Perform Lloyd relaxation on a mesh and its dual
To run: mpiexec -np <np> LloydRelaxation [filename]

Briefly, Lloyd relaxation is a technique to smooth out a mesh. The centroid of each cell is computed from its vertex positions, then vertices are placed at the average of their connected cells' centroids.

In the parallel algorithm, an extra ghost layer of cells is exchanged. This allows us to compute the centroids for boundary cells on each processor where they appear; this eliminates the need for one round of data exchange (for those centroids) between processors. New vertex positions must be sent from owning processors to processors sharing those vertices. Convergence is measured as the maximum distance moved by any vertex.

In this implementation, a fixed number of iterations is performed. The final mesh is output to 'lloydfinal.h5m' in the current directory (H5M format must be used since the file is written in parallel).

#ifdef USE_MPI
#  include "moab/ParallelComm.hpp"
#  include "MBParallelConventions.h"
#endif
#include "moab/Core.hpp"
#include "moab/Skinner.hpp"
#include "moab/CN.hpp"
#include "moab/CartVect.hpp"
#include <iostream>
#include <sstream>

using namespace moab;
using namespace std;

string test_file_name = string(MESH_DIR) + string("/surfrandomtris-4part.h5m");

#define RC if (MB_SUCCESS != rval) return rval

ErrorCode perform_lloyd_relaxation(Interface *mb, Range &verts, Range &cells, Tag fixed, 
                                   int num_its, int report_its);

int main(int argc, char **argv)
{
  int num_its = 10;
  int report_its = 1;

#ifdef USE_MPI
  MPI_Init(&argc, &argv);
#endif

    // need option handling here for input filename
  if (argc > 1){
    //user has input a mesh file
    test_file_name = argv[1];
  }  

  // get MOAB and ParallelComm instances
  Interface *mb = new Core;
  if (NULL == mb) return 1;
  int nprocs = 1;
  
#ifdef USE_MPI
  // get the ParallelComm instance
  ParallelComm *pcomm = new ParallelComm(mb, MPI_COMM_WORLD);
  nprocs = pcomm->size();
#endif
  string options;
  if (nprocs > 1) // if reading in parallel, need to tell it how
    options = "PARALLEL=READ_PART;PARTITION=PARALLEL_PARTITION;PARALLEL_RESOLVE_SHARED_ENTS;PARALLEL_GHOSTS=2.0.1;DEBUG_IO=0;DEBUG_PIO=0";

    // read the file
  ErrorCode rval = mb->load_file(test_file_name.c_str(), 0, options.c_str()); RC;

    // make tag to specify fixed vertices, since it's input to the algorithm; use a default value of non-fixed
    // so we only need to set the fixed tag for skin vertices
  Tag fixed;
  int def_val = 0;
  rval = mb->tag_get_handle("fixed", 1, MB_TYPE_INTEGER, fixed, MB_TAG_CREAT | MB_TAG_DENSE, &def_val); RC;

    // get all vertices and faces
  Range verts, faces, skin_verts;
  rval = mb->get_entities_by_type(0, MBVERTEX, verts); RC;
  rval = mb->get_entities_by_dimension(0, 2, faces); RC;
  
    // get the skin vertices of those faces and mark them as fixed; we don't want to fix the vertices on a
    // part boundary, but since we exchanged a layer of ghost faces, those vertices aren't on the skin locally
    // ok to mark non-owned skin vertices too, I won't move those anyway
    // use MOAB's skinner class to find the skin
  Skinner skinner(mb);
  rval = skinner.find_skin(0, faces, true, skin_verts); RC; // 'true' param indicates we want vertices back, not faces

  std::vector<int> fix_tag(skin_verts.size(), 1); // initialized to 1 to indicate fixed
  rval = mb->tag_set_data(fixed, skin_verts, &fix_tag[0]); RC;

    // now perform the Lloyd relaxation
  rval = perform_lloyd_relaxation(mb, verts, faces, fixed, num_its, report_its); RC;

    // delete fixed tag, since we created it here
  rval = mb->tag_delete(fixed); RC;
  
    // output file, using parallel write

#ifdef USE_MPI
  options = "PARALLEL=WRITE_PART";
#endif

  rval = mb->write_file("lloydfinal.h5m", NULL, options.c_str()); RC;

    // delete MOAB instance
  delete mb;
  
#ifdef USE_MPI
  MPI_Finalize();
#endif

  return 0;
}

ErrorCode perform_lloyd_relaxation(Interface *mb, Range &verts, Range &faces, Tag fixed, 
                                   int num_its, int report_its) 
{
  ErrorCode rval;
  int nprocs = 1;

#ifdef USE_MPI
  ParallelComm *pcomm = ParallelComm::get_pcomm(mb, 0);
  nprocs = pcomm->size();
#endif
  
    // perform Lloyd relaxation:
    // 1. setup: set vertex centroids from vertex coords; filter to owned verts; get fixed tags

    // get all verts coords into tag; don't need to worry about filtering out fixed verts, 
    // we'll just be setting to their fixed coords
  std::vector<double> vcentroids(3*verts.size());
  rval = mb->get_coords(verts, &vcentroids[0]); RC;

  Tag centroid;
  rval = mb->tag_get_handle("centroid", 3, MB_TYPE_DOUBLE, centroid, MB_TAG_CREAT | MB_TAG_DENSE); RC;
  rval = mb->tag_set_data(centroid, verts, &vcentroids[0]); RC;

    // filter verts down to owned ones and get fixed tag for them
  Range owned_verts, shared_owned_verts;
  if (nprocs > 1) {
#ifdef USE_MPI
    rval = pcomm->filter_pstatus(verts, PSTATUS_NOT_OWNED, PSTATUS_NOT, -1, &owned_verts);
    if (rval != MB_SUCCESS) return rval;
#endif
  }
  else
    owned_verts = verts;
  std::vector<int> fix_tag(owned_verts.size());
  rval = mb->tag_get_data(fixed, owned_verts, &fix_tag[0]); RC;

    // now fill vcentroids array with positions of just owned vertices, since those are the ones
    // we're actually computing
  vcentroids.resize(3*owned_verts.size());
  rval = mb->tag_get_data(centroid, owned_verts, &vcentroids[0]); RC;

#ifdef USE_MPI
    // get shared owned verts, for exchanging tags
  rval = pcomm->get_shared_entities(-1, shared_owned_verts, 0, false, true); RC;
    // workaround: if no shared owned verts, put a non-shared one in the list, to prevent exchanging tags
    // for all shared entities
  if (shared_owned_verts.empty()) shared_owned_verts.insert(*verts.begin());
#endif
  
    // some declarations for later iterations
  std::vector<double> fcentroids(3*faces.size()); // fcentroids for face centroids
  std::vector<double> ctag(3*CN::MAX_NODES_PER_ELEMENT);  // temporary coordinate storage for verts bounding a face
  const EntityHandle *conn;  // const ptr & size to face connectivity
  int nconn;
  Range::iterator fit, vit;  // for iterating over faces, verts
  int f, v;  // for indexing into centroid vectors
  std::vector<EntityHandle> adj_faces;  // used in vertex iteration
  
    // 2. for num_its iterations:
  for (int nit = 0; nit < num_its; nit++) {
    
    double mxdelta = 0.0;

    // 2a. foreach face: centroid = sum(vertex centroids)/num_verts_in_cell
    for (fit = faces.begin(), f = 0; fit != faces.end(); fit++, f++) {
        // get verts for this face
      rval = mb->get_connectivity(*fit, conn, nconn); RC;
        // get centroid tags for those verts
      rval = mb->tag_get_data(centroid, conn, nconn, &ctag[0]); RC;
      fcentroids[3*f+0] = fcentroids[3*f+1] = fcentroids[3*f+2] = 0.0;
      for (v = 0; v < nconn; v++) {
        fcentroids[3*f+0] += ctag[3*v+0];
        fcentroids[3*f+1] += ctag[3*v+1];
        fcentroids[3*f+2] += ctag[3*v+2];
      }
      for (v = 0; v < 3; v++) fcentroids[3*f+v] /= nconn;
    }
    rval = mb->tag_set_data(centroid, faces, &fcentroids[0]); RC;

      // 2b. foreach owned vertex: 
    for (vit = owned_verts.begin(), v = 0; vit != owned_verts.end(); vit++, v++) {
        // if !fixed
      if (fix_tag[v]) continue;
        // vertex centroid = sum(cell centroids)/ncells
      adj_faces.clear();
      rval = mb->get_adjacencies(&(*vit), 1, 2, false, adj_faces); RC;
      rval = mb->tag_get_data(centroid, &adj_faces[0], adj_faces.size(), &fcentroids[0]); RC;
      double vnew[] = {0.0, 0.0, 0.0};
      for (f = 0; f < (int)adj_faces.size(); f++) {
        vnew[0] += fcentroids[3*f+0];
        vnew[1] += fcentroids[3*f+1];
        vnew[2] += fcentroids[3*f+2];
      }
      for (f = 0; f < 3; f++) vnew[f] /= adj_faces.size();
      double delta = (CartVect(vnew)-CartVect(&vcentroids[3*v])).length();
      mxdelta = std::max(delta, mxdelta);
      for (f = 0; f < 3; f++) vcentroids[3*v+f] = vnew[f];
    }

      // set the centroid tag; having them only in vcentroids array isn't enough, as vertex centroids are
      // accessed randomly in loop over faces
    rval = mb->tag_set_data(centroid, owned_verts, &vcentroids[0]); RC;

    // 2c. exchange tags on owned verts
    if (nprocs > 1) {
#ifdef USE_MPI
      rval = pcomm->exchange_tags(centroid, shared_owned_verts); RC;
#endif
    }


    if (!(nit%report_its)) {
        // global reduce for maximum delta, then report it
      double global_max = mxdelta;
      int myrank = 0;
#ifdef USE_MPI
      if (nprocs > 1)
        MPI_Reduce(&mxdelta, &global_max, 1, MPI_DOUBLE, MPI_MAX, 0, pcomm->comm());
      myrank = pcomm->rank();
#endif
      if (1 == nprocs || !myrank) 
        cout << "Max delta = " << global_max << endl;
    }
  }
  
    // write the tag back onto vertex coordinates
  rval = mb->set_coords(owned_verts, &vcentroids[0]); RC;

    // delete the centroid tag, since we don't need it anymore
  rval = mb->tag_delete(centroid); RC;
  
  return MB_SUCCESS;
}