
using DomainEleOp = DomainEle::UserDataOperator;
 
using AssemblyDomainEleOp =
    FormsIntegrators<DomainEleOp>::Assembly<PETSC>::OpBase;
 
// Namespace that contains necessary UDOs, will be included in the main program
namespace Poisson2DHomogeneousOperators {
 
// Declare FTensor index for 2D problem
FTensor::Index<'i', SPACE_DIM> i;
 
// For simplicity, source term f will be constant throughout the domain
const double body_source = 5.;
 
struct OpDomainLhsMatrixK : public AssemblyDomainEleOp {
public:
  OpDomainLhsMatrixK(std::string row_field_name, std::string col_field_name)
      : AssemblyDomainEleOp(row_field_name, col_field_name,
                            DomainEleOp::OPROWCOL) {}
 
  MoFEMErrorCode iNtegrate(EntitiesFieldData::EntData &row_data,
                           EntitiesFieldData::EntData &col_data) {
    MoFEMFunctionBegin;
 
    const int nb_row_dofs = row_data.getIndices().size();
    const int nb_col_dofs = col_data.getIndices().size();
 
    this->locMat.resize(nb_row_dofs, nb_col_dofs, false);
    this->locMat.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 derivatives of base functions on row
    auto t_row_diff_base = row_data.getFTensor1DiffN<SPACE_DIM>();
 
    // 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 derivatives of base functions on column
        auto t_col_diff_base = col_data.getFTensor1DiffN<SPACE_DIM>(gg, 0);
 
        for (int cc = 0; cc != nb_col_dofs; cc++) {
          this->locMat(rr, cc) += t_row_diff_base(i) * t_col_diff_base(i) * a;
 
          // move to the derivatives of the next base functions on column
          ++t_col_diff_base;
        }
 
        // move to the derivatives of the next base functions on row
        ++t_row_diff_base;
      }
 
      // move to the weight of the next integration point
      ++t_w;
    }
 
    MoFEMFunctionReturn(0);
  }
};
 
struct OpDomainRhsVectorF : public AssemblyDomainEleOp {
public:
  OpDomainRhsVectorF(std::string field_name)
      : AssemblyDomainEleOp(field_name, field_name, DomainEleOp::OPROW) {}
 
  MoFEMErrorCode iNtegrate(EntitiesFieldData::EntData &data) {
    MoFEMFunctionBegin;
 
    const int nb_dofs = data.getIndices().size();
 
    this->locF.resize(nb_dofs, false);
    this->locF.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 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 * area;
 
      for (int rr = 0; rr != nb_dofs; rr++) {
        this->locF[rr] += t_base * body_source * a;
 
        // move to the next base function
        ++t_base;
      }
 
      // move to the weight of the next integration point
      ++t_w;
    }
 
    MoFEMFunctionReturn(0);
  }
 
};
 
}; // namespace Poisson2DHomogeneousOperators
 
#endif //__POISSON_2D_HOMOGENEOUS_HPP__