diffusion_mip_02c_assembleAand_b.cc

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#include "diffusion_mip.h"
#include "acceleration.h"
 
#include "mesh/MeshContinuum/chi_meshcontinuum.h"
 
#include "math/SpatialDiscretization/SpatialDiscretization.h"
#include "math/SpatialDiscretization/FiniteElement/QuadraturePointData.h"
 
#include "physics/PhysicsMaterial/MultiGroupXS/multigroup_xs.h"
 
#include "A_LBSSolver/lbs_structs.h"
 
#include "chi_runtime.h"
#include "chi_log.h"
#include "utils/chi_timer.h"
#include "console/chi_console.h"
 
#define DefaultBCDirichlet BoundaryCondition{BCType::DIRICHLET,{0,0,0}}
 
//###################################################################
/**Assembles both the matrix and the RHS using unit cell-matrices. These are
 * the routines used in the production versions.*/
void lbs::acceleration::DiffusionMIPSolver::
  AssembleAand_b(const std::vector<double>& q_vector)
{
  const std::string fname = "lbs::acceleration::DiffusionMIPSolver::"
                            "AssembleAand_b";
  if (A_ == nullptr or rhs_ == nullptr or ksp_ == nullptr)
    throw std::logic_error(fname + ": Some or all PETSc elements are null. "
                                   "Check that Initialize has been called.");
  if (options.verbose)
    Chi::log.Log() << Chi::program_timer.GetTimeString() << " Starting assembly";
 
  const size_t num_groups   = uk_man_.unknowns_.front().num_components_;
 
  VecSet(rhs_, 0.0);
  for (const auto& cell : grid_.local_cells)
  {
    const size_t num_faces    = cell.faces_.size();
    const auto&  cell_mapping = sdm_.GetCellMapping(cell);
    const size_t num_nodes    = cell_mapping.NumNodes();
    const auto   cc_nodes     = cell_mapping.GetNodeLocations();
    const auto&  unit_cell_matrices = unit_cell_matrices_[cell.local_id_];
 
    const auto& cell_K_matrix = unit_cell_matrices.K_matrix;
    const auto& cell_M_matrix = unit_cell_matrices.M_matrix;
 
    const auto& xs = mat_id_2_xs_map_.at(cell.material_id_);
 
    for (size_t g=0; g<num_groups; ++g)
    {
      //==================================== Get coefficient and nodal src
      const double Dg     = xs.Dg[g];
      const double sigr_g = xs.sigR[g];
 
      std::vector<double> qg(num_nodes, 0.0);
      for (size_t j=0; j<num_nodes; j++)
        qg[j] = q_vector[sdm_.MapDOFLocal(cell, j, uk_man_, 0, g)];
 
      //==================================== Assemble continuous terms
      for (size_t i=0; i<num_nodes; i++)
      {
        const int64_t imap = sdm_.MapDOF(cell, i, uk_man_, 0, g);
        double entry_rhs_i = 0.0;
        for (size_t j=0; j<num_nodes; j++)
        {
          const int64_t jmap = sdm_.MapDOF(cell, j, uk_man_, 0, g);
 
          const double entry_aij =
            Dg * cell_K_matrix[i][j] +
            sigr_g * cell_M_matrix[i][j];
 
          entry_rhs_i += qg[j]* cell_M_matrix[i][j];
 
          MatSetValue(A_, imap, jmap, entry_aij, ADD_VALUES);
        }//for j
 
        VecSetValue(rhs_, imap, entry_rhs_i, ADD_VALUES);
      }//for i
 
      //==================================== Assemble face terms
      for (size_t f=0; f<num_faces; ++f)
      {
        const auto&  face           = cell.faces_[f];
        const auto&  n_f            = face.normal_;
        const size_t num_face_nodes = cell_mapping.NumFaceNodes(f);
 
        const auto& face_M = unit_cell_matrices.face_M_matrices[f];
        const auto& face_G = unit_cell_matrices.face_G_matrices[f];
        const auto& face_Si = unit_cell_matrices.face_Si_vectors[f];
 
        const double hm = HPerpendicular(cell, f);
 
        typedef chi_mesh::MeshContinuum Grid;
 
        if (face.has_neighbor_)
        {
          const auto&  adj_cell         = grid_.cells[face.neighbor_id_];
          const auto&  adj_cell_mapping = sdm_.GetCellMapping(adj_cell);
          const auto   ac_nodes         = adj_cell_mapping.GetNodeLocations();
          const size_t acf              = Grid::MapCellFace(cell, adj_cell, f);
          const double hp               = HPerpendicular(adj_cell, acf);
 
          const auto&  adj_xs   = mat_id_2_xs_map_.at(adj_cell.material_id_);
          const double adj_Dg   = adj_xs.Dg[g];
 
          //========================= Compute kappa
          double kappa = 1.0;
          if (cell.Type() == chi_mesh::CellType::SLAB)
            kappa = fmax(options.penalty_factor*(adj_Dg/hp + Dg/hm)*0.5,0.25);
          if (cell.Type() == chi_mesh::CellType::POLYGON)
            kappa = fmax(options.penalty_factor*(adj_Dg/hp + Dg/hm)*0.5,0.25);
          if (cell.Type() == chi_mesh::CellType::POLYHEDRON)
            kappa = fmax(options.penalty_factor*2.0*(adj_Dg/hp + Dg/hm)*0.5,0.25);
 
          //========================= Assembly penalty terms
          for (size_t fi=0; fi<num_face_nodes; ++fi)
          {
            const int i  = cell_mapping.MapFaceNode(f,fi);
            const int64_t imap = sdm_.MapDOF(cell, i, uk_man_, 0, g);
 
            for (size_t fj=0; fj<num_face_nodes; ++fj)
            {
              const int jm = cell_mapping.MapFaceNode(f,fj);      //j-minus
              const int jp = MapFaceNodeDisc(cell, adj_cell, cc_nodes, ac_nodes,
                                             f, acf, fj);         //j-plus
              const int64_t jmmap = sdm_.MapDOF(cell, jm, uk_man_, 0, g);
              const int64_t jpmap = sdm_.MapDOF(adj_cell, jp, uk_man_, 0, g);
 
              const double aij = kappa * face_M[i][jm];
 
              MatSetValue(A_, imap, jmmap, aij, ADD_VALUES);
              MatSetValue(A_, imap, jpmap, -aij, ADD_VALUES);
            }//for fj
          }//for fi
 
          //========================= Assemble gradient terms
          // For the following comments we use the notation:
          // Dk = 0.5* n dot nabla bk
 
          // 0.5*D* n dot (b_j^+ - b_j^-)*nabla b_i^-
          for (int i=0; i<num_nodes; i++)
          {
            const int64_t imap = sdm_.MapDOF(cell, i, uk_man_, 0, g);
 
            for (int fj=0; fj<num_face_nodes; fj++)
            {
              const int jm = cell_mapping.MapFaceNode(f,fj);      //j-minus
              const int jp = MapFaceNodeDisc(cell, adj_cell, cc_nodes, ac_nodes,
                                             f, acf, fj);         //j-plus
              const int64_t jmmap = sdm_.MapDOF(cell, jm, uk_man_, 0, g);
              const int64_t jpmap = sdm_.MapDOF(adj_cell, jp, uk_man_, 0, g);
 
              const double aij = -0.5*Dg*n_f.Dot(face_G[jm][i]);
 
              MatSetValue(A_, imap, jmmap, aij, ADD_VALUES);
              MatSetValue(A_, imap, jpmap, -aij, ADD_VALUES);
            }//for fj
          }//for i
 
          // 0.5*D* n dot (b_i^+ - b_i^-)*nabla b_j^-
          for (int fi=0; fi<num_face_nodes; fi++)
          {
            const int im = cell_mapping.MapFaceNode(f,fi);       //i-minus
            const int ip = MapFaceNodeDisc(cell,adj_cell,cc_nodes,ac_nodes,
                                           f,acf,fi);            //i-plus
            const int64_t immap = sdm_.MapDOF(cell, im, uk_man_, 0, g);
            const int64_t ipmap = sdm_.MapDOF(adj_cell, ip, uk_man_, 0, g);
 
            for (int j=0; j<num_nodes; j++)
            {
              const int64_t jmap = sdm_.MapDOF(cell, j, uk_man_, 0, g);
 
              const double aij = -0.5*Dg*n_f.Dot(face_G[im][j]);
 
              MatSetValue(A_, immap, jmap, aij, ADD_VALUES);
              MatSetValue(A_, ipmap, jmap, -aij, ADD_VALUES);
            }//for j
          }//for fi
 
        }//internal face
        else
        {
          auto bc = DefaultBCDirichlet;
          if (bcs_.count(face.neighbor_id_) > 0)
            bc = bcs_.at(face.neighbor_id_);
 
          if (bc.type == BCType::DIRICHLET)
          {
            const double bc_value = bc.values[0];
 
            //========================= Compute kappa
            double kappa = 1.0;
            if (cell.Type() == chi_mesh::CellType::SLAB)
              kappa = fmax(options.penalty_factor*Dg/hm,0.25);
            if (cell.Type() == chi_mesh::CellType::POLYGON)
              kappa = fmax(options.penalty_factor*Dg/hm,0.25);
            if (cell.Type() == chi_mesh::CellType::POLYHEDRON)
              kappa = fmax(options.penalty_factor*2.0*Dg/hm,0.25);
 
            //========================= Assembly penalty terms
            for (size_t fi=0; fi<num_face_nodes; ++fi)
            {
              const int i  = cell_mapping.MapFaceNode(f,fi);
              const int64_t imap = sdm_.MapDOF(cell, i, uk_man_, 0, g);
 
              for (size_t fj=0; fj<num_face_nodes; ++fj)
              {
                const int jm = cell_mapping.MapFaceNode(f,fj);
                const int64_t jmmap = sdm_.MapDOF(cell, jm, uk_man_, 0, g);
 
                const double aij = kappa*face_M[i][jm];
                const double aij_bc_value = aij*bc_value;
 
                MatSetValue(A_  , imap, jmmap, aij, ADD_VALUES);
                VecSetValue(rhs_, imap, aij_bc_value, ADD_VALUES);
              }//for fj
            }//for fi
 
            //========================= Assemble gradient terms
            // For the following comments we use the notation:
            // Dk = n dot nabla bk
 
            // D* n dot (b_j^+ - b_j^-)*nabla b_i^-
            for (size_t i=0; i<num_nodes; i++)
            {
              const int64_t imap = sdm_.MapDOF(cell, i, uk_man_, 0, g);
 
              for (size_t j=0; j<num_nodes; j++)
              {
                const int64_t jmap = sdm_.MapDOF(cell, j, uk_man_, 0, g);
 
                const double aij = -Dg*n_f.Dot(face_G[j][i] + face_G[i][j]);
                const double aij_bc_value = aij*bc_value;
 
 
                MatSetValue(A_, imap, jmap, aij, ADD_VALUES);
                VecSetValue(rhs_, imap, aij_bc_value, ADD_VALUES);
              }//for fj
            }//for i
          }//Dirichlet BC
          else if (bc.type == BCType::ROBIN)
          {
            const double aval = bc.values[0];
            const double bval = bc.values[1];
            const double fval = bc.values[2];
 
            if (std::fabs(bval) < 1.0e-12) continue; //a and f assumed zero
 
            for (size_t fi=0; fi<num_face_nodes; fi++)
            {
              const int i  = cell_mapping.MapFaceNode(f,fi);
              const int64_t ir = sdm_.MapDOF(cell, i, uk_man_, 0, g);
 
              if (std::fabs(aval) >= 1.0e-12)
              {
                for (size_t fj=0; fj<num_face_nodes; fj++)
                {
                  const int j  = cell_mapping.MapFaceNode(f,fj);
                  const int64_t jr = sdm_.MapDOF(cell, j, uk_man_, 0, g);
 
                  const double aij = (aval/bval) * face_M[i][j];
 
                  MatSetValue(A_, ir , jr, aij, ADD_VALUES);
                }//for fj
              }//if a nonzero
 
              if (std::fabs(fval) >= 1.0e-12)
              {
                const double rhs_val = (fval/bval) * face_Si[i];
 
                VecSetValue(rhs_, ir, rhs_val, ADD_VALUES);
              }//if f nonzero
            }//for fi
          }//Robin BC
        }//boundary face
      }//for face
    }//for g
  }//for cell
 
  MatAssemblyBegin(A_, MAT_FINAL_ASSEMBLY);
  MatAssemblyEnd(A_, MAT_FINAL_ASSEMBLY);
  VecAssemblyBegin(rhs_);
  VecAssemblyEnd(rhs_);
 
  if (options.verbose)
  {
    MatInfo info;
    MatGetInfo(A_, MAT_GLOBAL_SUM, &info);
 
    Chi::log.Log() << "Number of mallocs used = " << info.mallocs
                   << "\nNumber of non-zeros allocated = "
                   << info.nz_allocated
                   << "\nNumber of non-zeros used = "
                   << info.nz_used
                   << "\nNumber of unneeded non-zeros = "
                   << info.nz_unneeded;
  }
 
  if (options.perform_symmetry_check)
  {
    PetscBool symmetry = PETSC_FALSE;
    MatIsSymmetric(A_, 1.0e-6, &symmetry);
    if (symmetry == PETSC_FALSE)
      throw std::logic_error(fname + ":Symmetry check failed");
  }
 
  KSPSetOperators(ksp_, A_, A_);
 
  if (options.verbose)
    Chi::log.Log() << Chi::program_timer.GetTimeString() << " Assembly completed";
 
  PC pc;
  KSPGetPC(ksp_, &pc);
  PCSetUp(pc);
 
  KSPSetUp(ksp_);
}