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msm.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 authors: Paul Crozier, Stan Moore, Stephen Bond, (all SNL)
------------------------------------------------------------------------- */
#include "lmptype.h"
#include "mpi.h"
#include "string.h"
#include "stdio.h"
#include "stdlib.h"
#include "math.h"
#include "msm.h"
#include "atom.h"
#include "comm.h"
#include "commgrid.h"
#include "neighbor.h"
#include "force.h"
#include "pair.h"
#include "bond.h"
#include "angle.h"
#include "domain.h"
#include "memory.h"
#include "error.h"
#include "math_const.h"
using namespace LAMMPS_NS;
using namespace MathConst;
#define MAX_LEVELS 10
#define OFFSET 16384
#define SMALL 0.00001
#define LARGE 10000.0
enum{REVERSE_RHO,REVERSE_AD,REVERSE_AD_PERATOM};
enum{FORWARD_RHO,FORWARD_AD,FORWARD_AD_PERATOM};
/* ---------------------------------------------------------------------- */
MSM::MSM(LAMMPS *lmp, int narg, char **arg) : KSpace(lmp, narg, arg)
{
if (narg < 1) error->all(FLERR,"Illegal kspace_style msm command");
msmflag = 1;
accuracy_relative = atof(arg[0]);
nfactors = 1;
factors = new int[nfactors];
factors[0] = 2;
MPI_Comm_rank(world,&me);
MPI_Comm_size(world,&nprocs);
phi1d = dphi1d = NULL;
nmax = 0;
part2grid = NULL;
g_direct = NULL;
g_direct_top = NULL;
v0_direct = v1_direct = v2_direct = NULL;
v3_direct = v4_direct = v5_direct = NULL;
v0_direct_top = v1_direct_top = v2_direct_top = NULL;
v3_direct_top = v4_direct_top = v5_direct_top = NULL;
cg = cg_peratom = NULL;
levels = 0;
peratom_allocate_flag = 0;
order = 8;
}
/* ----------------------------------------------------------------------
free all memory
------------------------------------------------------------------------- */
MSM::~MSM()
{
delete [] factors;
deallocate();
deallocate_peratom();
memory->destroy(part2grid);
memory->destroy(g_direct);
memory->destroy(g_direct_top);
memory->destroy(v0_direct);
memory->destroy(v1_direct);
memory->destroy(v2_direct);
memory->destroy(v3_direct);
memory->destroy(v4_direct);
memory->destroy(v5_direct);
memory->destroy(v0_direct_top);
memory->destroy(v1_direct_top);
memory->destroy(v2_direct_top);
memory->destroy(v3_direct_top);
memory->destroy(v4_direct_top);
memory->destroy(v5_direct_top);
deallocate_levels();
}
/* ----------------------------------------------------------------------
called once before run
------------------------------------------------------------------------- */
void MSM::init()
{
if (me == 0) {
if (screen) fprintf(screen,"MSM initialization ...\n");
if (logfile) fprintf(logfile,"MSM initialization ...\n");
}
// error check
if (domain->triclinic)
error->all(FLERR,"Cannot (yet) use MSM with triclinic box");
if (domain->dimension == 2)
error->all(FLERR,"Cannot (yet) use MSM with 2d simulation");
if (!atom->q_flag) error->all(FLERR,"Kspace style requires atom attribute q");
if (slabflag == 1)
error->all(FLERR,"Cannot use slab correction with MSM");
if (order < 4 || order > 10) {
char str[128];
sprintf(str,"MSM order must be 4, 6, 8, or 10");
error->all(FLERR,str);
}
if (order%2 != 0) error->all(FLERR,"MSM order must be 4, 6, 8, or 10");
if (sizeof(FFT_SCALAR) != 8) error->all(FLERR,"Cannot (yet) use single precision with MSM (remove -DFFT_SINGLE from Makefile and recompile)");
// extract short-range Coulombic cutoff from pair style
qqrd2e = force->qqrd2e;
scale = 1.0;
pair_check();
int itmp;
double *p_cutoff = (double *) force->pair->extract("cut_msm",itmp);
if (p_cutoff == NULL)
error->all(FLERR,"KSpace style is incompatible with Pair style");
cutoff = *p_cutoff;
// compute qsum & qsqsum and give error if not charge-neutral
qsum = qsqsum = 0.0;
for (int i = 0; i < atom->nlocal; i++) {
qsum += atom->q[i];
qsqsum += atom->q[i]*atom->q[i];
}
double tmp;
MPI_Allreduce(&qsum,&tmp,1,MPI_DOUBLE,MPI_SUM,world);
qsum = tmp;
MPI_Allreduce(&qsqsum,&tmp,1,MPI_DOUBLE,MPI_SUM,world);
qsqsum = tmp;
q2 = qsqsum * force->qqrd2e / force->dielectric;
if (qsqsum == 0.0)
error->all(FLERR,"Cannot use kspace solver on system with no charge");
// not yet sure of the correction needed for non-neutral systems
if (fabs(qsum) > SMALL) {
char str[128];
sprintf(str,"System is not charge neutral, net charge = %g",qsum);
error->all(FLERR,str);
}
// set accuracy (force units) from accuracy_relative or accuracy_absolute
if (accuracy_absolute >= 0.0) accuracy = accuracy_absolute;
else accuracy = accuracy_relative * two_charge_force;
// setup MSM grid resolution
set_grid_global();
setup();
double estimated_error = estimate_total_error();
// output grid stats
int ngrid_max;
MPI_Allreduce(&ngrid[0],&ngrid_max,1,MPI_INT,MPI_MAX,world);
if (me == 0) {
if (screen) {
fprintf(screen," 3d grid size/proc = %d\n",
ngrid_max);
fprintf(screen," estimated absolute RMS force accuracy = %g\n",
estimated_error);
fprintf(screen," estimated relative force accuracy = %g\n",
estimated_error/two_charge_force);
}
if (logfile) {
fprintf(logfile," 3d grid size/proc = %d\n",
ngrid_max);
fprintf(logfile," estimated absolute RMS force accuracy = %g\n",
estimated_error);
fprintf(logfile," estimated relative force accuracy = %g\n",
estimated_error/two_charge_force);
}
}
if (me == 0) {
if (screen) {
fprintf(screen," grid = %d %d %d\n",nx_msm[0],ny_msm[0],nz_msm[0]);
fprintf(screen," order = %d\n",order);
}
if (logfile) {
fprintf(logfile," grid = %d %d %d\n",nx_msm[0],ny_msm[0],nz_msm[0]);
fprintf(logfile," order = %d\n",order);
}
}
}
/* ----------------------------------------------------------------------
estimate cutoff for a given grid spacing and error
------------------------------------------------------------------------- */
double MSM::estimate_cutoff(double h, double prd)
{
double a;
int p = order - 1;
double Mp,cprime,error_scaling;
Mp = cprime = error_scaling = 1;
// Mp values from Table 5.1 of Hardy's thesis
// cprime values from equation 4.17 of Hardy's thesis
// error scaling from empirical fitting to convert to rms force errors
if (p == 3) {
Mp = 9;
cprime = 1.0/6.0;
error_scaling = 0.39189561;
} else if (p == 5) {
Mp = 825;
cprime = 1.0/30.0;
error_scaling = 0.150829428;
} else if (p == 7) {
Mp = 130095;
cprime = 1.0/140.0;
error_scaling = 0.049632967;
} else if (p == 9) {
Mp = 34096545;
cprime = 1.0/630.0;
error_scaling = 0.013520855;
} else {
error->all(FLERR,"MSM order must be 4, 6, 8, or 10");
}
// equation 4.1 from Hardy's thesis
double C_p = 4.0*cprime*Mp/3.0;
// use empirical parameters to convert to rms force errors
C_p *= error_scaling;
// equation 3.200 from Hardy's thesis
a = C_p*pow(h,(p-1))/accuracy;
// include dependency of error on other terms
a *= q2/(prd*sqrt(atom->natoms));
a = pow(a,1.0/double(p));
return a;
}
/* ----------------------------------------------------------------------
estimate 1d grid RMS force error for MSM
------------------------------------------------------------------------- */
double MSM::estimate_1d_error(double h, double prd)
{
double a = cutoff;
int p = order - 1;
double Mp,cprime,error_scaling;
Mp = cprime = error_scaling = 1;
// Mp values from Table 5.1 of Hardy's thesis
// cprime values from equation 4.17 of Hardy's thesis
// error scaling from empirical fitting to convert to rms force errors
if (p == 3) {
Mp = 9;
cprime = 1.0/6.0;
error_scaling = 0.39189561;
} else if (p == 5) {
Mp = 825;
cprime = 1.0/30.0;
error_scaling = 0.150829428;
} else if (p == 7) {
Mp = 130095;
cprime = 1.0/140.0;
error_scaling = 0.049632967;
} else if (p == 9) {
Mp = 34096545;
cprime = 1.0/630.0;
error_scaling = 0.013520855;
} else {
error->all(FLERR,"MSM order must be 4, 6, 8, or 10");
}
// equation 4.1 from Hardy's thesis
double C_p = 4.0*cprime*Mp/3.0;
// use empirical parameters to convert to rms force errors
C_p *= error_scaling;
// equation 3.197 from Hardy's thesis
double error_1d = C_p*pow(h,(p-1))/pow(a,(p+1));
// include dependency of error on other terms
error_1d *= q2*a/(prd*sqrt(atom->natoms));
return error_1d;
}
/* ----------------------------------------------------------------------
estimate 3d grid RMS force error
------------------------------------------------------------------------- */
double MSM::estimate_3d_error()
{
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
double error_x = estimate_1d_error(xprd/nx_msm[0],xprd);
double error_y = estimate_1d_error(yprd/ny_msm[0],yprd);
double error_z = estimate_1d_error(zprd/nz_msm[0],zprd);
double error_3d =
sqrt(error_x*error_x + error_y*error_y + error_z*error_z) / sqrt(3.0);
return error_3d;
}
/* ----------------------------------------------------------------------
estimate total RMS force error
------------------------------------------------------------------------- */
double MSM::estimate_total_error()
{
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
bigint natoms = atom->natoms;
double grid_error = estimate_3d_error();
double q2_over_sqrt = q2 / sqrt(natoms*cutoff*xprd*yprd*zprd);
double short_range_error = 0.0;
double table_error =
estimate_table_accuracy(q2_over_sqrt,short_range_error);
double estimated_total_error = sqrt(grid_error*grid_error +
short_range_error*short_range_error + table_error*table_error);
return estimated_total_error;
}
/* ----------------------------------------------------------------------
adjust MSM coeffs, called initially and whenever volume has changed
------------------------------------------------------------------------- */
void MSM::setup()
{
int i,j,k,l,m,n;
double *prd;
double a = cutoff;
// volume-dependent factors
prd = domain->prd;
double xprd = prd[0];
double yprd = prd[1];
double zprd = prd[2];
volume = xprd * yprd * zprd;
// loop over grid levels
for (int n=0; n<levels; n++) {
delxinv[n] = nx_msm[n]/xprd;
delyinv[n] = ny_msm[n]/yprd;
delzinv[n] = nz_msm[n]/zprd;
delvolinv[n] = delxinv[n]*delyinv[n]*delzinv[n];
}
nxhi_direct = static_cast<int> (2.0*a*delxinv[0]);
nxlo_direct = -nxhi_direct;
nyhi_direct = static_cast<int> (2.0*a*delyinv[0]);
nylo_direct = -nyhi_direct;
nzhi_direct = static_cast<int> (2.0*a*delzinv[0]);
nzlo_direct = -nzhi_direct;
nmax_direct = 8*(nxhi_direct+1)*(nyhi_direct+1)*(nzhi_direct+1);
deallocate();
deallocate_peratom();
if (!peratom_allocate_flag) { // Timestep 0
get_g_direct();
get_virial_direct();
if (domain->nonperiodic) {
get_g_direct_top(levels-1);
get_virial_direct_top(levels-1);
}
} else {
get_g_direct();
if (domain->nonperiodic) get_g_direct_top(levels-1);
if (vflag_either) {
get_virial_direct();
if (domain->nonperiodic) get_virial_direct_top(levels-1);
}
}
boxlo = domain->boxlo;
set_grid_local();
// allocate K-space dependent memory
// don't invoke allocate_peratom(), compute() will allocate when needed
allocate();
peratom_allocate_flag = 0;
for (int n=0; n<levels; n++) {
cg[n]->ghost_notify();
cg[n]->setup();
}
}
/* ----------------------------------------------------------------------
compute the MSM long-range force, energy, virial
------------------------------------------------------------------------- */
void MSM::compute(int eflag, int vflag)
{
int i,j;
// set energy/virial flags
// invoke allocate_peratom() if needed for first time
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = evflag_atom = eflag_global = vflag_global =
eflag_atom = vflag_atom = eflag_either = vflag_either = 0;
if (vflag_atom && !peratom_allocate_flag) {
allocate_peratom();
for (int n=0; n<levels; n++) {
cg_peratom[n]->ghost_notify();
cg_peratom[n]->setup();
}
peratom_allocate_flag = 1;
}
// extend size of per-atom arrays if necessary
if (atom->nlocal > nmax) {
memory->destroy(part2grid);
nmax = atom->nmax;
memory->create(part2grid,nmax,3,"msm:part2grid");
}
// find grid points for all my particles
// map my particle charge onto my local 3d density grid (aninterpolation)
particle_map();
make_rho();
current_level = 0;
cg[0]->reverse_comm(this,REVERSE_RHO);
// all procs communicate density values from their ghost cells
// to fully sum contribution in their 3d bricks
for (int n=0; n<=levels-2; n++) {
current_level = n;
cg[n]->forward_comm(this,FORWARD_RHO);
direct(n);
if (vflag_atom) direct_peratom(n);
restriction(n);
}
// top grid level
current_level = levels-1;
cg[levels-1]->forward_comm(this,FORWARD_RHO);
direct_top(levels-1);
if (vflag_atom) direct_peratom_top(levels-1);
for (int n=levels-2; n>=0; n--) {
prolongation(n);
current_level = n;
cg[n]->reverse_comm(this,REVERSE_AD);
// extra per-atom virial communication
if (vflag_atom)
cg_peratom[n]->reverse_comm(this,REVERSE_AD_PERATOM);
}
// all procs communicate E-field values
// to fill ghost cells surrounding their 3d bricks
current_level = 0;
cg[0]->forward_comm(this,FORWARD_AD);
// extra per-atom energy/virial communication
if (vflag_atom)
cg_peratom[0]->forward_comm(this,FORWARD_AD_PERATOM);
// calculate the force on my particles (interpolation)
fieldforce();
// calculate the per-atom energy for my particles
if (evflag_atom) fieldforce_peratom();
const double qscale = force->qqrd2e * scale;
// Total long-range energy
if (eflag_global) {
double energy_all;
MPI_Allreduce(&energy,&energy_all,1,MPI_DOUBLE,MPI_SUM,world);
energy = energy_all;
double e_self = qsqsum*gamma(0.0)/cutoff; // Self-energy term
energy -= e_self;
energy *= 0.5*qscale;
}
// Total long-range virial
if (vflag_global) {
double virial_all[6];
MPI_Allreduce(virial,virial_all,6,MPI_DOUBLE,MPI_SUM,world);
for (i = 0; i < 6; i++) virial[i] = 0.5*qscale*virial_all[i];
}
// per-atom energy/virial
// energy includes self-energy correction
if (evflag_atom) {
double *q = atom->q;
int nlocal = atom->nlocal;
if (eflag_atom) {
for (i = 0; i < nlocal; i++) {
eatom[i] -= q[i]*q[i]*gamma(0.0)/cutoff;
eatom[i] *= 0.5*qscale;
}
}
if (vflag_atom) {
for (i = 0; i < nlocal; i++)
for (j = 0; j < 6; j++) vatom[i][j] *= 0.5*qscale;
}
}
}
/* ----------------------------------------------------------------------
allocate memory that depends on # of grid points
------------------------------------------------------------------------- */
void MSM::allocate()
{
// summation coeffs
memory->create2d_offset(phi1d,3,-order,order,"msm:phi1d");
memory->create2d_offset(dphi1d,3,-order,order,"msm:dphi1d");
// allocate grid levels
for (int n=0; n<levels; n++) {
memory->create3d_offset(qgrid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:qgrid");
memory->create3d_offset(egrid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:egrid");
// create ghost grid object for rho and electric field communication
int (*procneigh)[2] = comm->procneigh;
cg[n] = new CommGrid(lmp,world,1,1,
nxlo_in[n],nxhi_in[n],nylo_in[n],nyhi_in[n],nzlo_in[n],nzhi_in[n],
nxlo_out[n],nxhi_out[n],nylo_out[n],nyhi_out[n],nzlo_out[n],nzhi_out[n],
procneigh[0][0],procneigh[0][1],procneigh[1][0],
procneigh[1][1],procneigh[2][0],procneigh[2][1]);
}
}
/* ----------------------------------------------------------------------
allocate per-atom memory that depends on # of grid points
------------------------------------------------------------------------- */
void MSM::allocate_peratom()
{
// allocate grid levels
for (int n=0; n<levels; n++) {
memory->create3d_offset(v0grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v0grid");
memory->create3d_offset(v1grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v1grid");
memory->create3d_offset(v2grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v2grid");
memory->create3d_offset(v3grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v3grid");
memory->create3d_offset(v4grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v4grid");
memory->create3d_offset(v5grid[n],nzlo_out[n],nzhi_out[n],
nylo_out[n],nyhi_out[n],nxlo_out[n],nxhi_out[n],"msm:v5grid");
// create ghost grid object for per-atom energy/virial
int (*procneigh)[2] = comm->procneigh;
cg_peratom[n] =
new CommGrid(lmp,world,6,6,
nxlo_in[n],nxhi_in[n],nylo_in[n],nyhi_in[n],nzlo_in[n],nzhi_in[n],
nxlo_out[n],nxhi_out[n],nylo_out[n],nyhi_out[n],nzlo_out[n],nzhi_out[n],
procneigh[0][0],procneigh[0][1],procneigh[1][0],
procneigh[1][1],procneigh[2][0],procneigh[2][1]);
}
}
/* ----------------------------------------------------------------------
deallocate memory that depends on # of grid points
------------------------------------------------------------------------- */
void MSM::deallocate()
{
memory->destroy2d_offset(phi1d,-order);
memory->destroy2d_offset(dphi1d,-order);
// deallocate grid levels
for (int n=0; n<levels; n++) {
if (qgrid[n])
memory->destroy3d_offset(qgrid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (egrid[n])
memory->destroy3d_offset(egrid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (cg)
if (cg[n]) delete cg[n];
}
}
/* ----------------------------------------------------------------------
deallocate per-atom memory that depends on # of grid points
------------------------------------------------------------------------- */
void MSM::deallocate_peratom()
{
for (int n=0; n<levels; n++) {
if (v0grid[n])
memory->destroy3d_offset(v0grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (v1grid[n])
memory->destroy3d_offset(v1grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (v2grid[n])
memory->destroy3d_offset(v2grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (v3grid[n])
memory->destroy3d_offset(v3grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (v4grid[n])
memory->destroy3d_offset(v4grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (v5grid[n])
memory->destroy3d_offset(v5grid[n],nzlo_out[n],nylo_out[n],nxlo_out[n]);
if (cg_peratom)
if (cg_peratom[n]) delete cg_peratom[n];
}
}
/* ----------------------------------------------------------------------
allocate memory that depends on # of grid levels
------------------------------------------------------------------------- */
void MSM::allocate_levels()
{
ngrid = new int[levels];
cg = new CommGrid*[levels];
cg_peratom = new CommGrid*[levels];
alpha = new int[levels];
betax = new int[levels];
betay = new int[levels];
betaz = new int[levels];
nx_msm = new int[levels];
ny_msm = new int[levels];
nz_msm = new int[levels];
nxlo_in = new int[levels];
nylo_in = new int[levels];
nzlo_in = new int[levels];
nxhi_in = new int[levels];
nyhi_in = new int[levels];
nzhi_in = new int[levels];
nxlo_out = new int[levels];
nylo_out = new int[levels];
nzlo_out = new int[levels];
nxhi_out = new int[levels];
nyhi_out = new int[levels];
nzhi_out = new int[levels];
delxinv = new double[levels];
delyinv = new double[levels];
delzinv = new double[levels];
delvolinv = new double[levels];
qgrid = new double***[levels];
egrid = new double***[levels];
v0grid = new double***[levels];
v1grid = new double***[levels];
v2grid = new double***[levels];
v3grid = new double***[levels];
v4grid = new double***[levels];
v5grid = new double***[levels];
for (int n=0; n<levels; n++) {
cg[n] = NULL;
cg_peratom[n] = NULL;
qgrid[n] = NULL;
egrid[n] = NULL;
v0grid[n] = NULL;
v1grid[n] = NULL;
v2grid[n] = NULL;
v3grid[n] = NULL;
v4grid[n] = NULL;
v5grid[n] = NULL;
}
}
/* ----------------------------------------------------------------------
deallocate memory that depends on # of grid levels
------------------------------------------------------------------------- */
void MSM::deallocate_levels()
{
delete [] ngrid;
delete [] cg;
delete [] cg_peratom;
delete [] alpha;
delete [] betax;
delete [] betay;
delete [] betaz;
delete [] nx_msm;
delete [] ny_msm;
delete [] nz_msm;
delete [] nxlo_in;
delete [] nylo_in;
delete [] nzlo_in;
delete [] nxhi_in;
delete [] nyhi_in;
delete [] nzhi_in;
delete [] nxlo_out;
delete [] nylo_out;
delete [] nzlo_out;
delete [] nxhi_out;
delete [] nyhi_out;
delete [] nzhi_out;
delete [] delxinv;
delete [] delyinv;
delete [] delzinv;
delete [] delvolinv;
delete [] qgrid;
delete [] egrid;
delete [] v0grid;
delete [] v1grid;
delete [] v2grid;
delete [] v3grid;
delete [] v4grid;
delete [] v5grid;
}
/* ----------------------------------------------------------------------
set size of MSM grids
------------------------------------------------------------------------- */
void MSM::set_grid_global()
{
if (accuracy_relative <= 0.0)
error->all(FLERR,"KSpace accuracy must be > 0");
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
int nx_max,ny_max,nz_max;
double hx,hy,hz;
if (adjust_cutoff_flag && !gridflag) {
int p = order - 1;
double hmin = 3072.0*(p+1)/(p-1)/
(448.0*MY_PI + 56.0*MY_PI*order/2 + 1701.0);
hmin = pow(hmin,1.0/6.0)/pow(atom->natoms,1.0/3.0);
hx = hmin*xprd;
hy = hmin*yprd;
hz = hmin*zprd;
nx_max = static_cast<int>(xprd/hx);
ny_max = static_cast<int>(yprd/hy);
nz_max = static_cast<int>(zprd/hz);
} else if (!gridflag) {
nx_max = ny_max = nz_max = 2;
hx = xprd/nx_max;
hy = yprd/ny_max;
hz = zprd/nz_max;
double x_error = 2.0*accuracy;
double y_error = 2.0*accuracy;
double z_error = 2.0*accuracy;
while (x_error > accuracy) {
nx_max *= 2;
hx = xprd/nx_max;
x_error = estimate_1d_error(hx,xprd);
}
while (y_error > accuracy) {
ny_max *= 2;
hy = yprd/ny_max;
y_error = estimate_1d_error(hy,yprd);
}
while (z_error > accuracy) {
nz_max *= 2;
hz = zprd/nz_max;
z_error = estimate_1d_error(hz,zprd);
}
} else {
nx_max = nx_msm_max;
ny_max = ny_msm_max;
nz_max = nz_msm_max;
}
// boost grid size until it is factorable
int flag = 0;
int xlevels,ylevels,zlevels;
while (!factorable(nx_max,flag,xlevels)) nx_max++;
while (!factorable(ny_max,flag,ylevels)) ny_max++;
while (!factorable(nz_max,flag,zlevels)) nz_max++;
if (flag && gridflag && me == 0)
error->warning(FLERR,"Number of MSM mesh points increased to be a multiple of 2");
// Find maximum number of levels
levels = MAX(xlevels,ylevels);
levels = MAX(levels,zlevels);
if (levels > MAX_LEVELS)
error->all(FLERR,"Too many MSM grid levels");
// Need at least 2 MSM levels for periodic systems
if (levels <= 1) {
levels = xlevels = ylevels = zlevels = 2;
nx_max = ny_max = nz_max = 2;
if (gridflag)
error->warning(FLERR,"MSM mesh too small, increasing to 2 points in each direction)");
}
if (adjust_cutoff_flag) {
hx = xprd/nx_max;
hy = yprd/ny_max;
hz = zprd/nz_max;
double ax,ay,az;
ax = estimate_cutoff(hx,xprd);
ay = estimate_cutoff(hy,yprd);
az = estimate_cutoff(hz,zprd);
cutoff = sqrt(ax*ax + ay*ay + az*az)/sqrt(3.0);
int itmp;
double *p_cutoff = (double *) force->pair->extract("cut_msm",itmp);
*p_cutoff = cutoff;
char str[128];
sprintf(str,"Adjusting Coulombic cutoff for MSM, new cutoff = %g",cutoff);
if (me == 0) error->warning(FLERR,str);
}
allocate_levels();
for (int n = 0; n < levels; n++) {
if (xlevels-n-1 > 0)
nx_msm[n] = static_cast<int> (pow(2.0,xlevels-n-1));
else
nx_msm[n] = 1;
if (ylevels-n-1 > 0)
ny_msm[n] = static_cast<int> (pow(2.0,ylevels-n-1));
else
ny_msm[n] = 1;
if (zlevels-n-1 > 0)
nz_msm[n] = static_cast<int> (pow(2.0,zlevels-n-1));
else
nz_msm[n] = 1;
}
if (nx_msm[0] >= OFFSET || ny_msm[0] >= OFFSET || nz_msm[0] >= OFFSET)
error->all(FLERR,"MSM grid is too large");
if (domain->nonperiodic) {
alpha[0] = -(order/2 - 1);
betax[0] = nx_msm[0] + (order/2 - 1);
betay[0] = ny_msm[0] + (order/2 - 1);
betaz[0] = nz_msm[0] + (order/2 - 1);
for (int n = 1; n < levels; n++) {
alpha[n] = -((-alpha[n-1]+1)/2) - (order/2 - 1);
betax[n] = ((betax[n-1]+1)/2) + (order/2 - 1);
betay[n] = ((betay[n-1]+1)/2) + (order/2 - 1);
betaz[n] = ((betaz[n-1]+1)/2) + (order/2 - 1);
}
}
}
/* ----------------------------------------------------------------------
set local subset of MSM grid that I own
n xyz lo/hi in = 3d brick that I own (inclusive)
n xyz lo/hi out = 3d brick + ghost cells in 6 directions (inclusive)
------------------------------------------------------------------------- */
void MSM::set_grid_local()
{
// global indices of MSM grid range from 0 to N-1
// nlo_in,nhi_in = lower/upper limits of the 3d sub-brick of
// global MSM grid that I own without ghost cells
// loop over grid levels
for (int n=0; n<levels; n++) {
// global indices of MSM grid range from 0 to N-1
// nlo_in,nhi_in = lower/upper limits of the 3d sub-brick of
// global MSM grid that I own without ghost cells
nxlo_in[n] = static_cast<int> (comm->xsplit[comm->myloc[0]] * nx_msm[n]);
nxhi_in[n] = static_cast<int> (comm->xsplit[comm->myloc[0]+1] * nx_msm[n]) - 1;
nylo_in[n] = static_cast<int> (comm->ysplit[comm->myloc[1]] * ny_msm[n]);
nyhi_in[n] = static_cast<int> (comm->ysplit[comm->myloc[1]+1] * ny_msm[n]) - 1;
nzlo_in[n] = static_cast<int> (comm->zsplit[comm->myloc[2]] * nz_msm[n]);
nzhi_in[n] = static_cast<int> (comm->zsplit[comm->myloc[2]+1] * nz_msm[n]) - 1;
// nlower,nupper = stencil size for mapping particles to MSM grid
nlower = -(order-1)/2;
nupper = order/2;
double *prd,*sublo,*subhi,*boxhi;
prd = domain->prd;
boxlo = domain->boxlo;
boxhi = domain->boxhi;
double xprd = prd[0];
double yprd = prd[1];
double zprd = prd[2];
// shift values for particle <-> grid mapping
// add/subtract OFFSET to avoid int(-0.75) = 0 when want it to be -1
// nlo_out,nhi_out = lower/upper limits of the 3d sub-brick of
// global MSM grid that my particles can contribute charge to
// effectively nlo_in,nhi_in + ghost cells
// nlo,nhi = global coords of grid pt to "lower left" of smallest/largest
// position a particle in my box can be at
// dist[3] = particle position bound = subbox + skin/2.0
// nlo_out,nhi_out = nlo,nhi + stencil size for particle mapping
sublo = domain->sublo;
subhi = domain->subhi;
double dist[3];
double cuthalf = 0.0;
if (n == 0) cuthalf = 0.5*neighbor->skin; // Only applies to finest grid
dist[0] = dist[1] = dist[2] = cuthalf;
int nlo,nhi;
nlo = static_cast<int> ((sublo[0]-dist[0]-boxlo[0]) *
nx_msm[n]/xprd + OFFSET) - OFFSET;
nhi = static_cast<int> ((subhi[0]+dist[0]-boxlo[0]) *
nx_msm[n]/xprd + OFFSET) - OFFSET;
nxlo_out[n] = nlo + MIN(-order,nxlo_direct);
nxhi_out[n] = nhi + MAX(order,nxhi_direct);
nlo = static_cast<int> ((sublo[1]-dist[1]-boxlo[1]) *
ny_msm[n]/yprd + OFFSET) - OFFSET;
nhi = static_cast<int> ((subhi[1]+dist[1]-boxlo[1]) *
ny_msm[n]/yprd + OFFSET) - OFFSET;
nylo_out[n] = nlo + MIN(-order,nylo_direct);
nyhi_out[n] = nhi + MAX(order,nyhi_direct);
nlo = static_cast<int> ((sublo[2]-dist[2]-boxlo[2]) *
nz_msm[n]/zprd + OFFSET) - OFFSET;
nhi = static_cast<int> ((subhi[2]+dist[2]-boxlo[2]) *
nz_msm[n]/zprd + OFFSET) - OFFSET;
nzlo_out[n] = nlo + MIN(-order,nzlo_direct);
nzhi_out[n] = nhi + MAX(order,nzhi_direct);
// Add extra grid points for nonperiodic boundary conditions
if (domain->nonperiodic) {
if (!domain->xperiodic) {
if (nxlo_in[n] == 0)
nxlo_in[n] = alpha[n];
nxlo_out[n] = MAX(nxlo_out[n],alpha[n]);
if (nxhi_in[n] == nx_msm[n] - 1)
nxhi_in[n] = betax[n];
nxhi_out[n] = MIN(nxhi_out[n],betax[n]);
if (nxhi_in[n] < 0)
nxhi_in[n] = alpha[n] - 1;
}
if (!domain->yperiodic) {
if (nylo_in[n] == 0)
nylo_in[n] = alpha[n];
nylo_out[n] = MAX(nylo_out[n],alpha[n]);
if (nyhi_in[n] == ny_msm[n] - 1)
nyhi_in[n] = betay[n];
nyhi_out[n] = MIN(nyhi_out[n],betay[n]);
if (nyhi_in[n] < 0)
nyhi_in[n] = alpha[n] - 1;
}
if (!domain->zperiodic) {
if (nzlo_in[n] == 0)
nzlo_in[n] = alpha[n];
nzlo_out[n] = MAX(nzlo_out[n],alpha[n]);
if (nzhi_in[n] == nz_msm[n] - 1)
nzhi_in[n] = betaz[n];
nzhi_out[n] = MIN(nzhi_out[n],betaz[n]);
if (nzhi_in[n] < 0)
nzhi_in[n] = alpha[n] - 1;
}
}
// MSM grids for this proc, including ghosts
ngrid[n] = (nxhi_out[n]-nxlo_out[n]+1) * (nyhi_out[n]-nylo_out[n]+1) *
(nzhi_out[n]-nzlo_out[n]+1);
}
}
/* ----------------------------------------------------------------------
reset local grid arrays and communication stencils
called by fix balance b/c it changed sizes of processor sub-domains
------------------------------------------------------------------------- */
void MSM::setup_grid()
{
// free all arrays previously allocated
// pre-compute volume-dependent coeffs
// reset portion of global grid that each proc owns
// reallocate MSM long-range dependent memory
// don't invoke allocate_peratom(), compute() will allocate when needed
setup();
}
/* ----------------------------------------------------------------------
check if all factors of n are in list of factors
return 1 if yes, 0 if no
------------------------------------------------------------------------- */
int MSM::factorable(int n, int &flag, int &levels)
{
int i,norig;
norig = n;
levels = 1;
while (n > 1) {
for (i = 0; i < nfactors; i++) {
if (n % factors[i] == 0) {
n /= factors[i];
levels++;
break;
}
}
if (i == nfactors) {
flag = 1;
return 0;
}
}
return 1;
}
/* ----------------------------------------------------------------------
find center grid pt for each of my particles
check that full stencil for the particle will fit in my 3d brick
store central grid pt indices in part2grid array
------------------------------------------------------------------------- */
void MSM::particle_map()
{
int nx,ny,nz;
double **x = atom->x;
int nlocal = atom->nlocal;
int flag = 0;
for (int i = 0; i < nlocal; i++) {
// (nx,ny,nz) = global coords of grid pt to "lower left" of charge
// current particle coord can be outside global and local box
// add/subtract OFFSET to avoid int(-0.75) = 0 when want it to be -1
nx = static_cast<int> ((x[i][0]-boxlo[0])*delxinv[0]+OFFSET) - OFFSET;
ny = static_cast<int> ((x[i][1]-boxlo[1])*delyinv[0]+OFFSET) - OFFSET;
nz = static_cast<int> ((x[i][2]-boxlo[2])*delzinv[0]+OFFSET) - OFFSET;
part2grid[i][0] = nx;
part2grid[i][1] = ny;
part2grid[i][2] = nz;
// check that entire stencil around nx,ny,nz will fit in my 3d brick
if (nx+nlower < nxlo_out[0] || nx+nupper > nxhi_out[0] ||
ny+nlower < nylo_out[0] || ny+nupper > nyhi_out[0] ||
nz+nlower < nzlo_out[0] || nz+nupper > nzhi_out[0]) flag = 1;
}
if (flag) error->one(FLERR,"Out of range atoms - cannot compute MSM");
}
/* ----------------------------------------------------------------------
create discretized "density" on section of global grid due to my particles
density(x,y,z) = charge "density" at grid points of my 3d brick
(nxlo:nxhi,nylo:nyhi,nzlo:nzhi) is extent of my brick (including ghosts)
in global grid
------------------------------------------------------------------------- */
void MSM::make_rho()
{
//fprintf(screen,"MSM aninterpolation\n\n");
int i,l,m,n,nn,nx,ny,nz,mx,my,mz;
double dx,dy,dz,x0,y0,z0;
// clear 3d density array
double ***qgridn = qgrid[0];
memset(&(qgridn[nzlo_out[0]][nylo_out[0]][nxlo_out[0]]),0,ngrid[0]*sizeof(double));
// loop over my charges, add their contribution to nearby grid points
// (nx,ny,nz) = global coords of grid pt to "lower left" of charge
// (dx,dy,dz) = distance to "lower left" grid pt
// (mx,my,mz) = global coords of moving stencil pt
double *q = atom->q;
double **x = atom->x;
int nlocal = atom->nlocal;
for (i = 0; i < nlocal; i++) {
nx = part2grid[i][0];
ny = part2grid[i][1];
nz = part2grid[i][2];
dx = nx - (x[i][0]-boxlo[0])*delxinv[0];
dy = ny - (x[i][1]-boxlo[1])*delyinv[0];
dz = nz - (x[i][2]-boxlo[2])*delzinv[0];
compute_phis_and_dphis(dx,dy,dz);
z0 = q[i];
for (n = nlower; n <= nupper; n++) {
mz = n+nz;
y0 = z0*phi1d[2][n];
for (m = nlower; m <= nupper; m++) {
my = m+ny;
x0 = y0*phi1d[1][m];
for (l = nlower; l <= nupper; l++) {
mx = l+nx;
qgridn[mz][my][mx] += x0*phi1d[0][l];
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM direct part procedure for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::direct(int n)
{
//fprintf(screen,"Direct contribution on level %i\n\n",n);
double ***egridn = egrid[n];
double ***qgridn = qgrid[n];
// zero out electric potential
memset(&(egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
int icx,icy,icz,ix,iy,iz,zk,zyk,k;
int jj,kk;
int imin,imax,jmin,jmax,kmin,kmax;
double qtmp;
double esum,v0sum,v1sum,v2sum,v3sum,v4sum,v5sum;
int nx = nxhi_direct - nxlo_direct + 1;
int ny = nyhi_direct - nylo_direct + 1;
int nz = nzhi_direct - nzlo_direct + 1;
for (icz = nzlo_in[n]; icz <= nzhi_in[n]; icz++) {
if (domain->zperiodic) {
kmin = nzlo_direct;
kmax = nzhi_direct;
} else {
kmin = MAX(nzlo_direct,alpha[n] - icz);
kmax = MIN(nzhi_direct,betaz[n] - icz);
}
for (icy = nylo_in[n]; icy <= nyhi_in[n]; icy++) {
if (domain->yperiodic) {
jmin = nylo_direct;
jmax = nyhi_direct;
} else {
jmin = MAX(nylo_direct,alpha[n] - icy);
jmax = MIN(nyhi_direct,betay[n] - icy);
}
for (icx = nxlo_in[n]; icx <= nxhi_in[n]; icx++) {
if (domain->xperiodic) {
imin = nxlo_direct;
imax = nxhi_direct;
} else {
imin = MAX(nxlo_direct,alpha[n] - icx);
imax = MIN(nxhi_direct,betax[n] - icx);
}
if (evflag) {
esum = 0.0;
v0sum = v1sum = v2sum = 0.0;
v3sum = v4sum = v5sum = 0.0;
}
for (iz = kmin; iz <= kmax; iz++) {
kk = icz+iz;
zk = (iz + nzhi_direct)*ny;
for (iy = jmin; iy <= jmax; iy++) {
jj = icy+iy;
zyk = (zk + iy + nyhi_direct)*nx;
for (ix = imin; ix <= imax; ix++) {
qtmp = qgridn[kk][jj][icx+ix];
k = zyk + ix + nxhi_direct;
egridn[icz][icy][icx] += g_direct[n][k] * qtmp;
if (evflag) {
if (eflag_global) esum += g_direct[n][k] * qtmp;
if (vflag_global) {
v0sum += v0_direct[n][k] * qtmp;
v1sum += v1_direct[n][k] * qtmp;
v2sum += v2_direct[n][k] * qtmp;
v3sum += v3_direct[n][k] * qtmp;
v4sum += v4_direct[n][k] * qtmp;
v5sum += v5_direct[n][k] * qtmp;
}
}
}
}
}
if (evflag) {
qtmp = qgridn[icz][icy][icx];
if (eflag_global) energy += esum * qtmp;
if (vflag_global) {
virial[0] += v0sum * qtmp;
virial[1] += v1sum * qtmp;
virial[2] += v2sum * qtmp;
virial[3] += v3sum * qtmp;
virial[4] += v4sum * qtmp;
virial[5] += v5sum * qtmp;
}
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM direct part procedure for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::direct_peratom(int n)
{
double ***qgridn = qgrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
// zero out virial
if (vflag_atom) {
memset(&(v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
}
int icx,icy,icz,ix,iy,iz,zk,zyk,k;
int jj,kk;
int imin,imax,jmin,jmax,kmin,kmax;
double qtmp;
int nx = nxhi_direct - nxlo_direct + 1;
int ny = nyhi_direct - nylo_direct + 1;
int nz = nzhi_direct - nzlo_direct + 1;
for (icz = nzlo_in[n]; icz <= nzhi_in[n]; icz++) {
if (domain->zperiodic) {
kmin = nzlo_direct;
kmax = nzhi_direct;
} else {
kmin = MAX(nzlo_direct,alpha[n] - icz);
kmax = MIN(nzhi_direct,betaz[n] - icz);
}
for (icy = nylo_in[n]; icy <= nyhi_in[n]; icy++) {
if (domain->yperiodic) {
jmin = nylo_direct;
jmax = nyhi_direct;
} else {
jmin = MAX(nylo_direct,alpha[n] - icy);
jmax = MIN(nyhi_direct,betay[n] - icy);
}
for (icx = nxlo_in[n]; icx <= nxhi_in[n]; icx++) {
if (domain->xperiodic) {
imin = nxlo_direct;
imax = nxhi_direct;
} else {
imin = MAX(nxlo_direct,alpha[n] - icx);
imax = MIN(nxhi_direct,betax[n] - icx);
}
for (iz = kmin; iz <= kmax; iz++) {
kk = icz+iz;
zk = (iz + nzhi_direct)*ny;
for (iy = jmin; iy <= jmax; iy++) {
jj = icy+iy;
zyk = (zk + iy + nyhi_direct)*nx;
for (ix = imin; ix <= imax; ix++) {
qtmp = qgridn[kk][jj][icx+ix];
k = zyk + ix + nxhi_direct;
v0gridn[icz][icy][icx] += v0_direct[n][k] * qtmp;
v1gridn[icz][icy][icx] += v1_direct[n][k] * qtmp;
v2gridn[icz][icy][icx] += v2_direct[n][k] * qtmp;
v3gridn[icz][icy][icx] += v3_direct[n][k] * qtmp;
v4gridn[icz][icy][icx] += v4_direct[n][k] * qtmp;
v5gridn[icz][icy][icx] += v5_direct[n][k] * qtmp;
}
}
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM direct part procedure for top grid level
------------------------------------------------------------------------- */
void MSM::direct_top(int n)
{
//fprintf(screen,"Direct contribution on level %i\n\n",n);
double ***egridn = egrid[n];
double ***qgridn = qgrid[n];
// zero out electric potential
memset(&(egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
if (!domain->nonperiodic) return; // omit top grid level for periodic systems
int icx,icy,icz,ix,iy,iz,zk,zyk,k;
int jj,kk;
int imin,imax,jmin,jmax,kmin,kmax;
double qtmp;
double esum,v0sum,v1sum,v2sum,v3sum,v4sum,v5sum;
int nx_top = betax[n] - alpha[n];
int ny_top = betay[n] - alpha[n];
int nz_top = betaz[n] - alpha[n];
int nx = 2*nx_top + 1;
int ny = 2*ny_top + 1;
int nz = 2*nz_top + 1;
for (icz = nzlo_in[n]; icz <= nzhi_in[n]; icz++) {
kmin = alpha[n] - icz;
kmax = betaz[n] - icz;
for (icy = nylo_in[n]; icy <= nyhi_in[n]; icy++) {
jmin = alpha[n] - icy;
jmax = betay[n] - icy;
for (icx = nxlo_in[n]; icx <= nxhi_in[n]; icx++) {
imin = alpha[n] - icx;
imax = betax[n] - icx;
if (evflag) {
esum = 0.0;
v0sum = v1sum = v2sum = 0.0;
v3sum = v4sum = v5sum = 0.0;
}
for (iz = kmin; iz <= kmax; iz++) {
kk = icz+iz;
zk = (iz + nz_top)*ny;
for (iy = jmin; iy <= jmax; iy++) {
jj = icy+iy;
zyk = (zk + iy + ny_top)*nx;
for (ix = imin; ix <= imax; ix++) {
qtmp = qgridn[kk][jj][icx+ix];
k = zyk + ix + nx_top;
qtmp = qgridn[kk][jj][icx+ix];
egridn[icz][icy][icx] += g_direct_top[k] * qtmp;
if (evflag) {
if (eflag_global) esum += g_direct_top[k] * qtmp;
if (vflag_global) {
v0sum += v0_direct_top[k] * qtmp;
v1sum += v1_direct_top[k] * qtmp;
v2sum += v2_direct_top[k] * qtmp;
v3sum += v3_direct_top[k] * qtmp;
v4sum += v4_direct_top[k] * qtmp;
v5sum += v5_direct_top[k] * qtmp;
}
}
}
}
}
if (evflag) {
qtmp = qgridn[icz][icy][icx];
if (eflag_global) energy += esum * qtmp;
if (vflag_global) {
virial[0] += v0sum * qtmp;
virial[1] += v1sum * qtmp;
virial[2] += v2sum * qtmp;
virial[3] += v3sum * qtmp;
virial[4] += v4sum * qtmp;
virial[5] += v5sum * qtmp;
}
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM direct part procedure for top grid level
------------------------------------------------------------------------- */
void MSM::direct_peratom_top(int n)
{
//fprintf(screen,"Direct contribution on level %i\n\n",n);
double ***qgridn = qgrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
// zero out virial
if (vflag_atom) {
memset(&(v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
memset(&(v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]]),0,ngrid[n]*sizeof(double));
}
if (!domain->nonperiodic) return; // omit top grid level for periodic systems
int icx,icy,icz,ix,iy,iz,zk,zyk,k;
int jj,kk;
int imin,imax,jmin,jmax,kmin,kmax;
double qtmp;
int nx_top = betax[n] - alpha[n];
int ny_top = betay[n] - alpha[n];
int nz_top = betaz[n] - alpha[n];
int nx = 2*nx_top + 1;
int ny = 2*ny_top + 1;
int nz = 2*nz_top + 1;
for (icz = nzlo_in[n]; icz <= nzhi_in[n]; icz++) {
kmin = alpha[n] - icz;
kmax = betaz[n] - icz;
for (icy = nylo_in[n]; icy <= nyhi_in[n]; icy++) {
jmin = alpha[n] - icy;
jmax = betay[n] - icy;
for (icx = nxlo_in[n]; icx <= nxhi_in[n]; icx++) {
imin = alpha[n] - icx;
imax = betax[n] - icx;
for (iz = kmin; iz <= kmax; iz++) {
kk = icz+iz;
zk = (iz + nz_top)*ny;
for (iy = jmin; iy <= jmax; iy++) {
jj = icy+iy;
zyk = (zk + iy + ny_top)*nx;
for (ix = imin; ix <= imax; ix++) {
qtmp = qgridn[kk][jj][icx+ix];
k = zyk + ix + nx_top;
qtmp = qgridn[kk][jj][icx+ix];
v0gridn[icz][icy][icx] += v0_direct_top[k] * qtmp;
v1gridn[icz][icy][icx] += v1_direct_top[k] * qtmp;
v2gridn[icz][icy][icx] += v2_direct_top[k] * qtmp;
v3gridn[icz][icy][icx] += v3_direct_top[k] * qtmp;
v4gridn[icz][icy][icx] += v4_direct_top[k] * qtmp;
v5gridn[icz][icy][icx] += v5_direct_top[k] * qtmp;
}
}
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM restriction procedure for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::restriction(int n)
{
//fprintf(screen,"Restricting from level %i to %i\n\n",n,n+1);
int p = order-1;
double ***qgrid1 = qgrid[n];
double ***qgrid2 = qgrid[n+1];
//restrict grid (going from grid n to grid n+1, i.e. to a coarser grid)
int k = 0;
int index[p+1];
for (int nu=-p; nu<=p; nu++) {
if (nu%2 == 0 && nu != 0) continue;
phi1d[0][k] = compute_phi(nu*delxinv[n+1]/delxinv[n]);
phi1d[1][k] = compute_phi(nu*delyinv[n+1]/delyinv[n]);
phi1d[2][k] = compute_phi(nu*delzinv[n+1]/delzinv[n]);
index[k] = nu;
k++;
}
int ip,jp,kp,ic,jc,kc,i,j;
int ii,jj,kk;
double phiz,phizy;
// zero out charge on coarser grid
memset(&(qgrid2[nzlo_out[n+1]][nylo_out[n+1]][nxlo_out[n+1]]),0,ngrid[n+1]*sizeof(double));
for (kp = nzlo_in[n+1]; kp <= nzhi_in[n+1]; kp++)
for (jp = nylo_in[n+1]; jp <= nyhi_in[n+1]; jp++)
for (ip = nxlo_in[n+1]; ip <= nxhi_in[n+1]; ip++) {
ic = ip * static_cast<int> (delxinv[n]/delxinv[n+1]);
jc = jp * static_cast<int> (delyinv[n]/delyinv[n+1]);
kc = kp * static_cast<int> (delzinv[n]/delzinv[n+1]);
for (k=0; k<=p+1; k++) {
kk = kc+index[k];
if (!domain->zperiodic) {
if (kk < alpha[n]) continue;
if (kk > betaz[n]) break;
}
phiz = phi1d[2][k];
for (j=0; j<=p+1; j++) {
jj = jc+index[j];
if (!domain->yperiodic) {
if (jj < alpha[n]) continue;
if (jj > betay[n]) break;
}
phizy = phi1d[1][j]*phiz;
for (i=0; i<=p+1; i++) {
ii = ic+index[i];
if (!domain->xperiodic) {
if (ii < alpha[n]) continue;
if (ii > betax[n]) break;
}
qgrid2[kp][jp][ip] += qgrid1[kk][jj][ii] *
phi1d[0][i]*phizy;
}
}
}
}
}
/* ----------------------------------------------------------------------
MSM prolongation procedure for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::prolongation(int n)
{
//fprintf(screen,"Prolongating from level %i to %i\n\n",n+1,n);
int p = order-1;
double ***egrid1 = egrid[n];
double ***egrid2 = egrid[n+1];
double ***v0grid1 = v0grid[n];
double ***v0grid2 = v0grid[n+1];
double ***v1grid1 = v1grid[n];
double ***v1grid2 = v1grid[n+1];
double ***v2grid1 = v2grid[n];
double ***v2grid2 = v2grid[n+1];
double ***v3grid1 = v3grid[n];
double ***v3grid2 = v3grid[n+1];
double ***v4grid1 = v4grid[n];
double ***v4grid2 = v4grid[n+1];
double ***v5grid1 = v5grid[n];
double ***v5grid2 = v5grid[n+1];
//prolongate grid (going from grid n to grid n-1, i.e. to a finer grid)
int k = 0;
int index[p+1];
for (int nu=-p; nu<=p; nu++) {
if (nu%2 == 0 && nu != 0) continue;
phi1d[0][k] = compute_phi(nu*delxinv[n+1]/delxinv[n]);
phi1d[1][k] = compute_phi(nu*delyinv[n+1]/delyinv[n]);
phi1d[2][k] = compute_phi(nu*delzinv[n+1]/delzinv[n]);
index[k] = nu;
k++;
}
int ip,jp,kp,ic,jc,kc,i,j;
int ii,jj,kk;
double phiz,phizy,phi3d;
for (kp = nzlo_in[n+1]; kp <= nzhi_in[n+1]; kp++)
for (jp = nylo_in[n+1]; jp <= nyhi_in[n+1]; jp++)
for (ip = nxlo_in[n+1]; ip <= nxhi_in[n+1]; ip++) {
ic = ip * static_cast<int> (delxinv[n]/delxinv[n+1]);
jc = jp * static_cast<int> (delyinv[n]/delyinv[n+1]);
kc = kp * static_cast<int> (delzinv[n]/delzinv[n+1]);
for (k=0; k<=p+1; k++) {
kk = kc+index[k];
if (!domain->zperiodic) {
if (kk < alpha[n]) continue;
if (kk > betaz[n]) break;
}
phiz = phi1d[2][k];
for (j=0; j<=p+1; j++) {
jj = jc+index[j];
if (!domain->yperiodic) {
if (jj < alpha[n]) continue;
if (jj > betay[n]) break;
}
phizy = phi1d[1][j]*phiz;
for (i=0; i<=p+1; i++) {
ii = ic+index[i];
if (!domain->xperiodic) {
if (ii < alpha[n]) continue;
if (ii > betax[n]) break;
}
phi3d = phi1d[0][i]*phizy;
egrid1[kk][jj][ii] += egrid2[kp][jp][ip] * phi3d;
if (vflag_atom) {
v0grid1[kk][jj][ii] += v0grid2[kp][jp][ip] * phi3d;
v1grid1[kk][jj][ii] += v1grid2[kp][jp][ip] * phi3d;
v2grid1[kk][jj][ii] += v2grid2[kp][jp][ip] * phi3d;
v3grid1[kk][jj][ii] += v3grid2[kp][jp][ip] * phi3d;
v4grid1[kk][jj][ii] += v4grid2[kp][jp][ip] * phi3d;
v5grid1[kk][jj][ii] += v5grid2[kp][jp][ip] * phi3d;
}
}
}
}
}
}
/* ----------------------------------------------------------------------
pack own values to buf to send to another proc
------------------------------------------------------------------------- */
void MSM::pack_forward(int flag, double *buf, int nlist, int *list)
{
int n = current_level;
double ***qgridn = qgrid[n];
double ***egridn = egrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
int k = 0;
if (flag == FORWARD_RHO) {
double *qsrc = &qgridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
buf[k++] = qsrc[list[i]];
}
} else if (flag == FORWARD_AD) {
double *src = &egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++)
buf[i] = src[list[i]];
} else if (flag == FORWARD_AD_PERATOM) {
double *v0src = &v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v1src = &v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v2src = &v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v3src = &v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v4src = &v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v5src = &v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
buf[k++] = v0src[list[i]];
buf[k++] = v1src[list[i]];
buf[k++] = v2src[list[i]];
buf[k++] = v3src[list[i]];
buf[k++] = v4src[list[i]];
buf[k++] = v5src[list[i]];
}
}
}
/* ----------------------------------------------------------------------
unpack another proc's own values from buf and set own ghost values
------------------------------------------------------------------------- */
void MSM::unpack_forward(int flag, double *buf, int nlist, int *list)
{
int n = current_level;
double ***qgridn = qgrid[n];
double ***egridn = egrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
int k = 0;
if (flag == FORWARD_RHO) {
double *dest = &qgridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
dest[list[i]] = buf[k++];
}
} else if (flag == FORWARD_AD) {
double *dest = &egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++)
dest[list[i]] = buf[k++];
} else if (flag == FORWARD_AD_PERATOM) {
double *v0src = &v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v1src = &v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v2src = &v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v3src = &v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v4src = &v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v5src = &v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
v0src[list[i]] = buf[k++];
v1src[list[i]] = buf[k++];
v2src[list[i]] = buf[k++];
v3src[list[i]] = buf[k++];
v4src[list[i]] = buf[k++];
v5src[list[i]] = buf[k++];
}
}
}
/* ----------------------------------------------------------------------
pack ghost values into buf to send to another proc
------------------------------------------------------------------------- */
void MSM::pack_reverse(int flag, double *buf, int nlist, int *list)
{
int n = current_level;
double ***qgridn = qgrid[n];
double ***egridn = egrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
int k = 0;
if (flag == REVERSE_RHO) {
double *qsrc = &qgridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
buf[k++] = qsrc[list[i]];
}
} else if (flag == REVERSE_AD) {
double *src = &egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++)
buf[i] = src[list[i]];
} else if (flag == REVERSE_AD_PERATOM) {
double *v0src = &v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v1src = &v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v2src = &v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v3src = &v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v4src = &v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v5src = &v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
buf[k++] = v0src[list[i]];
buf[k++] = v1src[list[i]];
buf[k++] = v2src[list[i]];
buf[k++] = v3src[list[i]];
buf[k++] = v4src[list[i]];
buf[k++] = v5src[list[i]];
}
}
}
/* ----------------------------------------------------------------------
unpack another proc's ghost values from buf and add to own values
------------------------------------------------------------------------- */
void MSM::unpack_reverse(int flag, double *buf, int nlist, int *list)
{
int n = current_level;
double ***qgridn = qgrid[n];
double ***egridn = egrid[n];
double ***v0gridn = v0grid[n];
double ***v1gridn = v1grid[n];
double ***v2gridn = v2grid[n];
double ***v3gridn = v3grid[n];
double ***v4gridn = v4grid[n];
double ***v5gridn = v5grid[n];
int k = 0;
if (flag == REVERSE_RHO) {
double *dest = &qgridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
dest[list[i]] += buf[k++];
}
} else if (flag == REVERSE_AD) {
double *dest = &egridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++)
dest[list[i]] += buf[k++];
} else if (flag == REVERSE_AD_PERATOM) {
double *v0src = &v0gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v1src = &v1gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v2src = &v2gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v3src = &v3gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v4src = &v4gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
double *v5src = &v5gridn[nzlo_out[n]][nylo_out[n]][nxlo_out[n]];
for (int i = 0; i < nlist; i++) {
v0src[list[i]] += buf[k++];
v1src[list[i]] += buf[k++];
v2src[list[i]] += buf[k++];
v3src[list[i]] += buf[k++];
v4src[list[i]] += buf[k++];
v5src[list[i]] += buf[k++];
}
}
}
/* ----------------------------------------------------------------------
interpolate from grid to get force on my particles
------------------------------------------------------------------------- */
void MSM::fieldforce()
{
//fprintf(screen,"MSM interpolation\n\n");
double ***egridn = egrid[0];
int i,l,m,n,nx,ny,nz,mx,my,mz;
double dx,dy,dz;
double phi_x,phi_y,phi_z;
double dphi_x,dphi_y,dphi_z;
double ekx,eky,ekz;
// loop over my charges, interpolate electric field from nearby grid points
// (nx,ny,nz) = global coords of grid pt to "lower left" of charge
// (dx,dy,dz) = distance to "lower left" grid pt
// (mx,my,mz) = global coords of moving stencil pt
// ek = 3 components of E-field on particle
double *q = atom->q;
double **x = atom->x;
double **f = atom->f;
int nlocal = atom->nlocal;
for (i = 0; i < nlocal; i++) {
nx = part2grid[i][0];
ny = part2grid[i][1];
nz = part2grid[i][2];
dx = nx - (x[i][0]-boxlo[0])*delxinv[0];
dy = ny - (x[i][1]-boxlo[1])*delyinv[0];
dz = nz - (x[i][2]-boxlo[2])*delzinv[0];
compute_phis_and_dphis(dx,dy,dz);
ekx = eky = ekz = 0.0;
for (n = nlower; n <= nupper; n++) {
mz = n+nz;
phi_z = phi1d[2][n];
dphi_z = dphi1d[2][n];
for (m = nlower; m <= nupper; m++) {
my = m+ny;
phi_y = phi1d[1][m];
dphi_y = dphi1d[1][m];
for (l = nlower; l <= nupper; l++) {
mx = l+nx;
phi_x = phi1d[0][l];
dphi_x = dphi1d[0][l];
ekx += dphi_x*phi_y*phi_z*egridn[mz][my][mx];
eky += phi_x*dphi_y*phi_z*egridn[mz][my][mx];
ekz += phi_x*phi_y*dphi_z*egridn[mz][my][mx];
}
}
}
ekx *= delxinv[0];
eky *= delyinv[0];
ekz *= delzinv[0];
// convert E-field to force
const double qfactor = force->qqrd2e*scale*q[i];
f[i][0] += qfactor*ekx;
f[i][1] += qfactor*eky;
f[i][2] += qfactor*ekz;
}
}
/* ----------------------------------------------------------------------
interpolate from grid to get per-atom energy/virial
------------------------------------------------------------------------- */
void MSM::fieldforce_peratom()
{
int i,l,m,n,nx,ny,nz,mx,my,mz;
double dx,dy,dz,x0,y0,z0;
double u,v0,v1,v2,v3,v4,v5;
double ***egridn = egrid[0];
double ***v0gridn = v0grid[0];
double ***v1gridn = v1grid[0];
double ***v2gridn = v2grid[0];
double ***v3gridn = v3grid[0];
double ***v4gridn = v4grid[0];
double ***v5gridn = v5grid[0];
// loop over my charges, interpolate from nearby grid points
// (nx,ny,nz) = global coords of grid pt to "lower left" of charge
// (dx,dy,dz) = distance to "lower left" grid pt
// (mx,my,mz) = global coords of moving stencil pt
double *q = atom->q;
double **x = atom->x;
int nlocal = atom->nlocal;
for (i = 0; i < nlocal; i++) {
nx = part2grid[i][0];
ny = part2grid[i][1];
nz = part2grid[i][2];
dx = nx - (x[i][0]-boxlo[0])*delxinv[0];
dy = ny - (x[i][1]-boxlo[1])*delyinv[0];
dz = nz - (x[i][2]-boxlo[2])*delzinv[0];
compute_phis_and_dphis(dx,dy,dz);
u = v0 = v1 = v2 = v3 = v4 = v5 = 0.0;
for (n = nlower; n <= nupper; n++) {
mz = n+nz;
z0 = phi1d[2][n];
for (m = nlower; m <= nupper; m++) {
my = m+ny;
y0 = z0*phi1d[1][m];
for (l = nlower; l <= nupper; l++) {
mx = l+nx;
x0 = y0*phi1d[0][l];
if (eflag_atom) u += x0*egridn[mz][my][mx];
if (vflag_atom) {
v0 += x0*v0gridn[mz][my][mx];
v1 += x0*v1gridn[mz][my][mx];
v2 += x0*v2gridn[mz][my][mx];
v3 += x0*v3gridn[mz][my][mx];
v4 += x0*v4gridn[mz][my][mx];
v5 += x0*v5gridn[mz][my][mx];
}
}
}
}
if (eflag_atom) eatom[i] += q[i]*u;
if (vflag_atom) {
vatom[i][0] += q[i]*v0;
vatom[i][1] += q[i]*v1;
vatom[i][2] += q[i]*v2;
vatom[i][3] += q[i]*v3;
vatom[i][4] += q[i]*v4;
vatom[i][5] += q[i]*v5;
}
}
}
/* ----------------------------------------------------------------------
charge assignment into phi1d
------------------------------------------------------------------------- */
void MSM::compute_phis_and_dphis(const double &dx, const double &dy,
const double &dz)
{
double delx,dely,delz;
for (int nu = nlower; nu <= nupper; nu++) {
delx = dx + double(nu);
dely = dy + double(nu);
delz = dz + double(nu);
phi1d[0][nu] = compute_phi(delx);
phi1d[1][nu] = compute_phi(dely);
phi1d[2][nu] = compute_phi(delz);
dphi1d[0][nu] = compute_dphi(delx);
dphi1d[1][nu] = compute_dphi(dely);
dphi1d[2][nu] = compute_dphi(delz);
}
}
/* ----------------------------------------------------------------------
compute phi using interpolating polynomial
see Eq 7 from Parallel Computing 35 (2009) 164–177
and Hardy's thesis
------------------------------------------------------------------------- */
double MSM::compute_phi(const double &xi)
{
double phi;
double abs_xi = fabs(xi);
double xi2 = xi*xi;
if (order == 4) {
if (abs_xi <= 1) {
phi = (1.0 - abs_xi)*(1.0 + abs_xi - 1.5*xi2);
} else if (abs_xi <= 2) {
phi = -0.5*(abs_xi - 1.0)*(2.0 - abs_xi)*(2.0 - abs_xi);
} else {
phi = 0.0;
}
} else if (order == 6) {
if (abs_xi <= 1) {
phi = (1.0 - xi2)*(2.0 - abs_xi)*(6.0 + 3.0*abs_xi -
5.0*xi2)/12.0;
} else if (abs_xi <= 2) {
phi = -(abs_xi - 1.0)*(2.0 - abs_xi)*(3.0 - abs_xi)*
(4.0 + 9.0*abs_xi - 5.0*xi2)/24.0;
} else if (abs_xi <= 3) {
phi = (abs_xi - 1.0)*(abs_xi - 2.0)*(3.0 - abs_xi)*
(3.0 - abs_xi)*(4.0 - abs_xi)/24.0;
} else {
phi = 0.0;
}
} else if (order == 8) {
if (abs_xi <= 1) {
phi = (1.0 - xi2)*(4.0 - xi2)*(3.0 - abs_xi)*
(12.0 + 4.0*abs_xi - 7.0*xi2)/144.0;
} else if (abs_xi <= 2) {
phi = -(xi2 - 1.0)*(2.0 - abs_xi)*(3.0 - abs_xi)*
(4.0 - abs_xi)*(10.0 + 12.0*abs_xi - 7.0*xi2)/240.0;
} else if (abs_xi <= 3) {
phi = (abs_xi - 1.0)*(abs_xi - 2.0)*(3.0 - abs_xi)*(4.0 - abs_xi)*
(5.0 - abs_xi)*(6.0 + 20.0*abs_xi - 7.0*xi2)/720.0;
} else if (abs_xi <= 4) {
phi = -(abs_xi - 1.0)*(abs_xi - 2.0)*(abs_xi - 3.0)*(4.0 - abs_xi)*
(4.0 - abs_xi)*(5.0 - abs_xi)*(6.0 - abs_xi)/720.0;
} else {
phi = 0.0;
}
} else if (order == 10) {
if (abs_xi <= 1) {
phi = (1.0 - xi2)*(4.0 - xi2)*(9.0 - xi2)*
(4.0 - abs_xi)*(20.0 + 5.0*abs_xi - 9.0*xi2)/2880.0;
} else if (abs_xi <= 2) {
phi = -(xi2 - 1.0)*(4.0 - xi2)*(3.0 - abs_xi)*(4.0 - abs_xi)*
(5.0 - abs_xi)*(6.0 + 5.0*abs_xi - 3.0*xi2)/1440.0;
} else if (abs_xi <= 3) {
phi = (xi2 - 1.0)*(abs_xi - 2.0)*(3.0 - abs_xi)*(4.0 - abs_xi)*
(5.0 - abs_xi)*(6.0 - abs_xi)*(14.0 + 25.0*abs_xi - 9.0*xi2)/10080.0;
} else if (abs_xi <= 4) {
phi = -(abs_xi - 1.0)*(abs_xi - 2.0)*(abs_xi - 3.0)*(4.0 - abs_xi)*
(5.0 - abs_xi)*(6.0 - abs_xi)*(7.0 - abs_xi)*
(8.0 + 35.0*abs_xi - 9.0*xi2)/40320.0;
} else if (abs_xi <= 5) {
phi = (abs_xi - 1.0)*(abs_xi - 2.0)*(abs_xi - 3.0)*
(abs_xi - 4.0)*(5.0 - abs_xi)*(5.0 - abs_xi)*(6.0 - abs_xi)*
(7.0 - abs_xi)*(8.0 - abs_xi)/40320.0;
} else {
phi = 0.0;
}
}
return phi;
}
/* ----------------------------------------------------------------------
compute the derivative of phi
phi is an interpolating polynomial
see Eq 7 from Parallel Computing 35 (2009) 164–177
and Hardy's thesis
------------------------------------------------------------------------- */
double MSM::compute_dphi(const double &xi)
{
double dphi;
double abs_xi = fabs(xi);
if (order == 4) {
double xi2 = xi*xi;
double abs_xi2 = abs_xi*abs_xi;
if (abs_xi == 0.0) {
dphi = 0.0;
} else if (abs_xi <= 1) {
dphi = xi*(3*xi2 + 6*abs_xi2 - 10*abs_xi)/2.0/abs_xi;
} else if (abs_xi <= 2) {
dphi = xi*(2 - abs_xi)*(3*abs_xi - 4)/2.0/abs_xi;
} else {
dphi = 0.0;
}
} else if (order == 6) {
double xi2 = xi*xi;
double xi4 = xi2*xi2;
double abs_xi2 = abs_xi*abs_xi;
double abs_xi3 = abs_xi2*abs_xi;
double abs_xi4 = abs_xi2*abs_xi2;
if (abs_xi == 0.0) {
dphi = 0.0;
} else if (abs_xi <= 1) {
dphi = xi*(46*xi2*abs_xi - 20*xi2*abs_xi2 - 5*xi4 + 5*xi2 +
6*abs_xi3 + 10*abs_xi2 - 50*abs_xi)/12.0/abs_xi;
} else if (abs_xi <= 2) {
dphi = xi*(15*xi2*abs_xi2 - 60*xi2*abs_xi + 55*xi2 +
10*abs_xi4 - 96*abs_xi3 + 260*abs_xi2 - 210*abs_xi + 10)/
24.0/abs_xi;
} else if (abs_xi <= 3) {
dphi = -xi*(abs_xi - 3)*(5*abs_xi3 - 37*abs_xi2 +
84*abs_xi - 58)/24.0/abs_xi;
} else {
dphi = 0.0;
}
} else if (order == 8) {
double xi2 = xi*xi;
double xi4 = xi2*xi2;
double xi6 = xi4*xi2;
double abs_xi2 = abs_xi*abs_xi;
double abs_xi3 = abs_xi2*abs_xi;
double abs_xi4 = abs_xi2*abs_xi2;
double abs_xi5 = abs_xi4*abs_xi;
double abs_xi6 = abs_xi5*abs_xi;
if (abs_xi == 0.0) {
dphi = 0.0;
} else if (abs_xi <= 1) {
dphi = xi*(7*xi6 + 42*xi4*abs_xi2 - 134*xi4*abs_xi - 35*xi4 -
16*xi2*abs_xi3 - 140*xi2*abs_xi2 + 604*xi2*abs_xi + 28*xi2 +
40*abs_xi3 + 56*abs_xi2 - 560*abs_xi)/144.0/abs_xi;
} else if (abs_xi <= 2) {
dphi = xi*(126*xi4*abs_xi - 21*xi4*abs_xi2 - 182*xi4 -
28*xi2*abs_xi4 + 300*xi2*abs_xi3 - 1001*xi2*abs_xi2 +
990*xi2*abs_xi + 154*xi2 + 24*abs_xi5 - 182*abs_xi4 +
270*abs_xi3 + 602*abs_xi2 - 1260*abs_xi + 28)/240.0/abs_xi;
} else if (abs_xi <= 3) {
dphi = xi*(35*xi2*abs_xi4 - 420*xi2*abs_xi3 +
1785*xi2*abs_xi2 - 3150*xi2*abs_xi + 1918*xi2 +
14*abs_xi6 - 330*abs_xi5 + 2660*abs_xi4 -
9590*abs_xi3 + 15806*abs_xi2 - 9940*abs_xi + 756)/720.0/abs_xi;
} else if (abs_xi <= 4) {
dphi = -xi*(abs_xi - 4)*(7*abs_xi5 - 122*abs_xi4 +
807*abs_xi3 - 2512*abs_xi2 + 3644*abs_xi - 1944)/720.0/abs_xi;
} else {
dphi = 0.0;
}
} else if (order == 10) {
double xi2 = xi*xi;
double xi4 = xi2*xi2;
double xi6 = xi4*xi2;
double xi8 = xi6*xi2;
double abs_xi2 = abs_xi*abs_xi;
double abs_xi3 = abs_xi2*abs_xi;
double abs_xi4 = abs_xi2*abs_xi2;
double abs_xi5 = abs_xi4*abs_xi;
double abs_xi6 = abs_xi5*abs_xi;
double abs_xi7 = abs_xi6*abs_xi;
double abs_xi8 = abs_xi7*abs_xi;
if (abs_xi == 0.0) {
dphi = 0.0;
} else if (abs_xi <= 1) {
dphi = xi*(298*xi6*abs_xi - 72*xi6*abs_xi2 - 9*xi8 +
126*xi6 + 30*xi4*abs_xi3 + 756*xi4*abs_xi2 - 3644*xi4*abs_xi -
441*xi4 - 280*xi2*abs_xi3 - 1764*xi2*abs_xi2 + 12026*xi2*abs_xi +
324*xi2 + 490*abs_xi3 + 648*abs_xi2 - 10792*abs_xi)/2880.0/abs_xi;
} else if (abs_xi <= 2) {
dphi = xi*(9*xi6*abs_xi2 - 72*xi6*abs_xi + 141*xi6 +
18*xi4*abs_xi4 - 236*xi4*abs_xi3 + 963*xi4*abs_xi2 -
1046*xi4*abs_xi - 687*xi4 - 20*xi2*abs_xi5 + 156*xi2*abs_xi4 +
168*xi2*abs_xi3 - 3522*xi2*abs_xi2 + 6382*xi2*abs_xi + 474*xi2 +
50*abs_xi5 - 516*abs_xi4 + 1262*abs_xi3 + 1596*abs_xi2 -
6344*abs_xi + 72)/1440.0/abs_xi;
} else if (abs_xi <= 3) {
dphi = xi*(720*xi4*abs_xi3 - 45*xi4*abs_xi4 - 4185*xi4*abs_xi2 +
10440*xi4*abs_xi - 9396*xi4 - 36*xi2*abs_xi6 + 870*xi2*abs_xi5 -
7965*xi2*abs_xi4 + 34540*xi2*abs_xi3 - 70389*xi2*abs_xi2 +
51440*xi2*abs_xi + 6012*xi2 + 50*abs_xi7 - 954*abs_xi6 +
6680*abs_xi5 - 19440*abs_xi4 + 11140*abs_xi3 + 49014*abs_xi2 -
69080*abs_xi + 3384)/10080.0/abs_xi;
} else if (abs_xi <= 4) {
dphi = xi*(63*xi2*abs_xi6 - 1512*xi2*abs_xi5 + 14490*xi2*abs_xi4 -
70560*xi2*abs_xi3 + 182763*xi2*abs_xi2 - 236376*xi2*abs_xi +
117612*xi2 + 18*abs_xi8 - 784*abs_xi7 + 12600*abs_xi6 -
101556*abs_xi5 + 451962*abs_xi4 - 1121316*abs_xi3 +
1451628*abs_xi2 - 795368*abs_xi + 71856)/40320.0/abs_xi;
} else if (abs_xi <= 5) {
dphi = -xi*(abs_xi - 5)*(9*abs_xi7 - 283*abs_xi6 +
3667*abs_xi5 - 25261*abs_xi4 + 99340*abs_xi3 -
221416*abs_xi2 + 256552*abs_xi - 117648)/40320.0/abs_xi;
} else {
dphi = 0.0;
}
}
return dphi;
}
/* ----------------------------------------------------------------------
Compute direct interaction for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::get_g_direct()
{
if (g_direct) memory->destroy(g_direct);
memory->create(g_direct,levels,nmax_direct,"msm:g_direct");
double a = cutoff;
int n,zk,zyk,k,ix,iy,iz;
double xdiff,ydiff,zdiff;
double rsq,rho,two_n;
two_n = 1.0;
int nx = nxhi_direct - nxlo_direct + 1;
int ny = nyhi_direct - nylo_direct + 1;
int nz = nzhi_direct - nzlo_direct + 1;
for (n=0; n<levels; n++) {
for (iz = nzlo_direct; iz <= nzhi_direct; iz++) {
zdiff = iz/delzinv[n];
zk = (iz + nzhi_direct)*ny;
for (iy = nylo_direct; iy <= nyhi_direct; iy++) {
ydiff = iy/delyinv[n];
zyk = (zk + iy + nyhi_direct)*nx;
for (ix = nxlo_direct; ix <= nxhi_direct; ix++) {
xdiff = ix/delxinv[n];
rsq = xdiff*xdiff + ydiff*ydiff + zdiff*zdiff;
rho = sqrt(rsq)/(two_n*a);
k = zyk + ix + nxhi_direct;
g_direct[n][k] = gamma(rho)/(two_n*a) - gamma(rho/2.0)/(2.0*two_n*a);
}
}
}
two_n *= 2.0;
}
}
/* ----------------------------------------------------------------------
Compute direct interaction for intermediate grid levels
------------------------------------------------------------------------- */
void MSM::get_virial_direct()
{
if (v0_direct) memory->destroy(v0_direct);
memory->create(v0_direct,levels,nmax_direct,"msm:v0_direct");
if (v1_direct) memory->destroy(v1_direct);
memory->create(v1_direct,levels,nmax_direct,"msm:v1_direct");
if (v2_direct) memory->destroy(v2_direct);
memory->create(v2_direct,levels,nmax_direct,"msm:v2_direct");
if (v3_direct) memory->destroy(v3_direct);
memory->create(v3_direct,levels,nmax_direct,"msm:v3_direct");
if (v4_direct) memory->destroy(v4_direct);
memory->create(v4_direct,levels,nmax_direct,"msm:v4_direct");
if (v5_direct) memory->destroy(v5_direct);
memory->create(v5_direct,levels,nmax_direct,"msm:v5_direct");
double a = cutoff;
double a_sq = cutoff*cutoff;
int n,zk,zyk,k,ix,iy,iz;
double xdiff,ydiff,zdiff;
double rsq,r,rho,two_n,two_nsq,dg;
two_n = 1.0;
int nx = nxhi_direct - nxlo_direct + 1;
int ny = nyhi_direct - nylo_direct + 1;
int nz = nzhi_direct - nzlo_direct + 1;
for (n=0; n<levels; n++) {
two_nsq = two_n * two_n;
for (iz = nzlo_direct; iz <= nzhi_direct; iz++) {
zdiff = iz/delzinv[n];
zk = (iz + nzhi_direct)*ny;
for (iy = nylo_direct; iy <= nyhi_direct; iy++) {
ydiff = iy/delyinv[n];
zyk = (zk + iy + nyhi_direct)*nx;
for (ix = nxlo_direct; ix <= nxhi_direct; ix++) {
xdiff = ix/delxinv[n];
rsq = xdiff*xdiff + ydiff*ydiff + zdiff*zdiff;
k = zyk + ix + nxhi_direct;
r = sqrt(rsq);
if (r == 0) {
v0_direct[n][k] = 0.0;
v1_direct[n][k] = 0.0;
v2_direct[n][k] = 0.0;
v3_direct[n][k] = 0.0;
v4_direct[n][k] = 0.0;
v5_direct[n][k] = 0.0;
} else {
rho = r/(two_n*a);
dg = -(dgamma(rho)/(two_nsq*a_sq) -
dgamma(rho/2.0)/(4.0*two_nsq*a_sq))/r;
v0_direct[n][k] = dg * xdiff * xdiff;
v1_direct[n][k] = dg * ydiff * ydiff;
v2_direct[n][k] = dg * zdiff * zdiff;
v3_direct[n][k] = dg * xdiff * ydiff;
v4_direct[n][k] = dg * xdiff * zdiff;
v5_direct[n][k] = dg * ydiff * zdiff;
}
}
}
}
two_n *= 2.0;
}
}
/* ----------------------------------------------------------------------
Compute direct interaction for top grid level
------------------------------------------------------------------------- */
void MSM::get_g_direct_top(int n)
{
int nx_top = betax[n] - alpha[n];
int ny_top = betay[n] - alpha[n];
int nz_top = betaz[n] - alpha[n];
int nx = 2*nx_top + 1;
int ny = 2*ny_top + 1;
int nz = 2*nz_top + 1;
int nmax_top = 8*(nx+1)*(ny*1)*(nz+1);
if (g_direct_top) memory->destroy(g_direct_top);
memory->create(g_direct_top,nmax_top,"msm:g_direct_top");
double a = cutoff;
int zk,zyk,k,ix,iy,iz;
double xdiff,ydiff,zdiff;
double rsq,rho,two_n;
two_n = pow(2.0,n);
for (iz = -nz_top; iz <= nz_top; iz++) {
zdiff = iz/delzinv[n];
zk = (iz + nz_top)*ny;
for (iy = -ny_top; iy <= ny_top; iy++) {
ydiff = iy/delyinv[n];
zyk = (zk + iy + ny_top)*nx;
for (ix = -nx_top; ix <= nx_top; ix++) {
xdiff = ix/delxinv[n];
rsq = xdiff*xdiff + ydiff*ydiff + zdiff*zdiff;
rho = sqrt(rsq)/(two_n*a);
k = zyk + ix + nx_top;
g_direct_top[k] = gamma(rho)/(two_n*a);
}
}
}
}
/* ----------------------------------------------------------------------
Compute direct interaction for top grid level
------------------------------------------------------------------------- */
void MSM::get_virial_direct_top(int n)
{
int nx_top = betax[n] - alpha[n];
int ny_top = betay[n] - alpha[n];
int nz_top = betaz[n] - alpha[n];
int nx = 2*nx_top + 1;
int ny = 2*ny_top + 1;
int nz = 2*nz_top + 1;
int nmax_top = 8*(nx+1)*(ny*1)*(nz+1);
if (v0_direct_top) memory->destroy(v0_direct_top);
memory->create(v0_direct_top,nmax_top,"msm:v0_direct_top");
if (v1_direct_top) memory->destroy(v1_direct_top);
memory->create(v1_direct_top,nmax_top,"msm:v1_direct_top");
if (v2_direct_top) memory->destroy(v2_direct_top);
memory->create(v2_direct_top,nmax_top,"msm:v2_direct_top");
if (v3_direct_top) memory->destroy(v3_direct_top);
memory->create(v3_direct_top,nmax_top,"msm:v3_direct_top");
if (v4_direct_top) memory->destroy(v4_direct_top);
memory->create(v4_direct_top,nmax_top,"msm:v4_direct_top");
if (v5_direct_top) memory->destroy(v5_direct_top);
memory->create(v5_direct_top,nmax_top,"msm:v5_direct_top");
double a = cutoff;
double a_sq = cutoff*cutoff;
int zk,zyk,k,ix,iy,iz;
double xdiff,ydiff,zdiff;
double rsq,r,rho,two_n,two_nsq,dg;
two_n = pow(2.0,n);
two_nsq = two_n * two_n;
for (iz = -nz_top; iz <= nz_top; iz++) {
zdiff = iz/delzinv[n];
zk = (iz + nz_top)*ny;
for (iy = -ny_top; iy <= ny_top; iy++) {
ydiff = iy/delyinv[n];
zyk = (zk + iy + ny_top)*nx;
for (ix = -nx_top; ix <= nx_top; ix++) {
xdiff = ix/delxinv[n];
rsq = xdiff*xdiff + ydiff*ydiff + zdiff*zdiff;
k = zyk + ix + nx_top;
r = sqrt(rsq);
if (r == 0) {
v0_direct_top[k] = 0.0;
v1_direct_top[k] = 0.0;
v2_direct_top[k] = 0.0;
v3_direct_top[k] = 0.0;
v4_direct_top[k] = 0.0;
v5_direct_top[k] = 0.0;
} else {
rho = r/(two_n*a);
dg = -(dgamma(rho)/(two_nsq*a_sq))/r;
v0_direct_top[k] = dg * xdiff * xdiff;
v1_direct_top[k] = dg * ydiff * ydiff;
v2_direct_top[k] = dg * zdiff * zdiff;
v3_direct_top[k] = dg * xdiff * ydiff;
v4_direct_top[k] = dg * xdiff * zdiff;
v5_direct_top[k] = dg * ydiff * zdiff;
}
}
}
}
}

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