dofhandler.cc

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/*!
 *
 * Copyright (C) 2015 Technical University of Liberec.  All rights reserved.
 * 
 * This program is free software; you can redistribute it and/or modify it under
 * the terms of the GNU General Public License version 3 as published by the
 * Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)
 * 
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
 *
 * 
 * @file    dofhandler.cc
 * @brief   Declaration of class which handles the ordering of degrees of freedom (dof) and mappings between local and global dofs.
 * @author  Jan Stebel
 */
 
#include "system/index_types.hh"
#include "fem/dofhandler.hh"
#include "fem/finite_element.hh"
#include "fem/fe_system.hh"
#include "fem/dh_cell_accessor.hh"
#include "mesh/mesh.h"
#include "mesh/duplicate_nodes.h"
#include "mesh/partitioning.hh"
#include "mesh/accessors.hh"
#include "mesh/range_wrapper.hh"
#include "mesh/neighbours.h"
#include "la/distribution.hh"
 
 
const int DOFHandlerMultiDim::INVALID_NFACE  = 1;
const int DOFHandlerMultiDim::VALID_NFACE    = 2;
const int DOFHandlerMultiDim::ASSIGNED_NFACE = 3;
const int DOFHandlerMultiDim::INVALID_DOF   = -1;
 
 
 
 
DOFHandlerBase::~DOFHandlerBase()
{}
 
 
 
 
 
 
DOFHandlerMultiDim::DOFHandlerMultiDim(MeshBase& _mesh, bool make_elem_part)
    : DOFHandlerBase(_mesh),
      ds_(nullptr),
      is_parallel_(true),
      dh_seq_(nullptr),
      scatter_to_seq_(nullptr),
      el_ds_(nullptr)
{
    if (make_elem_part) make_elem_partitioning();
}
 
 
std::shared_ptr<DOFHandlerMultiDim> DOFHandlerMultiDim::sequential()
{
    create_sequential();
    return dh_seq_;
}
 
 
std::shared_ptr<VecScatter> DOFHandlerMultiDim::sequential_scatter()
{
    create_sequential();
    return scatter_to_seq_;
}
 
 
void DOFHandlerMultiDim::init_cell_starts()
{
    // get number of dofs per element and then set up cell_starts
    cell_starts = std::vector<LongIdx>(el_ds_->lsize()+ghost_4_loc.size()+1, 0);
    for (auto cell : this->local_range())
    {
        cell_starts[cell.local_idx()+1] = cell.n_dofs();
        max_elem_dofs_ = max( (int)max_elem_dofs_, (int)cell.n_dofs() );
    }
    for (unsigned int i=0; i<cell_starts.size()-1; ++i)
        cell_starts[i+1] += cell_starts[i];
}
 
 
void DOFHandlerMultiDim::init_dof_starts(
    std::vector<LongIdx> &node_dof_starts,
    std::vector<LongIdx> &edge_dof_starts)
{
    // initialize dofs on nodes
    // We must separate dofs for dimensions because FE functions
    // may be discontinuous on nodes shared by different
    // dimensions.
    unsigned int n_node_dofs = 0;
    for (unsigned int nid=0; nid<mesh_->duplicate_nodes()->n_nodes(); nid++)
    {
      node_dof_starts.push_back(n_node_dofs);
      n_node_dofs += ds_->n_node_dofs(nid);
    }
    node_dof_starts.push_back(n_node_dofs);
    
    unsigned int n_edge_dofs = 0;
    for (auto edge : mesh_->edge_range())
    {
        edge_dof_starts.push_back(n_edge_dofs);
        n_edge_dofs += ds_->n_edge_dofs(edge);
    }
    edge_dof_starts.push_back(n_edge_dofs);
}
 
 
void DOFHandlerMultiDim::init_status(
    std::vector<short int> &node_status,
    std::vector<short int> &edge_status)
{
    // mark local dofs
    for (auto cell : this->own_range())
    {
      for (unsigned int n=0; n<cell.dim()+1; n++)
      {
        unsigned int nid = mesh_->duplicate_nodes()->objects(cell.dim())[mesh_->duplicate_nodes()->obj_4_el()[cell.elm_idx()]].nodes[n];
        node_status[nid] = VALID_NFACE;
      }
    }
    
    // unmark dofs on ghost cells from lower procs
    for (auto cell : this->ghost_range())
    {
      if (cell.elm().proc() < el_ds_->myp())
      {
        for (unsigned int n=0; n<cell.dim()+1; n++)
        {
          unsigned int nid = mesh_->duplicate_nodes()->objects(cell.dim())[mesh_->duplicate_nodes()->obj_4_el()[cell.elm_idx()]].nodes[n];
          node_status[nid] = INVALID_NFACE;
        }
      }
    }
    
    // mark local edges
    for (auto eid : edg_4_loc)
        edge_status[eid] = VALID_NFACE;
    
    // unmark dofs on ghost cells from lower procs
    for (auto cell : this->ghost_range())
    {
      if (cell.elm().proc() < el_ds_->myp())
      {
        for (unsigned int n=0; n<cell.dim()+1; n++)
        {
          unsigned int eid = cell.elm().side(n)->edge_idx();
          edge_status[eid] = INVALID_NFACE;
        }
      }
    }
}
 
 
void DOFHandlerMultiDim::receive_ghost_dofs(unsigned int proc, vector<LongIdx> &dofs)
{
    // send number of elements required from the other processor
    unsigned int n_elems = ghost_proc_el[proc].size();
    MPI_Send(&n_elems, 1, MPI_UNSIGNED, proc, 0, MPI_COMM_WORLD);
    
    // send indices of elements required
    MPI_Send(&(ghost_proc_el[proc][0]), n_elems, MPI_LONG_IDX, proc, 1, MPI_COMM_WORLD);
    
    // receive numbers of dofs on required elements
    vector<unsigned int> n_dofs(n_elems);
    MPI_Recv(&(n_dofs[0]), n_elems, MPI_UNSIGNED, proc, 2, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // receive dofs on required elements
    unsigned int n_dofs_sum = 0;
    for (auto nd : n_dofs) n_dofs_sum += nd;
    dofs.resize(n_dofs_sum);
    MPI_Recv(&(dofs[0]), n_dofs_sum, MPI_LONG_IDX, proc, 3, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
}
 
 
void DOFHandlerMultiDim::send_ghost_dofs(unsigned int proc)
{
    // receive number of elements required by the other processor
    unsigned int n_elems;
    MPI_Recv(&n_elems, 1, MPI_UNSIGNED, proc, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // receive indices of elements required
    vector<LongIdx> elems(n_elems);
    MPI_Recv(&(elems[0]), n_elems, MPI_LONG_IDX, proc, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // send numbers of dofs on required elements
    vector<unsigned int> n_dofs;
    for (LongIdx el : elems)
    {
        auto cell = this->cell_accessor_from_element(el);
        n_dofs.push_back(cell_starts[cell.local_idx()+1] - cell_starts[cell.local_idx()]);
    }
    MPI_Send(&(n_dofs[0]), n_elems, MPI_UNSIGNED, proc, 2, MPI_COMM_WORLD);
    
    // send dofs on the required elements
    vector<LongIdx> dofs;
    for (LongIdx el : elems)
    {
        auto cell = this->cell_accessor_from_element(el);
        for (LongIdx i=cell_starts[cell.local_idx()]; i<cell_starts[cell.local_idx()+1]; i++)
            dofs.push_back(local_to_global_dof_idx_[dof_indices[i]]);
    }
    MPI_Send(&(dofs[0]), dofs.size(), MPI_LONG_IDX, proc, 3, MPI_COMM_WORLD);
}
 
 
void DOFHandlerMultiDim::update_local_dofs(unsigned int proc,
                                           const std::vector<bool> &update_cells,
                                           const std::vector<LongIdx> &dofs, 
                                           const std::vector<LongIdx> &node_dof_starts,
                                           std::vector<LongIdx> &node_dofs,
                                           const std::vector<LongIdx> &edge_dof_starts,
                                           std::vector<LongIdx> &edge_dofs)
{
    // update dof_indices on ghost cells
    unsigned int dof_offset=0;
    for (unsigned int gid=0; gid<ghost_proc_el[proc].size(); gid++)
    {
        DHCellAccessor dh_cell = this->cell_accessor_from_element( ghost_proc_el[proc][gid] );
        
        vector<unsigned int> loc_node_dof_count(dh_cell.elm()->n_nodes(), 0);
        vector<unsigned int> loc_edge_dof_count(dh_cell.elm()->n_sides(), 0);
        for (unsigned int idof = 0; idof<dh_cell.n_dofs(); ++idof)
        {
            if (dh_cell.cell_dof(idof).dim == 0)
            {   // update nodal dof
                unsigned int dof_nface_idx = dh_cell.cell_dof(idof).n_face_idx;
                unsigned int nid = mesh_->duplicate_nodes()->objects(dh_cell.dim())[mesh_->duplicate_nodes()->obj_4_el()[dh_cell.elm_idx()]].nodes[dof_nface_idx];
                unsigned int node_dof_idx = node_dof_starts[nid]+loc_node_dof_count[dof_nface_idx];
                    
                if (node_dofs[node_dof_idx] == INVALID_DOF)
                {
                    node_dofs[node_dof_idx] = local_to_global_dof_idx_.size();
                    local_to_global_dof_idx_.push_back(dofs[dof_offset+idof]);
                }
                dof_indices[cell_starts[dh_cell.local_idx()]+idof] = node_dofs[node_dof_idx];
                
                loc_node_dof_count[dof_nface_idx]++;
            }
            else if (dh_cell.cell_dof(idof).dim == dh_cell.dim()-1)
            {   // update edge dof
                unsigned int dof_nface_idx = dh_cell.cell_dof(idof).n_face_idx;
                unsigned int eid = dh_cell.elm().side(dof_nface_idx)->edge_idx();
                unsigned int edge_dof_idx = edge_dof_starts[eid]+loc_edge_dof_count[dof_nface_idx];
                    
                if (edge_dofs[edge_dof_idx] == INVALID_DOF)
                {
                    edge_dofs[edge_dof_idx] = local_to_global_dof_idx_.size();
                    local_to_global_dof_idx_.push_back(dofs[dof_offset+idof]);
                }
                dof_indices[cell_starts[dh_cell.local_idx()]+idof] = edge_dofs[edge_dof_idx];
                
                loc_edge_dof_count[dof_nface_idx]++;
            } else if (dh_cell.cell_dof(idof).dim == dh_cell.dim())
            {
                dof_indices[cell_starts[dh_cell.local_idx()]+idof] = local_to_global_dof_idx_.size();
                local_to_global_dof_idx_.push_back(dofs[dof_offset+idof]);
            }
        }
        
        dof_offset += dh_cell.n_dofs();
    }
    
    // update dof_indices on local elements
    for (auto cell : this->own_range())
    {
        if (!update_cells[cell.local_idx()]) continue;
        
        // loop over element dofs
        vector<unsigned int> loc_node_dof_count(cell.elm()->n_nodes(), 0);
        vector<unsigned int> loc_edge_dof_count(cell.elm()->n_sides(), 0);
        for (unsigned int idof = 0; idof<cell.n_dofs(); ++idof)
        {
            unsigned int dof_nface_idx = cell.cell_dof(idof).n_face_idx;
            if (cell.cell_dof(idof).dim == 0)
            {
                if (dof_indices[cell_starts[cell.local_idx()]+idof] == INVALID_DOF)
                {   // update nodal dof
                    unsigned int nid = mesh_->duplicate_nodes()->objects(cell.dim())[mesh_->duplicate_nodes()->obj_4_el()[cell.elm_idx()]].nodes[dof_nface_idx];
                    dof_indices[cell_starts[cell.local_idx()]+idof] = node_dofs[node_dof_starts[nid]+loc_node_dof_count[dof_nface_idx]];
                }
                loc_node_dof_count[dof_nface_idx]++;
            } else if (cell.cell_dof(idof).dim == cell.dim()-1)
            {
                if (dof_indices[cell_starts[cell.local_idx()]+idof] == INVALID_DOF)
                {   // update edge dof
                    unsigned int eid = cell.elm().side(dof_nface_idx)->edge_idx();
                    dof_indices[cell_starts[cell.local_idx()]+idof] = edge_dofs[edge_dof_starts[eid]+loc_edge_dof_count[dof_nface_idx]];
                }
                loc_edge_dof_count[dof_nface_idx]++;
            }
        }
    }
}
 
 
void DOFHandlerMultiDim::distribute_dofs(std::shared_ptr<DiscreteSpace> ds)
{
    // First check if dofs are already distributed.
    ASSERT_PERMANENT(ds_ == nullptr).error("Attempt to distribute DOFs multiple times!");
    
    ds_ = ds;
 
    std::vector<LongIdx> node_dofs, node_dof_starts, edge_dofs, edge_dof_starts;
    std::vector<short int> node_status(mesh_->duplicate_nodes()->n_nodes(), INVALID_NFACE),
                           edge_status(mesh_->n_edges(), INVALID_NFACE);
    std::vector<bool> update_cells(el_ds_->lsize(), false);
    unsigned int next_free_dof = 0;
 
    init_cell_starts();
    init_dof_starts(node_dof_starts, edge_dof_starts);
    node_dofs.resize(node_dof_starts[node_dof_starts.size()-1], (LongIdx)INVALID_DOF);
    edge_dofs.resize(edge_dof_starts[edge_dof_starts.size()-1], (LongIdx)INVALID_DOF);
    init_status(node_status, edge_status);
    
    // Distribute dofs on local elements.
    dof_indices.resize(cell_starts[cell_starts.size()-1]);
    local_to_global_dof_idx_.reserve(dof_indices.size());
    for (auto cell : this->own_range())
    {
      
      // loop over element dofs
      vector<unsigned int> loc_node_dof_count(cell.elm()->n_nodes(), 0);
      vector<unsigned int> loc_edge_dof_count(cell.elm()->dim()+1, 0);
      for (unsigned int idof = 0; idof<cell.n_dofs(); ++idof)
      {
        unsigned int dof_dim = cell.cell_dof(idof).dim;
        unsigned int dof_nface_idx = cell.cell_dof(idof).n_face_idx;
        
        if (dof_dim == 0)
        {   // add dofs shared by nodes
            unsigned int nid = mesh_->duplicate_nodes()->objects(cell.dim())[mesh_->duplicate_nodes()->obj_4_el()[cell.elm_idx()]].nodes[dof_nface_idx];
            unsigned int node_dof_idx = node_dof_starts[nid]+loc_node_dof_count[dof_nface_idx];
                
            switch (node_status[nid])
            {
            case VALID_NFACE:
                for (int i=0; i<node_dof_starts[nid+1] - node_dof_starts[nid]; i++)
                {
                    local_to_global_dof_idx_.push_back(next_free_dof);
                    node_dofs[node_dof_starts[nid]+i] = next_free_dof++;
                }
                node_status[nid] = ASSIGNED_NFACE;
                break;
            case INVALID_NFACE:
                node_dofs[node_dof_idx] = INVALID_DOF;
                update_cells[cell.local_idx()] = true;
                break;
            }
            dof_indices[cell_starts[cell.local_idx()]+idof] = node_dofs[node_dof_idx];
            loc_node_dof_count[dof_nface_idx]++;
        }
        else if (dof_dim == cell.dim()-1)
        {   // add dofs shared by edges
            unsigned int eid = cell.elm().side(dof_nface_idx)->edge_idx();
            unsigned int edge_dof_idx = edge_dof_starts[eid]+loc_edge_dof_count[dof_nface_idx];
            switch (edge_status[eid])
            {
            case VALID_NFACE:
                for (int i=0; i<edge_dof_starts[eid+1] - edge_dof_starts[eid]; i++)
                {
                    local_to_global_dof_idx_.push_back(next_free_dof);
                    edge_dofs[edge_dof_starts[eid]+i] = next_free_dof++;
                }
                edge_status[eid] = ASSIGNED_NFACE;
                break;
            case INVALID_NFACE:
                edge_dofs[edge_dof_idx] = INVALID_DOF;
                update_cells[cell.local_idx()] = true;
                break;
            }
            dof_indices[cell_starts[cell.local_idx()]+idof] = edge_dofs[edge_dof_idx];
            loc_edge_dof_count[dof_nface_idx]++;
        }
        else if (dof_dim == cell.dim())
        {   // add dofs owned only by the element
            local_to_global_dof_idx_.push_back(next_free_dof);
            dof_indices[cell_starts[cell.local_idx()]+idof] = next_free_dof++;
        }
        else
            ASSERT_PERMANENT(false).error("Unsupported dof n_face.");
      }
    }
    node_status.clear();
    edge_status.clear();
    
    lsize_ = next_free_dof;
 
    // communicate n_dofs across all processes
    dof_ds_ = std::make_shared<Distribution>(lsize_, PETSC_COMM_WORLD);
    n_global_dofs_ = dof_ds_->size();
    
    // shift dof indices
    loffset_ = dof_ds_->get_starts_array()[dof_ds_->myp()];
    if (loffset_ > 0)
    {
      for (auto &i : local_to_global_dof_idx_)
          i += loffset_;
    }
    
    // communicate dofs from ghost cells
    // first propagate from lower procs to higher procs and then vice versa
    for (unsigned int from_higher = 0; from_higher < 2; from_higher++)
    {
        for (unsigned int proc : ghost_proc)
        {
            if ((proc > el_ds_->myp()) == from_higher)
            { // receive dofs from master processor
                vector<LongIdx> dofs;
                receive_ghost_dofs(proc, dofs);
                
                // update dof_indices and node_dofs on ghost elements
                update_local_dofs(proc,
                                  update_cells,
                                  dofs,
                                  node_dof_starts,
                                  node_dofs,
                                  edge_dof_starts,
                                  edge_dofs
                                 );
                
            }
            else
                send_ghost_dofs(proc);
        }
    }
    update_cells.clear();
    node_dofs.clear();
    node_dof_starts.clear();
    edge_dofs.clear();
    edge_dof_starts.clear();
}
 
 
void DOFHandlerMultiDim::create_sequential()
{
  if (dh_seq_ != nullptr) return;
  
  if ( !is_parallel_ )
  {
      dh_seq_ = std::make_shared<DOFHandlerMultiDim>(*this);
      return;
  }
  
  dh_seq_ = std::make_shared<DOFHandlerMultiDim>(*mesh_);
  
  dh_seq_->n_global_dofs_ = n_global_dofs_;
  dh_seq_->lsize_ = n_global_dofs_;
  dh_seq_->loffset_ = 0;
  dh_seq_->mesh_ = mesh_;
  dh_seq_->dof_ds_ = dof_ds_;  // should be sequential distribution
  dh_seq_->ds_ = ds_;
  dh_seq_->is_parallel_ = false;
  for (unsigned int i=0; i<n_global_dofs_; i++) dh_seq_->local_to_global_dof_idx_.push_back(i);
  
  MPI_Allreduce(
    &max_elem_dofs_,
    &dh_seq_->max_elem_dofs_,
    1,
    MPI_UNSIGNED,
    MPI_MAX,
    MPI_COMM_WORLD);
 
  for (unsigned int i=0; i<mesh_->n_elements(); i++) dh_seq_->global_to_local_el_idx_[i] = mesh_->get_row_4_el()[i];
  
  // Auxiliary vectors cell_starts_loc and dof_indices_loc contain
  // only local element data (without ghost elements).
  // Then it is possible to create sequential vectors by simple reduce/gather operation.
  vector<LongIdx> cell_starts_loc(mesh_->n_elements()+1, 0);
  vector<LongIdx> dof_indices_loc;
  
  // construct cell_starts_loc
  for (auto cell : this->own_range())
  {
    cell_starts_loc[mesh_->get_row_4_el()[cell.elm_idx()]+1] = cell.n_dofs();
  }
  for (unsigned int i=0; i<mesh_->n_elements(); ++i)
    cell_starts_loc[i+1] += cell_starts_loc[i];
 
  // construct dof_indices_loc
  dof_indices_loc.resize(cell_starts_loc[mesh_->n_elements()]);
  for (auto cell : this->own_range())
  {
    for (unsigned int idof=0; idof<cell.n_dofs(); idof++)
        dof_indices_loc[cell_starts_loc[mesh_->get_row_4_el()[cell.elm_idx()]]+idof] = local_to_global_dof_idx_[dof_indices[cell_starts[cell.local_idx()]+idof]];
  }
  
  Distribution distr(dof_indices_loc.size(), PETSC_COMM_WORLD);
  dh_seq_->cell_starts.resize(mesh_->n_elements()+1);
  dh_seq_->dof_indices.resize(distr.size());
  
  MPI_Allreduce( cell_starts_loc.data(),
                 dh_seq_->cell_starts.data(),
                 cell_starts_loc.size(),
                 MPI_LONG_IDX,
                 MPI_SUM,
                 MPI_COMM_WORLD );
  
  MPI_Allgatherv( dof_indices_loc.data(),
                  dof_indices_loc.size(),
                  MPI_LONG_IDX,
                  dh_seq_->dof_indices.data(),
                  (const int *)distr.get_lsizes_array(),
                  (const int *)distr.get_starts_array(),
                  MPI_LONG_IDX,
                  MPI_COMM_WORLD );
  
  // create scatter from parallel to sequential vector
  Vec v_from;
  VecCreateMPI(PETSC_COMM_WORLD, lsize_, PETSC_DETERMINE, &v_from);
  scatter_to_seq_ = std::make_shared<VecScatter>();
  VecScatterCreateToAll(v_from, scatter_to_seq_.get(), NULL);
  VecDestroy(&v_from);
  
  // create scatter for sequential dof handler (Warning: not tested)
  Vec v_seq;
  VecCreateSeq(PETSC_COMM_SELF, n_global_dofs_, &v_seq);
  dh_seq_->scatter_to_seq_ = std::make_shared<VecScatter>();
  VecScatterCreateToAll(v_seq, dh_seq_->scatter_to_seq_.get(), NULL);
  VecDestroy(&v_seq);
}
 
 
VectorMPI DOFHandlerMultiDim::create_vector()
{
    if (is_parallel_ && el_ds_->np() > 1)
    {   // for parallel DH create vector with ghost values
        std::vector<LongIdx> ghost_dofs(local_to_global_dof_idx_.begin() + lsize_, local_to_global_dof_idx_.end());
        VectorMPI vec(lsize_, ghost_dofs);
        return vec;
    } else {
        VectorMPI vec(lsize_, PETSC_COMM_SELF);
        return vec;
    }
}
 
 
unsigned int DOFHandlerMultiDim::get_dof_indices(const DHCellAccessor &cell, std::vector<LongIdx> &indices) const
{
  unsigned int ndofs = 0;
  ndofs = cell_starts[cell.local_idx()+1]-cell_starts[cell.local_idx()];
  indices.resize(ndofs);
  for (unsigned int k=0; k<ndofs; k++)
    indices[k] = local_to_global_dof_idx_[dof_indices[cell_starts[cell.local_idx()]+k]];
  
  return ndofs;
}
 
 
DOFHandlerMultiDim::~DOFHandlerMultiDim()
{}
 
 
 
void DOFHandlerMultiDim::make_elem_partitioning()
{
    // create local arrays of elements
    el_ds_ = mesh_->get_el_ds();
 
    // create local array of edges
    for (auto edge : mesh_->edge_range())
    {
        bool is_edge_local = false;
        for (uint sid=0; sid<edge.n_sides(); sid++)
            if ( el_is_local(edge.side(sid)->element().idx()) )
            {
                is_edge_local = true;
                break;
            }
        if (is_edge_local)
            edg_4_loc.push_back(edge.idx());
    }
 
    // create local array of neighbours
    for (unsigned int inb=0; inb<mesh_->n_vb_neighbours(); inb++)
    {
        const Neighbour *nb = &mesh_->vb_neighbour(inb);
        if ( el_is_local(nb->element().idx())
                || el_is_local(nb->side()->element().idx()) )
            nb_4_loc.push_back(inb);
    }
    
    // init global to local element map with locally owned elements (later add ghost elements)
    for ( unsigned int iel = 0; iel < el_ds_->lsize(); iel++ )
        global_to_local_el_idx_[mesh_->get_el_4_loc()[iel]] = iel;
    
    // create array of local nodes
    std::vector<bool> node_is_local(mesh_->duplicate_nodes()->n_nodes(), false);
    for (auto cell : this->own_range())
    {
      unsigned int obj_idx = mesh_->duplicate_nodes()->obj_4_el()[cell.elm_idx()];
      for (unsigned int nid=0; nid<cell.elm()->n_nodes(); nid++)
        node_is_local[mesh_->duplicate_nodes()->objects(cell.dim())[obj_idx].nodes[nid]] = true;
    }
    
    // create array of local ghost cells
    for ( auto cell : mesh_->elements_range() )
    {
      if (cell.proc() != el_ds_->myp())
      {
        bool has_local_node = false;
        unsigned int obj_idx = mesh_->duplicate_nodes()->obj_4_el()[cell.idx()];
        for (unsigned int nid=0; nid<cell->n_nodes(); nid++)
          if (node_is_local[mesh_->duplicate_nodes()->objects(cell->dim())[obj_idx].nodes[nid]])
          {
            has_local_node = true;
            break;
          }
        if (has_local_node)
        {
            ghost_4_loc.push_back(cell.idx());
            ghost_proc.insert(cell.proc());
            ghost_proc_el[cell.proc()].push_back(cell.idx());
            global_to_local_el_idx_[cell.idx()] = el_ds_->lsize() - 1 + ghost_4_loc.size();
        }
      }
    }
    for (auto nb : nb_4_loc)
    {
        auto cell = mesh_->vb_neighbour(nb).element();
        if (!el_is_local(cell.idx()) && find(ghost_4_loc.begin(), ghost_4_loc.end(), cell.idx()) == ghost_4_loc.end())
        {
            ghost_4_loc.push_back(cell.idx());
            ghost_proc.insert(cell.proc());
            ghost_proc_el[cell.proc()].push_back(cell.idx());
            global_to_local_el_idx_[cell.idx()] = el_ds_->lsize() - 1 + ghost_4_loc.size();
        }
        cell = mesh_->vb_neighbour(nb).side()->element();
        if (!el_is_local(cell.idx()) && find(ghost_4_loc.begin(), ghost_4_loc.end(), cell.idx()) == ghost_4_loc.end())
        {
            ghost_4_loc.push_back(cell.idx());
            ghost_proc.insert(cell.proc());
            ghost_proc_el[cell.proc()].push_back(cell.idx());
            global_to_local_el_idx_[cell.idx()] = el_ds_->lsize() - 1 + ghost_4_loc.size();
        }
    }
}
 
 
bool DOFHandlerMultiDim::el_is_local(int index) const
{
    return el_ds_->is_local(mesh_->get_row_4_el()[index]);
}
 
 
std::size_t DOFHandlerMultiDim::hash() const {
    return this->n_global_dofs_;
}
 
 
Range<DHCellAccessor> DOFHandlerMultiDim::own_range() const {
    auto bgn_it = make_iter<DHCellAccessor>( DHCellAccessor(this, 0) );
    auto end_it = make_iter<DHCellAccessor>( DHCellAccessor(this, el_ds_->lsize()) );
    return Range<DHCellAccessor>(bgn_it, end_it);
}
 
 
Range<DHCellAccessor> DOFHandlerMultiDim::local_range() const {
    auto bgn_it = make_iter<DHCellAccessor>( DHCellAccessor(this, 0) );
    auto end_it = make_iter<DHCellAccessor>( DHCellAccessor(this, el_ds_->lsize()+ghost_4_loc.size()) );
    return Range<DHCellAccessor>(bgn_it, end_it);
}
 
 
Range<DHCellAccessor> DOFHandlerMultiDim::ghost_range() const {
    auto bgn_it = make_iter<DHCellAccessor>( DHCellAccessor(this, el_ds_->lsize()) );
    auto end_it = make_iter<DHCellAccessor>( DHCellAccessor(this, el_ds_->lsize()+ghost_4_loc.size()) );
    return Range<DHCellAccessor>(bgn_it, end_it);
}
 
 
const DHCellAccessor DOFHandlerMultiDim::cell_accessor_from_element(unsigned int elm_idx) const {
    auto map_it = global_to_local_el_idx_.find((LongIdx)elm_idx); // find in global to local map
    ASSERT( map_it != global_to_local_el_idx_.end() )(elm_idx).error("DH accessor can be create only for own or ghost elements!\n");
    return DHCellAccessor(this, map_it->second);
}
 
 
void DOFHandlerMultiDim::print() const {
    stringstream s;
    std::vector<int> dofs(max_elem_dofs_);
    
    s << "DOFHandlerMultiDim structure:" << endl;
    s << "- is parallel: " << (is_parallel_?"true":"false") << endl;
    s << "- proc id: " << el_ds_->myp() << endl;
    s << "- global number of dofs: " << n_global_dofs_ << endl;
    s << "- number of locally owned cells: " << el_ds_->lsize() << endl;
    s << "- number of ghost cells: " << ghost_4_loc.size() << endl;
    s << "- dofs on locally owned cells:" << endl;
    
    for (auto cell : own_range())
    {
        auto ndofs = cell.get_dof_indices(dofs);
        s << "-- cell " << cell.elm().idx() << ": ";
        for (unsigned int idof=0; idof<ndofs; idof++) s << dofs[idof] << " "; s << endl;
    }
    s << "- dofs on ghost cells:" << endl;
    for (auto cell : ghost_range())
    {
        auto ndofs = cell.get_dof_indices(dofs);
        s << "-- cell " << cell.elm().idx() << ": ";
        for (unsigned int idof=0; idof<ndofs; idof++) s << dofs[idof] << " "; s << endl;
    }
    s << "- locally owned dofs (" << lsize_ << "): ";
    for (unsigned int i=0; i<lsize_; i++) s << local_to_global_dof_idx_[i] << " "; s << endl;
    s << "- ghost dofs (" << local_to_global_dof_idx_.size() - lsize_ << "): ";
    for (unsigned int i=lsize_; i<local_to_global_dof_idx_.size(); i++) s << local_to_global_dof_idx_[i] << " "; s << endl;
    s << "- global-to-local-cell map:" << endl;
    for (auto cell : global_to_local_el_idx_) s << "-- " << cell.first << " -> " << cell.second << " " << endl;
    s << endl;
    
    printf("%s", s.str().c_str());
}
 
 
 
 
 
 
 
 
 
SubDOFHandlerMultiDim::SubDOFHandlerMultiDim(std::shared_ptr<DOFHandlerMultiDim> dh, unsigned int component_idx)
: DOFHandlerMultiDim(*dh->mesh()),
  parent_(dh),
  fe_idx_(component_idx)
{
    // create discrete space, we assume equal type of FE on each cell.
    ASSERT( dynamic_cast<EqualOrderDiscreteSpace *>(dh->ds().get()) != nullptr )
                .error("sub_handler can be used only with dof handler using EqualOrderDiscreteSpace!");
    FESystem<0> *fe_sys0 = dynamic_cast<FESystem<0>*>( dh->ds()->fe()[0_d].get() );
    FESystem<1> *fe_sys1 = dynamic_cast<FESystem<1>*>( dh->ds()->fe()[1_d].get() );
    FESystem<2> *fe_sys2 = dynamic_cast<FESystem<2>*>( dh->ds()->fe()[2_d].get() );
    FESystem<3> *fe_sys3 = dynamic_cast<FESystem<3>*>( dh->ds()->fe()[3_d].get() );
    ASSERT( fe_sys0 != nullptr ).error("sub_handler assumes that dof handler uses FESystem<0>!");
    ASSERT( fe_sys1 != nullptr ).error("sub_handler assumes that dof handler uses FESystem<1>!");
    ASSERT( fe_sys2 != nullptr ).error("sub_handler assumes that dof handler uses FESystem<2>!");
    ASSERT( fe_sys3 != nullptr ).error("sub_handler assumes that dof handler uses FESystem<3>!");
    MixedPtr<FiniteElement> sub_mixed(fe_sys0->fe()[component_idx],
                                      fe_sys1->fe()[component_idx],
                                      fe_sys2->fe()[component_idx],
                                      fe_sys3->fe()[component_idx]);
    ds_ = std::make_shared<EqualOrderDiscreteSpace>( mesh_, sub_mixed);
    
    is_parallel_ = dh->is_parallel_;
    
    // create list of dofs for sub_dh on one cell
    FESystemFunctionSpace *fs[4] = {
        dynamic_cast<FESystemFunctionSpace*>( fe_sys0->function_space_.get() ),
        dynamic_cast<FESystemFunctionSpace*>( fe_sys1->function_space_.get() ),
        dynamic_cast<FESystemFunctionSpace*>( fe_sys2->function_space_.get() ),
        dynamic_cast<FESystemFunctionSpace*>( fe_sys3->function_space_.get() ) };
    for (unsigned int d=0; d<=3; d++)
        ASSERT( fs[d] != nullptr ).error("Function space must be of type FESystemFunctionSpace!" );
    vector<unsigned int> sub_fe_dofs[4];
    for (unsigned int i=0; i<fe_sys0->n_dofs(); i++)
        if (fs[0]->dof_indices()[i].fe_index == component_idx) sub_fe_dofs[0].push_back(i);
    for (unsigned int i=0; i<fe_sys1->n_dofs(); i++)
        if (fs[1]->dof_indices()[i].fe_index == component_idx) sub_fe_dofs[1].push_back(i);
    for (unsigned int i=0; i<fe_sys2->n_dofs(); i++)
        if (fs[2]->dof_indices()[i].fe_index == component_idx) sub_fe_dofs[2].push_back(i);
    for (unsigned int i=0; i<fe_sys3->n_dofs(); i++)
        if (fs[3]->dof_indices()[i].fe_index == component_idx) sub_fe_dofs[3].push_back(i);
    
    init_cell_starts();
    dof_indices.resize(cell_starts[cell_starts.size()-1]);
    // sub_local_indices maps local dofs of parent handler to local dofs of sub-handler
    vector<LongIdx> sub_local_indices(dh->local_to_global_dof_idx_.size(), INVALID_DOF);
    map<LongIdx,LongIdx> global_to_local_dof_idx;
    // first add owned dofs to local_to_global_dof_idx_ and sub_local_indices
    for (auto cell : dh->local_range())
    {
        LocDofVec cell_dof_indices = cell.get_loc_dof_indices();
        for (auto sub_dof : sub_fe_dofs[cell.dim()])
        {
            if (cell_dof_indices[sub_dof] < static_cast<int>(dh->lsize_) &&
                sub_local_indices[cell_dof_indices[sub_dof]] == INVALID_DOF)
            {
                sub_local_indices[cell_dof_indices[sub_dof]] = local_to_global_dof_idx_.size();
                parent_dof_idx_.push_back(cell_dof_indices[sub_dof]);
                global_to_local_dof_idx[parent_->local_to_global_dof_idx_[cell_dof_indices[sub_dof]]] = local_to_global_dof_idx_.size();
                local_to_global_dof_idx_.push_back(local_to_global_dof_idx_.size());
            }
        }
    }
    lsize_ = local_to_global_dof_idx_.size();
    // then do the same for ghost dofs and set dof_indices
    for (auto cell : dh->local_range())
    {
        LocDofVec cell_dof_indices = cell.get_loc_dof_indices();
        unsigned int idof = 0;
        for (auto sub_dof : sub_fe_dofs[cell.dim()])
        {
            if (sub_local_indices[cell_dof_indices[sub_dof]] == INVALID_DOF)
            {
                sub_local_indices[cell_dof_indices[sub_dof]] = local_to_global_dof_idx_.size();
                parent_dof_idx_.push_back(cell_dof_indices[sub_dof]);
                // temporarily we keep the global dof idx of parent dh, we replace it later from the owning processor
                local_to_global_dof_idx_.push_back(parent_->local_to_global_dof_idx_[cell_dof_indices[sub_dof]]);
            }
            dof_indices[cell_starts[cell.local_idx()]+idof++] = sub_local_indices[cell_dof_indices[sub_dof]];
        }
    }
    
    dof_ds_ = std::make_shared<Distribution>(lsize_, PETSC_COMM_WORLD);
    n_global_dofs_ = dof_ds_->size();
    loffset_ = dof_ds_->get_starts_array()[dof_ds_->myp()];
    
    // shift dof indices
    if (loffset_ > 0)
      for (unsigned int i=0; i<lsize_; i++)
          local_to_global_dof_idx_[i] += loffset_;
    
    // communicate ghost values
    // first propagate from lower procs to higher procs and then vice versa
    for (unsigned int from_higher = 0; from_higher < 2; from_higher++)
    {
        for (unsigned int proc : ghost_proc)
        {
            if ((proc > el_ds_->myp()) == from_higher)
            { // receive dofs from master processor
                vector<LongIdx> dofs;
                receive_sub_ghost_dofs(proc, dofs);
            }
            else
                send_sub_ghost_dofs(proc, global_to_local_dof_idx);
        }
    }
}
 
 
void SubDOFHandlerMultiDim::receive_sub_ghost_dofs(unsigned int proc, vector<LongIdx> &dofs)
{
    // send number of ghost dofs required from the other processor
    vector<LongIdx> dof_indices;
    for (unsigned int i=lsize_; i<local_to_global_dof_idx_.size(); i++)
        if (parent_->dof_ds_->get_proc(parent_->local_to_global_dof_idx_[parent_dof_idx_[i]]) == proc)
            dof_indices.push_back(parent_->local_to_global_dof_idx_[parent_dof_idx_[i]]);
    unsigned int n_ghosts = dof_indices.size();
    MPI_Send(&n_ghosts, 1, MPI_UNSIGNED, proc, 0, MPI_COMM_WORLD);
    
    // send indices of dofs required
    MPI_Send(dof_indices.data(), n_ghosts, MPI_LONG_IDX, proc, 1, MPI_COMM_WORLD);
    
    // receive dofs
    dofs.resize(n_ghosts);
    MPI_Recv(dofs.data(), n_ghosts, MPI_LONG_IDX, proc, 2, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // update ghost dofs
    unsigned int idof = 0;
    for (unsigned int i=lsize_; i<local_to_global_dof_idx_.size(); i++)
        if (parent_->dof_ds_->get_proc(parent_->local_to_global_dof_idx_[parent_dof_idx_[i]]) == proc)
            local_to_global_dof_idx_[i] = dofs[idof++];
}
 
 
void SubDOFHandlerMultiDim::send_sub_ghost_dofs(unsigned int proc, const map<LongIdx,LongIdx> &global_to_local_dof_idx)
{
    // receive number of dofs required by the other processor
    unsigned int n_ghosts;
    MPI_Recv(&n_ghosts, 1, MPI_UNSIGNED, proc, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // receive global indices of dofs required
    vector<LongIdx> dof_indices(n_ghosts);
    MPI_Recv(dof_indices.data(), n_ghosts, MPI_LONG_IDX, proc, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
    
    // send global dof indices relative to the sub-handler
    vector<LongIdx> dofs;
    for (auto global_dof : dof_indices)
        dofs.push_back(global_to_local_dof_idx.at(global_dof) + dof_ds_->begin());
    MPI_Send(dofs.data(), dofs.size(), MPI_LONG_IDX, proc, 2, MPI_COMM_WORLD);
}
 
 
void SubDOFHandlerMultiDim::update_subvector(const VectorMPI &vec, VectorMPI &subvec)
{
    ASSERT( vec.size() == parent_->local_to_global_dof_idx_.size() ).error("Incompatible parent vector in update_subvector()!");
    ASSERT( subvec.size() == local_to_global_dof_idx_.size() ).error("Incompatible subvector in update_subvector()!");
    
    for (unsigned int i=0; i<parent_dof_idx_.size(); i++)
        subvec.set( i, vec.get(parent_dof_idx_[i]) );
}
 
 
void SubDOFHandlerMultiDim::update_parent_vector(VectorMPI &vec, const VectorMPI &subvec)
{
    ASSERT( vec.size() == parent_->local_to_global_dof_idx_.size() ).error("Incompatible parent vector in update_subvector()!");
    ASSERT( subvec.size() == local_to_global_dof_idx_.size() ).error("Incompatible subvector in update_subvector()!");
    
    for (unsigned int i=0; i<parent_dof_idx_.size(); i++)
        vec.set( parent_dof_idx_[i], subvec.get(i) );
}