SF_parallel_layout.h

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// ----------------------------------------------------------------------------
// openCARP is an open cardiac electrophysiology simulator.
//
// Copyright (C) 2020 openCARP project
//
// This program is licensed under the openCARP Academic Public License (APL)
// v1.0: You can use and redistribute it and/or modify it in non-commercial
// academic environments under the terms of APL as published by the openCARP
// project v1.0, or (at your option) any later version. Commercial use requires
// a commercial license (info@opencarp.org).
//
// This program is distributed without any warranty; see the openCARP APL for
// more details.
//
// You should have received a copy of the openCARP APL along with this program
// and can find it online: http://www.opencarp.org/license
// ----------------------------------------------------------------------------
 
#ifndef _SF_PARALLEL_LAYOUT_H
#define _SF_PARALLEL_LAYOUT_H
 
 
#include <iostream>
 
#include "hashmap.hpp"
 
#include "mpi_utils.h"
#include "SF_vector.h"
#include "SF_container.h"
 
namespace SF {
 
template<class T>
inline void parallel_distribution(const vector<T> & gtarget,
                           const vector<T> & cnt,
                           const vector<T> & dsp,
                           const vector<T> & ranks,
                           const int myrank,
                           vector<T> & owner,
                           vector<T> & counts)
{
  int size = gtarget.size();
  size_t csize = cnt.size();
  vector<T> ltarget(size);
 
  // this small algorithm computes ltarget[i] = gtarget[i] / size,
  // but with a even distribution of the divisions remainder
  // among the processes
  for(int i=0; i<size; i++) {
    int idx = (i + myrank) % size;
    T gt = gtarget[idx];
    ltarget[idx] = (i * gt + gt) / size - (i * gt) / size;
  }
 
  // set initial distribution
  vector<T> act_idx(csize);
  counts.resize(size); counts.zero();
  owner.resize(csize);
  for(size_t nidx=0; nidx < csize; nidx++)
  {
    act_idx[nidx] = (unsigned int)(2147483647 * nidx) % cnt[nidx];
 
    T j = dsp[nidx] + act_idx[nidx];
    T p = ranks[j];
    owner[nidx] = p;
    counts[p]++;
  }
 
  // compute initial functional value
  unsigned int J = 0;
  for(int i = 0; i < size; i++) J += (counts[i] - ltarget[i])*(counts[i] - ltarget[i]);
 
  unsigned int k = 0, update = 0, osteps = 32;
 
  // optimize
  while(J > 0 && k++ < osteps)
  {
    for(size_t nidx = 0; nidx < csize; nidx++)
    {
      // round-robin incrementation
      act_idx[nidx]++;
      if(act_idx[nidx] == cnt[nidx]) act_idx[nidx] = 0;
 
      T j = dsp[nidx] + act_idx[nidx];
      T op = owner[nidx];
      T p  = ranks[j];
      T n0 = counts[op], n1 = counts[p];
      T n0_ = ltarget[op], n1_ = ltarget[p];
      if( ((n0 - n0_) - (n1 - n1_)) >= 1 )
      {
        owner[nidx] = p;
        counts[op]--; counts[p]++;
        update++;
        J += 2*(1 - (n0 - n0_) + (n1 - n1_));
 
        if (J == 0) break;
      }
    }
  }
}
 
 
template<class T>
inline void refine_distribution(const vector<T> & gtarget,
                         const vector<T> & cnt,
                         const vector<T> & dsp,
                         const vector<T> & ranks,
                         const int myrank,
                         vector<T> & owner,
                         vector<T> & counts)
{
  int size = gtarget.size();
  size_t csize = cnt.size();
  vector<T> ltarget(size);
 
  // this small algorithm computes ltarget[i] = gtarget[i] / size,
  // but with a even distribution of the divisions remainder
  // among the processes
  for(int i=0; i<size; i++) {
    int idx = (i + myrank) % size;
    T gt = gtarget[idx];
    ltarget[idx] = (i * gt + gt) / size - (i * gt) / size;
  }
 
  vector<T> act_idx(csize);
  counts.resize(size); counts.zero();
 
  // compute initial functional value
  unsigned int J = 0;
  for(int i = 0; i < size; i++) J += (counts[i] - ltarget[i])*(counts[i] - ltarget[i]);
 
  unsigned int k = 0, update = 0, osteps = 64;
 
  // choose random starting index
  for(size_t nidx=0; nidx < csize; nidx++)
    act_idx[nidx] = (unsigned int)(2147483647 * nidx) % cnt[nidx];
 
  // optimize
  while(J > 0 && k++ < osteps)
  {
    for(size_t nidx = 0; nidx < csize; nidx++)
    {
      // round-robin incrementation
      act_idx[nidx]++;
      if(act_idx[nidx] == cnt[nidx]) act_idx[nidx] = 0;
 
      T j = dsp[nidx] + act_idx[nidx];
      T op = owner[nidx];
      T p  = ranks[j];
      T n0 = counts[op], n1 = counts[p];
      T n0_ = ltarget[op], n1_ = ltarget[p];
      if( ((n0 - n0_) - (n1 - n1_)) >= 1 )
      {
        owner[nidx] = p;
        counts[op]--; counts[p]++;
        update++;
        J += 2*(1 - (n0 - n0_) + (n1 - n1_));
 
        if (J == 0) break;
      }
    }
  }
}
 
template<class T>
inline void parallel_distribution_minrank(const vector<T> & gtarget,
                           const vector<T> & cnt,
                           const vector<T> & dsp,
                           const vector<T> & ranks,
                           vector<T> & owner,
                           vector<T> & counts)
{
  owner.resize(cnt.size());
  counts.assign(gtarget.size(), 0);
 
  for(size_t i = 0; i < owner.size(); i++)
  {
    // get the smallest rank index that holds current node
    int minrank = ranks[dsp[i]];
    for(T j = dsp[i]; j < dsp[i+1]; j++)
      if(minrank > ranks[j]) minrank = ranks[j];
 
    // this rank gets assigned to this node
    owner[i] = minrank;
    counts[minrank]++;
  }
}
 
 
 
template<class T>
class parallel_layout
{
  protected:
  vector<T> _l2g;
  hashmap::unordered_map<T, T> _g2l;
 
  public:
  inline void globalize(vector<T> & lvec) const
  {
    size_t lsize = _l2g.size(), widx = 0;
 
    for(size_t ridx=0; ridx<lvec.size(); ridx++)
    {
      T loc = lvec[ridx];
      if(loc < (T)lsize)
        lvec[widx++] = _l2g[loc];
    }
    lvec.resize(widx);
  }
  inline T globalize(const T lidx) const
  {
    size_t lsize = _l2g.size();
 
    if(lidx < (T)lsize)
      return _l2g[lidx];
    else
      return T(-1);
  }
 
 
  inline void localize(vector<T> & gvec) const
  {
    size_t widx = 0;
    typename hashmap::unordered_map<T, T>::const_iterator it;
 
    for(size_t ridx=0; ridx<gvec.size(); ridx++)
    {
      T glob = gvec[ridx];
      it = _g2l.find(glob);
      if(it != _g2l.end())
        gvec[widx++] = it->second;
    }
    gvec.resize(widx);
  }
 
  template<class V>
  inline void localize(vector<T> & gidx, vector<V> & gdat) const
  {
    size_t widx = 0;
    typename hashmap::unordered_map<T, T>::const_iterator it;
 
    for(size_t ridx=0; ridx<gidx.size(); ridx++)
    {
      T glob = gidx[ridx];
      it = _g2l.find(glob);
      if(it != _g2l.end()) {
        gidx[widx] = it->second;
        gdat[widx] = gdat[ridx];
        widx++;
      }
    }
    gidx.resize(widx);
    gdat.resize(widx);
  }
 
  inline T localize(T gidx) const
  {
    auto it = _g2l.find(gidx);
    if(it != _g2l.end())
      return it->second;
    else
      return T(-1);
  }
 
  inline void assign(const vector<T> & idx)
  {
    _l2g.assign(idx.begin(), idx.end());
    _g2l.clear();
 
    for(size_t i=0; i<_l2g.size(); i++)
      _g2l[_l2g[i]] = i;
  }
 
};
 
 
template<class T>
class overlapping_layout : public parallel_layout<T>
{
  private:
  vector<T> _inod;
  size_t _glob_num_idx;
 
  vector<T> _alg_nod;
  vector<T> _alg_layout;
  vector<T> _layout;
  MPI_Comm _comm;
 
  inline void find_domain_interfaces()
  {
    int size, rank;
    MPI_Comm_size(_comm, &size); MPI_Comm_rank(_comm, &rank);
 
    // compute a destination for each index in local domain
    vector<T> sbuf(parallel_layout<T>::_l2g), dest(parallel_layout<T>::_l2g.size());
    for(size_t i=0; i<parallel_layout<T>::_l2g.size(); i++)
      dest[i] = parallel_layout<T>::_l2g[i] % size;
    binary_sort_copy(dest, sbuf);
 
    // set up a commgraph w.r.t. the destination
    commgraph<size_t> grph;
    grph.configure(dest, _comm);
    size_t numrecv = sum(grph.rcnt);
 
    // allocate receiving datastructs
    vector<T> rnod(numrecv);   // holds the received node indices
    vector<T> rproc(numrecv);  // holds the process rank each index was received from
    vector<T> acc_cnt(numrecv, 1), acc_dsp;
    grph.source_ranks(rproc);
 
    MPI_Exchange(grph, sbuf, rnod, _comm);
 
    binary_sort_copy(rnod, rproc);
    unique_accumulate(rnod, acc_cnt);
    acc_dsp.resize(acc_cnt.size()+1); dsp_from_cnt(acc_cnt, acc_dsp);
 
    // compute the global number of entities
    unsigned long int num_unique = acc_cnt.size(), gnum_unique;
    MPI_Allreduce(&num_unique, &gnum_unique, 1, MPI_UNSIGNED_LONG, MPI_SUM, _comm);
    _glob_num_idx = gnum_unique;
 
    // now for each unique node rnod[i] we know the multiplicity acc_cnt[i],
    // and the process ranks associated to it in rproc[acc_dsp[i]] till rproc[acc_dsp[i+1]]
 
    // compute commgraph for those entities with acc_cnt[i] > 1
    grph.scnt.zero();
    for(size_t i=0; i<acc_cnt.size(); i++) {
      if(acc_cnt[i] > 1) {
        for(T j=acc_dsp[i]; j<acc_dsp[i+1]; j++)
          grph.scnt[rproc[j]]++;
      }
    }
    dsp_from_cnt(grph.scnt, grph.sdsp);
    MPI_Alltoall(grph.scnt.data(), sizeof(size_t), MPI_BYTE, grph.rcnt.data(), sizeof(size_t), MPI_BYTE, _comm);
    dsp_from_cnt(grph.rcnt, grph.rdsp);
 
    // fill sbuf with those entities with acc_cnt[i] > 1
    size_t numsend = sum(grph.scnt);
    sbuf.resize(numsend);
 
    for(size_t i=0; i<acc_cnt.size(); i++) {
      if(acc_cnt[i] > 1) {
        for(T j=acc_dsp[i]; j<acc_dsp[i+1]; j++) {
          T sproc = rproc[j];
          sbuf[grph.sdsp[sproc]] = rnod[i];
          grph.sdsp[sproc]++;
        }
      }
    }
 
    dsp_from_cnt(grph.scnt, grph.sdsp);
    numrecv = sum(grph.rcnt);
    _inod.resize(numrecv);
    MPI_Exchange(grph, sbuf, _inod, _comm);
    binary_sort(_inod);
  }
 
  inline void find_algebraic_layout()
  {
    // whether we want to be verbose about suboptimal algebraic node distributions. from
    // a high-level view this is unimportant, so by default this is false.
    const bool dist_warnings = false;
 
    int size, rank;
    MPI_Comm_size(_comm, &size); MPI_Comm_rank(_comm, &rank);
 
    // first compute a unique ownership of a subset of the nodes in the local domain
    {
      // compute inner nodes via a set difference of all nodes and the interface nodes
      vector<T> inner_nodes(parallel_layout<T>::_l2g.size());
      {
        vector<T> nodes(parallel_layout<T>::_l2g), intf_nodes(_inod);
        binary_sort(nodes);
        T* end = std::set_difference(nodes.begin(), nodes.end(),
                                     intf_nodes.begin(), intf_nodes.end(), inner_nodes.begin());
        inner_nodes.resize(end - inner_nodes.begin());
      }
      _alg_nod.assign(inner_nodes.begin(), inner_nodes.end());
 
      // compute a destination for each interface index in the local domain
      vector<T> sbuf(_inod.size()), dest(_inod.size());
      for(size_t i=0; i < sbuf.size(); i++) {
        T nod = _inod[i];
        dest[i] = nod % size;
        sbuf[i] = nod;
      }
      binary_sort_copy(dest, sbuf);
 
      // set up a commgraph w.r.t. the destination
      commgraph<size_t> grph;
      grph.configure(dest, _comm);
 
      // allocate receiving datastructs
      size_t numrecv = sum(grph.rcnt);
      vector<T> rnod(numrecv);   // holds the received node indices
      vector<T> rproc(numrecv);  // holds the process rank each index was received from
 
      grph.source_ranks(rproc);
      MPI_Exchange(grph, sbuf, rnod, _comm);
 
      vector<T> acc_cnt(numrecv, 1), acc_dsp;
      binary_sort_copy(rnod, rproc);
      unique_accumulate(rnod, acc_cnt);
      acc_dsp.resize(acc_cnt.size()+1); dsp_from_cnt(acc_cnt, acc_dsp);
 
      const MPI_Datatype mpi_t = opencarp::mpi_datatype<T>();
 
      // initialize the target distribution to approx. _glob_num_idx / size
      vector<T> target;
      divide(_glob_num_idx, size, target);
 
      target[rank] -= inner_nodes.size();
      MPI_Allreduce(MPI_IN_PLACE, target.data(), target.size(), mpi_t, MPI_MIN, _comm);
 
      if(dist_warnings) {
        // treat negative values in target with warning.
        bool warn = false;
        for(int i=0; i<size; i++)
          if(target[i] < 0) {
            warn = true;
            break;
          }
        if(warn)
          if(!rank) std::cerr << "Warning: Domains too unbalanced for balanced re-indexing!" << std::endl;
      }
 
      vector<T> owners, counts;
 
      #if 1
      // use optimization algorithm to find a parallel distribution that fits the specified
      // target distribution
      parallel_distribution(target, acc_cnt, acc_dsp, rproc, rank, owners, counts);
      MPI_Allreduce(MPI_IN_PLACE, counts.data(), counts.size(), mpi_t, MPI_SUM, _comm);
      for(int i=0; i<size; i++) target[i] -= counts[i];
 
      unsigned int k = 0, numref = 10;
      while( !isEmpty(target) && k++ < numref)
      {
        refine_distribution(target, acc_cnt, acc_dsp, rproc, rank, owners, counts);
        MPI_Allreduce(MPI_IN_PLACE, counts.data(), counts.size(), mpi_t, MPI_SUM, _comm);
        for(int i=0; i<size; i++) target[i] -= counts[i];
      }
      #else
      parallel_distribution_minrank(target, acc_cnt, acc_dsp, rproc, owners, counts);
      MPI_Allreduce(MPI_IN_PLACE, counts.data(), counts.size(), mpi_t, MPI_SUM, _comm);
      for(int i=0; i<size; i++) target[i] -= counts[i];
      #endif
 
      if( dist_warnings && rank == 0 ) {
        if(!isEmpty(target)) {
          std::cerr << "Warning: Balanced re-indexing could not be computed." << std::endl;
          std::cerr << "Final differences to even distribution: " << std::endl;
          for(int i=0; i<size; i++) std::cerr << target[i] << " ";
          std::cerr << std::endl;
        }
      }
 
      // send the assigned nodes back to the respective processes
      binary_sort_copy(owners, rnod);
      grph.configure(owners, _comm);
      numrecv = sum(grph.rcnt);
      sbuf.resize(numrecv);
      MPI_Exchange(grph, rnod, sbuf, _comm);
 
      _alg_nod.append(sbuf.begin(), sbuf.end());
      binary_sort(_alg_nod);
    }
 
    // Generate the algebraic layout
    {
      commgraph<size_t> owned_layout;
      owned_layout.resize(size);
      size_t owned_idx_size = _alg_nod.size();
      MPI_Allgather(&owned_idx_size, sizeof(size_t), MPI_BYTE,
                    owned_layout.scnt.data(), sizeof(size_t), MPI_BYTE, _comm);
      dsp_from_cnt(owned_layout.scnt, owned_layout.sdsp);
 
      _alg_layout.resize(owned_layout.sdsp.size());
      vec_assign(_alg_layout.data(), owned_layout.sdsp.data(), owned_layout.sdsp.size());
    }
  }
 
  inline void compute_layout()
  {
    T size  = this->algebraic_layout().size()-1;
    T nlidx = this->num_local_idx();
 
    _layout.resize(size + 1);
    vector<T> cnt(size);
 
    MPI_Allgather(&nlidx, sizeof(T), MPI_BYTE, cnt.data(), sizeof(T), MPI_BYTE, _comm);
    dsp_from_cnt(cnt, _layout);
  }
 
  public:
  overlapping_layout() : _glob_num_idx(0), _comm(SF_COMM) {}
 
  inline void assign(const vector<T> & idx, MPI_Comm comm)
  {
    _comm = comm;
 
    parallel_layout<T>::assign(idx);
 
    this->find_domain_interfaces();
    this->find_algebraic_layout();
    this->compute_layout();
 
    this->localize(_inod);
    binary_sort(_inod);
    this->localize(_alg_nod);
    binary_sort(_alg_nod);
  }
 
 
  inline const vector<T>& interface() const
  {
    return _inod;
  }
 
  inline const vector<T> & algebraic_nodes() const
  {
    return _alg_nod;
  }
 
  inline const vector<T> & algebraic_layout() const
  {
    return _alg_layout;
  }
  inline const vector<T> & layout() const
  {
    return _layout;
  }
 
  inline T localize_algebraic(const T global_idx, const vector<T> & global_alg_nbr, const int rank)
  {
    T loc_nodal_idx = parallel_layout<T>::localize(global_idx);
    if(loc_nodal_idx == -1)
      return -1;
 
    T local_offset   = _alg_layout[rank], local_size = _alg_layout[rank+1] - local_offset;
    T local_alg_idx  = global_alg_nbr[loc_nodal_idx] - local_offset;
 
    if(local_alg_idx > -1 && local_alg_idx < local_size)
      return local_alg_idx;
    else
      return -1;
  }
 
  inline size_t num_global_idx() const
  {
    return _glob_num_idx;
  }
  inline size_t num_local_idx() const
  {
    return parallel_layout<T>::_l2g.size();
  }
  inline size_t num_algebraic_idx() const
  {
    return _alg_nod.size();
  }
 
  template<class V>
  inline void reduce(vector<V> & ndat, const char* op) const
  {
    int size, rank;
    MPI_Comm_size(_comm, &size); MPI_Comm_rank(_comm, &rank);
 
    // parallel layout of nodal data must match the one of the
    // overlapping_layout class
    assert(ndat.size() == parallel_layout<T>::_l2g.size());
 
    size_t isize = _inod.size();
    vector<T> nod_sbuf(isize), dest(isize), perm;
    vector<V> dat_sbuf(isize);
 
    for(size_t i=0; i<isize; i++) {
      T lidx = _inod[i];
      dest[i] = parallel_layout<T>::_l2g[lidx] % size;
    }
    interval(perm, 0, isize);
    binary_sort_copy(dest, perm);
 
    for(size_t i=0; i<perm.size(); i++)
    {
      T lidx = _inod[perm[i]];
      nod_sbuf[i] = parallel_layout<T>::_l2g[lidx];
      dat_sbuf[i] = ndat[lidx];
    }
 
    // set up a commgraph w.r.t. the destination
    commgraph<size_t> grph;
    grph.configure(dest, _comm);
 
    size_t numrecv = sum(grph.rcnt);
    vector<T> nod_rbuf(numrecv);
    vector<V> dat_rbuf(numrecv);
 
    MPI_Exchange(grph, nod_sbuf, nod_rbuf, _comm);
    MPI_Exchange(grph, dat_sbuf, dat_rbuf, _comm);
 
    vector<T> acc_cnt(numrecv, 1), acc_dsp, acc_col;
    interval(acc_col, 0, numrecv);
 
    binary_sort_copy(nod_rbuf, acc_col);
    unique_accumulate(nod_rbuf, acc_cnt);
 
    acc_dsp.resize(acc_cnt.size() + 1);
    dsp_from_cnt(acc_cnt, acc_dsp);
 
    short op_sw = 0;
    if(! strcmp(op, "max"))
      op_sw = 0;
    else if(! strcmp(op, "min"))
      op_sw = 1;
    else if(! strcmp(op, "sum"))
      op_sw = 2;
    else
      assert(0);
 
    for(size_t i=0; i<acc_cnt.size(); i++)
    {
      V val = 0.0;  // value we will set for all interface nodes
      // compute value based on selected operation
      switch(op_sw)
      {
        // max
        case 0:
        {
          V max = dat_rbuf[acc_col[acc_dsp[i]]];
          T idx=1;
          while(idx < acc_cnt[i])
          {
            T p = acc_col[acc_dsp[i]+idx];
            if(max < dat_rbuf[p]) max = dat_rbuf[p];
            idx++;
          }
          val = max;
          break;
        }
 
        // min
        case 1:
        {
          V min = dat_rbuf[acc_col[acc_dsp[i]]];
          T idx=1;
          while(idx < acc_cnt[i])
          {
            T p = acc_col[acc_dsp[i]+idx];
            if(min > dat_rbuf[p]) min = dat_rbuf[p];
            idx++;
          }
          val = min;
          break;
        }
 
        // sum
        case 2:
        {
          T idx=0;
          while(idx < acc_cnt[i])
          {
            T p = acc_col[acc_dsp[i]+idx];
            val += dat_rbuf[p];
            idx++;
          }
          break;
        }
      }
      for(T j = acc_dsp[i]; j < acc_dsp[i] + acc_cnt[i]; j++)
        dat_rbuf[acc_col[j]] = val;
    }
 
    grph.transpose();
    MPI_Exchange(grph, dat_rbuf, dat_sbuf, _comm);
 
    for(size_t i=0; i<perm.size(); i++)
    {
      T lidx = _inod[perm[i]];
      ndat[lidx] = dat_sbuf[i];
    }
  }
};
 
template<class T>
class non_overlapping_layout : public parallel_layout<T>
{
  private:
  vector<T> _elem_layout;  
  MPI_Comm  _comm;         
 
  public:
  non_overlapping_layout()
  {}
 
  inline void assign(const vector<T> & ref_eidx, MPI_Comm comm)
  {
    _comm = comm;
 
    parallel_layout<T>::assign(ref_eidx);
 
    int size; MPI_Comm_size(_comm, &size);
 
    T lsize = ref_eidx.size();
    vector<T> layout_cnt(size);
 
    MPI_Allgather(&lsize, sizeof(T), MPI_BYTE, layout_cnt.data(), sizeof(T), MPI_BYTE, _comm);
    dsp_from_cnt(layout_cnt, _elem_layout);
  }
  const vector<T> & algebraic_layout() const
  {
    return _elem_layout;
  }
};
 
 
 
template<class T, class S>
T local_nodal_to_local_petsc(const meshdata<T,S> & mesh, int rank, T local_nodal)
{
  const vector<T> & alg_layout = mesh.pl.algebraic_layout();
  const vector<T> & petsc_nbr  = mesh.get_numbering(NBR_PETSC);
 
  const T my_offset = alg_layout[rank];
 
  return petsc_nbr[local_nodal] - my_offset;
}
 
template<class T, class S>
T local_petsc_to_local_nodal(const meshdata<T,S> & mesh, int rank, T local_petsc)
{
  const vector<T> & alg_layout = mesh.pl.algebraic_layout();
  const vector<T> & alg_nod    = mesh.pl.algebraic_nodes();
  const vector<T> & petsc_nbr  = mesh.get_numbering(NBR_PETSC);
 
  const T my_offset = alg_layout[rank];
  const size_t num_alg = alg_nod.size();
 
  size_t idx = 0;
  while(idx < num_alg && petsc_nbr[alg_nod[idx]] != local_petsc + my_offset) idx++;
 
  if(idx == num_alg) return -1;
  else               return alg_nod[idx];
}
 
template<class T, class S>
void local_petsc_to_nodal_mapping(const meshdata<T,S> & mesh, index_mapping<T> & petsc_to_nodal)
{
  int rank; MPI_Comm_rank(mesh.comm, &rank);
  const vector<T> & alg_nod = mesh.pl.algebraic_nodes();
  vector<T> petsc_idx(alg_nod.size());
 
  size_t idx = 0;
  for(const T & n : alg_nod)
    petsc_idx[idx++] = local_nodal_to_local_petsc(mesh, rank, n);
 
  petsc_to_nodal.assign(petsc_idx, alg_nod);
}
 
 
}
 
#endif