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fix_eos_table_rx.cpp
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Sun, Nov 10, 19:43

fix_eos_table_rx.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing author: James Larentzos (U.S. Army Research Laboratory)
------------------------------------------------------------------------- */
#include <stdlib.h>
#include <string.h>
#include "fix_eos_table_rx.h"
#include "atom.h"
#include "error.h"
#include "force.h"
#include "memory.h"
#include "comm.h"
#include <math.h>
#include "modify.h"
#define MAXLINE 1024
using namespace LAMMPS_NS;
using namespace FixConst;
/* ---------------------------------------------------------------------- */
FixEOStableRX::FixEOStableRX(LAMMPS *lmp, int narg, char **arg) :
Fix(lmp, narg, arg)
{
if (narg != 8) error->all(FLERR,"Illegal fix eos/table/rx command");
restart_peratom = 1;
nevery = 1;
bool rx_flag = false;
for (int i = 0; i < modify->nfix; i++)
if (strncmp(modify->fix[i]->style,"rx",2) == 0) rx_flag = true;
if (!rx_flag) error->all(FLERR,"FixEOStableRX requires a fix rx command.");
nspecies = atom->nspecies_dpd;
if(nspecies==0) error->all(FLERR,"There are no rx species specified.");
if (strcmp(arg[3],"linear") == 0) tabstyle = LINEAR;
else error->all(FLERR,"Unknown table style in fix eos/table/rx");
tablength = force->inumeric(FLERR,arg[5]);
if (tablength < 2) error->all(FLERR,"Illegal number of eos/table/rx entries");
ntables = 0;
tables = NULL;
tables2 = NULL;
eosSpecies = NULL;
int me;
MPI_Comm_rank(world,&me);
for (int ii=0;ii<nspecies;ii++){
tables = (Table *)
memory->srealloc(tables,(ntables+1)*sizeof(Table),"eos:table/rx");
tables2 = (Table *)
memory->srealloc(tables2,(ntables+1)*sizeof(Table),"eos:table/rx");
Table *tb = &tables[ntables];
Table *tb2 = &tables2[ntables];
null_table(tb);
null_table(tb2);
ntables++;
}
ntables = 0;
Table *tb = &tables[ntables];
Table *tb2 = &tables2[ntables];
if (me == 0) read_table(tb,tb2,arg[4],arg[6]);
for (int ii=0;ii<nspecies;ii++){
Table *tb = &tables[ntables];
Table *tb2 = &tables2[ntables];
bcast_table(tb);
bcast_table(tb2);
// error check on table parameters
if (tb->ninput <= 1) error->one(FLERR,"Invalid eos/table/rx length");
tb->lo = tb->rfile[0];
tb->hi = tb->rfile[tb->ninput-1];
if (tb->lo >= tb->hi) error->all(FLERR,"eos/table/rx values are not increasing");
if (tb2->ninput <= 1) error->one(FLERR,"Invalid eos/table/rx length");
tb2->lo = tb2->rfile[0];
tb2->hi = tb2->rfile[tb2->ninput-1];
if (tb2->lo >= tb2->hi) error->all(FLERR,"eos/table/rx values are not increasing");
// spline read-in and compute r,e,f vectors within table
spline_table(tb);
compute_table(tb);
spline_table(tb2);
compute_table(tb2);
ntables++;
}
// Read the Formation Enthalpies
read_file(arg[7]);
comm_forward = 3;
comm_reverse = 2;
}
/* ---------------------------------------------------------------------- */
FixEOStableRX::~FixEOStableRX()
{
for (int m = 0; m < ntables; m++) {
free_table(&tables[m]);
free_table(&tables2[m]);
}
memory->sfree(tables);
memory->sfree(tables2);
delete [] dHf;
delete [] eosSpecies;
}
/* ---------------------------------------------------------------------- */
int FixEOStableRX::setmask()
{
int mask = 0;
mask |= POST_INTEGRATE;
mask |= END_OF_STEP;
return mask;
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::setup(int vflag)
{
int nlocal = atom->nlocal;
int *mask = atom->mask;
double *uCond = atom->uCond;
double *uMech = atom->uMech;
double *uChem = atom->uChem;
double *dpdTheta = atom->dpdTheta;
double duChem;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit){
duChem = uCG[i] - uCGnew[i];
uChem[i] += duChem;
uCG[i] = 0.0;
uCGnew[i] = 0.0;
}
// Communicate the updated momenta and velocities to all nodes
comm->forward_comm_fix(this);
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit)
temperature_lookup(i,uCond[i]+uMech[i]+uChem[i],dpdTheta[i]);
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::init()
{
int nlocal = atom->nlocal;
int *mask = atom->mask;
double *uCond = atom->uCond;
double *uMech = atom->uMech;
double *uChem = atom->uChem;
double *dpdTheta = atom->dpdTheta;
double tmp;
if(this->restart_reset){
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit)
temperature_lookup(i,uCond[i]+uMech[i]+uChem[i],dpdTheta[i]);
} else {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
if(dpdTheta[i] <= 0.0)
error->one(FLERR,"Internal temperature <= zero");
energy_lookup(i,dpdTheta[i],tmp);
uCond[i] = tmp / 2.0;
uMech[i] = tmp / 2.0;
uChem[i] = 0.0;
}
}
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::post_integrate()
{
int nlocal = atom->nlocal;
int *mask = atom->mask;
double *uCond = atom->uCond;
double *uMech = atom->uMech;
double *uChem = atom->uChem;
double *dpdTheta = atom->dpdTheta;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit){
temperature_lookup(i,uCond[i]+uMech[i]+uChem[i],dpdTheta[i]);
if(dpdTheta[i] <= 0.0)
error->one(FLERR,"Internal temperature <= zero");
}
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::end_of_step()
{
int nlocal = atom->nlocal;
int *mask = atom->mask;
double *uCond = atom->uCond;
double *uMech = atom->uMech;
double *uChem = atom->uChem;
double *dpdTheta = atom->dpdTheta;
double duChem;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
// Communicate the ghost uCGnew
comm->reverse_comm_fix(this);
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit){
duChem = uCG[i] - uCGnew[i];
uChem[i] += duChem;
uCG[i] = 0.0;
uCGnew[i] = 0.0;
}
// Communicate the updated momenta and velocities to all nodes
comm->forward_comm_fix(this);
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit){
temperature_lookup(i,uCond[i]+uMech[i]+uChem[i],dpdTheta[i]);
if(dpdTheta[i] <= 0.0)
error->one(FLERR,"Internal temperature <= zero");
}
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::read_file(char *file)
{
int params_per_line = 2;
char **words = new char*[params_per_line+1];
dHf = new double[nspecies];
// open file on proc 0
FILE *fp;
fp = NULL;
if (comm->me == 0) {
fp = fopen(file,"r");
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open eos table/rx potential file %s",file);
error->one(FLERR,str);
}
}
// one set of params can span multiple lines
int n,nwords,ispecies;
char line[MAXLINE],*ptr;
int eof = 0;
while (1) {
if (comm->me == 0) {
ptr = fgets(line,MAXLINE,fp);
if (ptr == NULL) {
eof = 1;
fclose(fp);
} else n = strlen(line) + 1;
}
MPI_Bcast(&eof,1,MPI_INT,0,world);
if (eof) break;
MPI_Bcast(&n,1,MPI_INT,0,world);
MPI_Bcast(line,n,MPI_CHAR,0,world);
// strip comment, skip line if blank
if ((ptr = strchr(line,'#'))) *ptr = '\0';
nwords = atom->count_words(line);
if (nwords == 0) continue;
// concatenate additional lines until have params_per_line words
while (nwords < params_per_line) {
n = strlen(line);
if (comm->me == 0) {
ptr = fgets(&line[n],MAXLINE-n,fp);
if (ptr == NULL) {
eof = 1;
fclose(fp);
} else n = strlen(line) + 1;
}
MPI_Bcast(&eof,1,MPI_INT,0,world);
if (eof) break;
MPI_Bcast(&n,1,MPI_INT,0,world);
MPI_Bcast(line,n,MPI_CHAR,0,world);
if ((ptr = strchr(line,'#'))) *ptr = '\0';
nwords = atom->count_words(line);
}
if (nwords != params_per_line)
error->all(FLERR,"Incorrect format in eos table/rx potential file");
// words = ptrs to all words in line
nwords = 0;
words[nwords++] = strtok(line," \t\n\r\f");
while ((words[nwords++] = strtok(NULL," \t\n\r\f"))) continue;
for (ispecies = 0; ispecies < nspecies; ispecies++)
if (strcmp(words[0],&atom->dname[ispecies][0]) == 0) break;
if (ispecies < nspecies)
dHf[ispecies] = atof(words[1]);
}
delete [] words;
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::null_table(Table *tb)
{
tb->rfile = tb->efile = NULL;
tb->e2file = NULL;
tb->r = tb->e = tb->de = NULL;
tb->e2 = NULL;
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::free_table(Table *tb)
{
memory->destroy(tb->rfile);
memory->destroy(tb->efile);
memory->destroy(tb->e2file);
memory->destroy(tb->r);
memory->destroy(tb->e);
memory->destroy(tb->de);
memory->destroy(tb->e2);
}
/* ----------------------------------------------------------------------
read table file, only called by proc 0
------------------------------------------------------------------------- */
void FixEOStableRX::read_table(Table *tb, Table *tb2, char *file, char *keyword)
{
char line[MAXLINE];
// open file
FILE *fp = fopen(file,"r");
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open file %s",file);
error->one(FLERR,str);
}
// loop until section found with matching keyword
while (1) {
if (fgets(line,MAXLINE,fp) == NULL)
error->one(FLERR,"Did not find keyword in table file");
if (strspn(line," \t\n\r") == strlen(line)) continue; // blank line
if (line[0] == '#') continue; // comment
char *word = strtok(line," \t\n\r");
if (strcmp(word,keyword) == 0) break; // matching keyword
fgets(line,MAXLINE,fp); // no match, skip section
param_extract(tb,line);
fgets(line,MAXLINE,fp);
for (int i = 0; i < tb->ninput; i++) fgets(line,MAXLINE,fp);
}
// read args on 2nd line of section
// allocate table arrays for file values
fgets(line,MAXLINE,fp);
param_extract(tb,line);
tb2->ninput = tb->ninput;
memory->create(tb->rfile,tb->ninput,"eos:rfile");
memory->create(tb->efile,tb->ninput,"eos:efile");
memory->create(tb2->rfile,tb2->ninput,"eos:rfile");
memory->create(tb2->efile,tb2->ninput,"eos:efile");
for (int ispecies=1;ispecies<nspecies;ispecies++){
Table *tbl = &tables[ispecies];
Table *tbl2 = &tables2[ispecies];
tbl->ninput = tb->ninput;
tbl2->ninput = tb2->ninput;
memory->create(tbl->rfile,tbl->ninput,"eos:rfile");
memory->create(tbl->efile,tbl->ninput,"eos:efile");
memory->create(tbl2->rfile,tbl2->ninput,"eos:rfile");
memory->create(tbl2->efile,tbl2->ninput,"eos:efile");
}
// read r,e table values from file
double rtmp, tmpE;
int nwords;
char * word;
int ispecies;
int ninputs = tb->ninput;
fgets(line,MAXLINE,fp);
for (int i = 0; i < ninputs; i++) {
fgets(line,MAXLINE,fp);
nwords = atom->count_words(line);
if(nwords != nspecies+2){
printf("nwords=%d nspecies=%d\n",nwords,nspecies);
error->all(FLERR,"Illegal fix eos/table/rx command");
}
nwords = 0;
word = strtok(line," \t\n\r\f");
word = strtok(NULL," \t\n\r\f");
rtmp = atof(word);
for (int icolumn=0;icolumn<ncolumn;icolumn++){
ispecies = eosSpecies[icolumn];
Table *tbl = &tables[ispecies];
Table *tbl2 = &tables2[ispecies];
word = strtok(NULL," \t\n\r\f");
tmpE = atof(word);
tbl->rfile[i] = rtmp;
tbl->efile[i] = tmpE;
tbl2->rfile[i] = tmpE;
tbl2->efile[i] = rtmp;
}
}
fclose(fp);
}
/* ----------------------------------------------------------------------
build spline representation of e,f over entire range of read-in table
this function sets these values in e2file
------------------------------------------------------------------------- */
void FixEOStableRX::spline_table(Table *tb)
{
memory->create(tb->e2file,tb->ninput,"eos:e2file");
double ep0 = 0.0;
double epn = 0.0;
spline(tb->rfile,tb->efile,tb->ninput,ep0,epn,tb->e2file);
}
/* ----------------------------------------------------------------------
compute r,e,f vectors from splined values
------------------------------------------------------------------------- */
void FixEOStableRX::compute_table(Table *tb)
{
// delta = table spacing for N-1 bins
int tlm1 = tablength-1;
tb->delta = (tb->hi - tb->lo)/ tlm1;
tb->invdelta = 1.0/tb->delta;
tb->deltasq6 = tb->delta*tb->delta / 6.0;
// N-1 evenly spaced bins in r from min to max
// r,e = value at lower edge of bin
// de values = delta values of e,f
// r,e are N in length so de arrays can compute difference
memory->create(tb->r,tablength,"eos:r");
memory->create(tb->e,tablength,"eos:e");
memory->create(tb->de,tlm1,"eos:de");
memory->create(tb->e2,tablength,"eos:e2");
double a;
for (int i = 0; i < tablength; i++) {
a = tb->lo + i*tb->delta;
tb->r[i] = a;
tb->e[i] = splint(tb->rfile,tb->efile,tb->e2file,tb->ninput,a);
}
for (int i = 0; i < tlm1; i++) {
tb->de[i] = tb->e[i+1] - tb->e[i];
}
}
/* ----------------------------------------------------------------------
extract attributes from parameter line in table section
format of line: N value
N is required, other params are optional
------------------------------------------------------------------------- */
void FixEOStableRX::param_extract(Table *tb, char *line)
{
int ispecies;
ncolumn = 0;
if (!eosSpecies)
eosSpecies = new int[nspecies];
for (ispecies = 0; ispecies < nspecies; ispecies++)
eosSpecies[ispecies] = -1;
tb->ninput = 0;
char *word = strtok(line," \t\n\r\f");
if (strcmp(word,"N") == 0) {
word = strtok(NULL," \t\n\r\f");
tb->ninput = atoi(word);
} else
error->one(FLERR,"Invalid keyword in fix eos/table/rx parameters");
word = strtok(NULL," \t\n\r\f");
while (word) {
for (ispecies = 0; ispecies < nspecies; ispecies++)
if (strcmp(word,&atom->dname[ispecies][0]) == 0){
eosSpecies[ncolumn] = ispecies;
ncolumn++;
break;
}
if (ispecies == nspecies){
printf("name=%s not found in species list\n",word);
error->one(FLERR,"Invalid keyword in fix eos/table/rx parameters");
}
word = strtok(NULL," \t\n\r\f");
}
for (int icolumn = 0; icolumn < ncolumn; icolumn++)
if(eosSpecies[icolumn]==-1)
error->one(FLERR,"EOS data is missing from fix eos/table/rx tabe");
if(ncolumn != nspecies){
printf("ncolumns=%d nspecies=%d\n",ncolumn,nspecies);
error->one(FLERR,"The number of columns in fix eos/table/rx does not match the number of species");
}
if (tb->ninput == 0) error->one(FLERR,"fix eos/table/rx parameters did not set N");
}
/* ----------------------------------------------------------------------
broadcast read-in table info from proc 0 to other procs
this function communicates these values in Table:
ninput,rfile,efile
------------------------------------------------------------------------- */
void FixEOStableRX::bcast_table(Table *tb)
{
MPI_Bcast(&tb->ninput,1,MPI_INT,0,world);
int me;
MPI_Comm_rank(world,&me);
if (me > 0) {
memory->create(tb->rfile,tb->ninput,"eos:rfile");
memory->create(tb->efile,tb->ninput,"eos:efile");
}
MPI_Bcast(tb->rfile,tb->ninput,MPI_DOUBLE,0,world);
MPI_Bcast(tb->efile,tb->ninput,MPI_DOUBLE,0,world);
}
/* ----------------------------------------------------------------------
spline and splint routines modified from Numerical Recipes
------------------------------------------------------------------------- */
void FixEOStableRX::spline(double *x, double *y, int n,
double yp1, double ypn, double *y2)
{
int i,k;
double p,qn,sig,un;
double *u = new double[n];
if (yp1 > 0.99e30) y2[0] = u[0] = 0.0;
else {
y2[0] = -0.5;
u[0] = (3.0/(x[1]-x[0])) * ((y[1]-y[0]) / (x[1]-x[0]) - yp1);
}
for (i = 1; i < n-1; i++) {
sig = (x[i]-x[i-1]) / (x[i+1]-x[i-1]);
p = sig*y2[i-1] + 2.0;
y2[i] = (sig-1.0) / p;
u[i] = (y[i+1]-y[i]) / (x[i+1]-x[i]) - (y[i]-y[i-1]) / (x[i]-x[i-1]);
u[i] = (6.0*u[i] / (x[i+1]-x[i-1]) - sig*u[i-1]) / p;
}
if (ypn > 0.99e30) qn = un = 0.0;
else {
qn = 0.5;
un = (3.0/(x[n-1]-x[n-2])) * (ypn - (y[n-1]-y[n-2]) / (x[n-1]-x[n-2]));
}
y2[n-1] = (un-qn*u[n-2]) / (qn*y2[n-2] + 1.0);
for (k = n-2; k >= 0; k--) y2[k] = y2[k]*y2[k+1] + u[k];
delete [] u;
}
/* ---------------------------------------------------------------------- */
double FixEOStableRX::splint(double *xa, double *ya, double *y2a, int n, double x)
{
int klo,khi,k;
double h,b,a,y;
klo = 0;
khi = n-1;
while (khi-klo > 1) {
k = (khi+klo) >> 1;
if (xa[k] > x) khi = k;
else klo = k;
}
h = xa[khi]-xa[klo];
a = (xa[khi]-x) / h;
b = (x-xa[klo]) / h;
y = a*ya[klo] + b*ya[khi] +
((a*a*a-a)*y2a[klo] + (b*b*b-b)*y2a[khi]) * (h*h)/6.0;
return y;
}
/* ----------------------------------------------------------------------
calculate potential ui at temperature thetai
------------------------------------------------------------------------- */
void FixEOStableRX::energy_lookup(int id, double thetai, double &ui)
{
int itable;
double fraction, uTmp, nTotal;
ui = 0.0;
nTotal = 0.0;
for(int ispecies=0;ispecies<nspecies;ispecies++){
Table *tb = &tables[ispecies];
thetai = MAX(thetai,tb->lo);
thetai = MIN(thetai,tb->hi);
if (tabstyle == LINEAR) {
itable = static_cast<int> ((thetai - tb->lo) * tb->invdelta);
fraction = (thetai - tb->r[itable]) * tb->invdelta;
uTmp = tb->e[itable] + fraction*tb->de[itable];
uTmp += dHf[ispecies];
// mol fraction form:
ui += atom->dvector[ispecies][id]*uTmp;
nTotal += atom->dvector[ispecies][id];
}
}
ui = ui - double(nTotal+1.5)*force->boltz*thetai;
}
/* ----------------------------------------------------------------------
calculate temperature thetai at energy ui
------------------------------------------------------------------------- */
void FixEOStableRX::temperature_lookup(int id, double ui, double &thetai)
{
Table *tb = &tables[0];
int it;
double t1,t2,u1,u2,f1,f2;
double maxit = 100;
double temp;
double delta = 0.001;
// Store the current thetai in t1
t1 = MAX(thetai,tb->lo);
t1 = MIN(thetai,tb->hi);
if(t1==tb->hi) delta = -delta;
// Compute u1 at thetai
energy_lookup(id,t1,u1);
// Compute f1
f1 = u1 - ui;
// Compute guess of t2
t2 = (1.0 + delta)*t1;
// Compute u2 at t2
energy_lookup(id,t2,u2);
// Compute f1
f2 = u2 - ui;
// Apply the Secant Method
for(it=0; it<maxit; it++){
if(fabs(f2-f1)<1e-15){
if(isnan(f1) || isnan(f2)) error->one(FLERR,"NaN detected in secant solver.");
temp = t1;
temp = MAX(temp,tb->lo);
temp = MIN(temp,tb->hi);
char str[256];
sprintf(str,"Secant solver did not converge because table bounds were exceeded: it=%d id=%d ui=%lf thetai=%lf t1=%lf t2=%lf f1=%lf f2=%lf dpdTheta=%lf\n",it,id,ui,thetai,t1,t2,f1,f2,temp);
error->warning(FLERR,str);
break;
}
temp = t2 - f2*(t2-t1)/(f2-f1);
if(fabs(temp-t2) < 1e-6) break;
f1 = f2;
t1 = t2;
t2 = temp;
energy_lookup(id,t2,u2);
f2 = u2 - ui;
}
if(it==maxit){
char str[256];
sprintf(str,"Maxit exceeded in secant solver: id=%d ui=%lf thetai=%lf t1=%lf t2=%lf f1=%lf f2=%lf\n",id,ui,thetai,t1,t2,f1,f2);
if(isnan(f1) || isnan(f2) || isnan(ui) || isnan(thetai) || isnan(t1) || isnan(t2))
error->one(FLERR,"NaN detected in secant solver.");
error->one(FLERR,str);
}
thetai = temp;
}
/* ---------------------------------------------------------------------- */
int FixEOStableRX::pack_forward_comm(int n, int *list, double *buf, int pbc_flag, int *pbc)
{
int ii,jj,m;
double *uChem = atom->uChem;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
m = 0;
for (ii = 0; ii < n; ii++) {
jj = list[ii];
buf[m++] = uChem[jj];
buf[m++] = uCG[jj];
buf[m++] = uCGnew[jj];
}
return m;
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::unpack_forward_comm(int n, int first, double *buf)
{
int ii,m,last;
double *uChem = atom->uChem;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
m = 0;
last = first + n ;
for (ii = first; ii < last; ii++){
uChem[ii] = buf[m++];
uCG[ii] = buf[m++];
uCGnew[ii] = buf[m++];
}
}
/* ---------------------------------------------------------------------- */
int FixEOStableRX::pack_reverse_comm(int n, int first, double *buf)
{
int i,m,last;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
m = 0;
last = first + n;
for (i = first; i < last; i++) {
buf[m++] = uCG[i];
buf[m++] = uCGnew[i];
}
return m;
}
/* ---------------------------------------------------------------------- */
void FixEOStableRX::unpack_reverse_comm(int n, int *list, double *buf)
{
int i,j,m;
double *uCG = atom->uCG;
double *uCGnew = atom->uCGnew;
m = 0;
for (i = 0; i < n; i++) {
j = list[i];
uCG[j] += buf[m++];
uCGnew[j] += buf[m++];
}
}

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