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/**********************************************************************
Poisson.c:
Poisson.c is a subrutine to solve Poisson's equation using
fast Fourier transformation.
Log of Poisson.c:
22/Nov/2001 Released by T.Ozaki
***********************************************************************/
#define measure_time 0
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include "openmx_common.h"
#ifdef nompi
#include "mimic_mpi.h"
#else
#include <mpi.h>
#endif
#include "tran_prototypes.h"
#include "tran_variables.h"
#ifdef fftw2
#include <fftw.h>
#else
#include <fftw3.h>
#endif
/* input: Density_Grid (-ADensity_Grid )
or input: ReV1, ImV1 ( which are FFT of Density_Grid (-ADensity_Grid ) )
work: ReV2, ImV2
output: dVHart_Grid = rho(G)/G^2
fft_charge_flag=1: density_matrix mixing
fft_charge_flag=0: k-transformed Density_Grid mixing
*/
double TRAN_Poisson(
int fft_charge_flag,
double ***ReV1, double ***ImV1,
double ***ReV2, double ***ImV2)
/*#define grid_l_ref(i,j,k) ( (i)*Ngrid2*(l3l[1]-l3l[0]+1)+(j)*(l3l[1]-l3l[0]+1)+(k)-l3l[0] )
*#define grid_r_ref(i,j,k) ( (i)*Ngrid2*(l3r[1]-l3r[0]+1)+(j)*(l3r[1]-l3r[0]+1)+(k)-l3r[0] )
*/
{
static int ct_AN,n1,n2,n3,k1,k2,k3,kk2,N3[4];
static int Cwan,NO0,NO1,Rn,N,Hwan,i,j;
static int nn0,nn1,nnn1,MN,MN0,MN1,MN2;
static double time0;
static int h_AN,Gh_AN,Rnh,spin,Nc,GNc,GN,Nh,Nog;
static double tmp0,tmp1,sk1,sk2,sk3,tot_den;
static double x,y,z,Gx,Gy,Gz,Eden[2],DenA,G2;
static double ReTmp,ImTmp,c_coe,p_coe;
static double *tmp_array0;
static double *tmp_array1;
static double TStime,TEtime;
static int numprocs,myid,tag=999,ID;
/* TRAN extension */
fftw_complex *fftin, *fftout;
fftw_plan p;
int ix0,ixlp1;
int l1l[2], l1r[2];
double *rev, *imv;
MPI_Status stat;
MPI_Request request;
MPI_Comm_size(mpi_comm_level1,&numprocs);
MPI_Comm_rank(mpi_comm_level1,&myid);
if (myid==Host_ID) printf("<TRAN_Poisson> Poisson's equation using FFT...\n");
dtime(&TStime);
#if 0
{
double R[4];
R[1]=0.0; R[2]=0.0; R[3]=0.0;
TRAN_Print_Grid_Cell0("zCharge_Density", Grid_Origin, gtv,
Ngrid1,Ngrid2, 0,Ngrid3-1, R,
My_Cell0,
Density_Grid[0]);
}
{
double R[4];
double *v;
int i;
R[1]=0.0; R[2]=0.0; R[3]=0.0;
v= (double*)malloc(sizeof(double)*Ngrid1*Ngrid2*Ngrid3);
for (i=0;i< Ngrid1*Ngrid2*Ngrid3; i++) {
v[i]= Density_Grid[0][i]+Density_Grid[1][i]-ADensity_Grid[i];
}
TRAN_Print_Grid_Cell0("zCharge_DensitySum", Grid_Origin, gtv,
Ngrid1,Ngrid2, 0,Ngrid3-1, R,
My_Cell0,
v);
free(v);
}
#endif
/****************************************************
FFT of charge density
****************************************************/
if (fft_charge_flag==1) FFT_Density(0,ReV1,ImV1,ReV2,ImV2);
#ifdef DEBUG
/*debug*/
{
char name[100];
sprintf(name,"ReV20.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson, Ngrid3,Start_Grid2[myid], ReV2);
sprintf(name,"ImV20.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson,Ngrid3,Start_Grid2[myid], ImV2);
}
#endif
/****************************************************
4*PI/G2/N^3
****************************************************/
/************************
x -> k, factor=1/N
************************/
tmp0 = 4.0*PI/(double)Ngrid1/(double)Ngrid2/(double)Ngrid3;
for (k2=0; k2<My_NGrid2_Poisson; k2++){
kk2 = k2 + Start_Grid2[myid];
if (kk2<Ngrid2/2) sk2 = (double)kk2;
else sk2 = (double)(kk2 - Ngrid2);
for (k1=0; k1<Ngrid1; k1++){
if (k1<Ngrid1/2) sk1 = (double)k1;
else sk1 = (double)(k1 - Ngrid1);
for (k3=0; k3<Ngrid3; k3++){
if (k3<Ngrid3/2) sk3 = (double)k3;
else sk3 = (double)(k3 - Ngrid3);
Gx = sk1*rtv[1][1] + sk2*rtv[2][1] + sk3*rtv[3][1];
Gy = sk1*rtv[1][2] + sk2*rtv[2][2] + sk3*rtv[3][2];
Gz = sk1*rtv[1][3] + sk2*rtv[2][3] + sk3*rtv[3][3];
G2 = Gx*Gx + Gy*Gy + Gz*Gz;
if (k1==0 && kk2==0 && k3==0){
ReV2[k2][k1][k3] = 0.0;
ImV2[k2][k1][k3] = 0.0;
}
else{
ReV2[k2][k1][k3] = tmp0*ReV2[k2][k1][k3]/G2;
ImV2[k2][k1][k3] = tmp0*ImV2[k2][k1][k3]/G2;
}
}
}
}
/****************************************************
* TRAN extension
****************************************************/
/* now (ReV2,ImV2) = Hartree potential(kx,ky,kz) */
/* factor=1, in kx->x */
#ifdef fftw2
fftin =(fftw_complex*)malloc(sizeof(fftw_complex)*Ngrid1);
fftout=(fftw_complex*)malloc(sizeof(fftw_complex)*Ngrid1);
p = fftw_create_plan(Ngrid1,1,FFTW_ESTIMATE);
#else
fftin =fftw_malloc(sizeof(fftw_complex)*Ngrid1);
fftout=fftw_malloc(sizeof(fftw_complex)*Ngrid1);
p = fftw_plan_dft_1d(Ngrid1,fftin,fftout,1,FFTW_ESTIMATE);
#endif
/*parallel global: k2 0:Ngrid2-1 */
/*parallel local: k2 0:My_NGrid2_Poisson-1 */
/*parallel local_to_global k2 = kk2 + Start_Grid2[myid] */
for (k2=0;k2<My_NGrid2_Poisson ;k2++) {
for (k3=0;k3<Ngrid3;k3++) {
for (k1=0;k1<Ngrid1;k1++) {
#ifdef fftw2
c_re(fftin[k1]) = ReV2[k2][k1][k3];
c_im(fftin[k1]) = ImV2[k2][k1][k3];
#else
fftin[k1][0] = ReV2[k2][k1][k3];
fftin[k1][1] = ImV2[k2][k1][k3];
#endif
}
#ifdef fftw2
fftw_one(p, fftin, fftout);
#else
fftw_execute(p);
#endif
for (k1=0;k1<Ngrid1;k1++) {
#ifdef fftw2
ReV2[k2][k1][k3] = c_re(fftout[k1]);
ImV2[k2][k1][k3] = c_im(fftout[k1]);
#else
ReV2[k2][k1][k3] = fftout[k1][0];
ImV2[k2][k1][k3] = fftout[k1][1];
#endif
}
}
}
fftw_destroy_plan(p);
/* now, (ReV2,ImV2)=Hartree potential(x,ky,kz) */
/* boundary */
l1l[0]=0;
l1l[1]=TRAN_grid_bound[0];
l1r[0]=TRAN_grid_bound[1];
l1r[1]=Ngrid1-1;
ix0 = TRAN_grid_bound[0];
ixlp1 = TRAN_grid_bound[1];
/*
* V_e(x) given
*
* V_c(x) <= solved by rho/ (G^2)
*
* d^2/dx^2 V(x) = rho(x), linear equation
* d^2/dx^2 (VH(x) + dVH(x)) = ( rho(x) + 0 )
*
* d^2/dx^2 VH(x) = rho(x) , solved via FFT
* d^2/dx^2 dVH(x) =0 with boundary condition, V_e(x)-V_c(x) at x=x_0 and x_(l+1)
*
*
* add correction,dVH(x), to the region x=[ix0+1:ixlp1-1]
*/
rev = (double*)malloc(sizeof(double)*Ngrid1);
imv = (double*)malloc(sizeof(double)*Ngrid1);
#define grid_l_ref(i,j,k) ( ((i)-l1l[0])*Ngrid2*Ngrid3 + (j)*Ngrid3+ (k) )
#define grid_r_ref(i,j,k) ( ((i)-l1r[0])*Ngrid2*Ngrid3 + (j)*Ngrid3+ (k) )
/*parallel global: kk2 0:Ngrid2-1 */
/*parallel local: k2 0:My_NGrid2_Poisson-1 */
/*parallel local_to_global kk2 = k2 + Start_Grid2[myid] */
for (k2=0;k2<My_NGrid2_Poisson;k2++) {
kk2 = k2 + Start_Grid2[myid];
for (k3=0;k3<Ngrid3;k3++) {
if (k3==0 && kk2==0) { /* G_para==0 */
for (k1=0;k1<Ngrid1;k1++) { rev[k1]=ReV2[k2][k1][k3]; imv[k1]=ImV2[k2][k1][k3]; }
TRAN_Calc_VHartree_G0(
ElectrodedVHart_Grid_c[0][grid_l_ref(ix0,kk2,k3)], /* (x,ky,kz), left edge */
ElectrodedVHart_Grid_c[1][grid_r_ref(ixlp1,kk2,k3)], /* right edge */
ReV2[k2][ix0][k3], ImV2[k2][ix0][k3], /* x0,ky,kz */
ReV2[k2][ixlp1][k3], ImV2[k2][ixlp1][k3], /* x_(l+1),ky,kz} */
ix0, ixlp1, gtv[1],
rev, imv /* output */
);
for (k1=0;k1<Ngrid1;k1++) { ReV2[k2][k1][k3]=rev[k1]; ImV2[k2][k1][k3]=imv[k1]; }
}
else { /* G_para .ne.0 */
for (k1=0;k1<Ngrid1;k1++) { rev[k1]=ReV2[k2][k1][k3]; imv[k1]=ImV2[k2][k1][k3]; }
TRAN_Calc_VHartree_Gnon0(
kk2,k3, ix0, ixlp1,gtv,
ReV2[k2][ix0][k3],ImV2[k2][ix0][k3], /* x0,ky,kz */
ReV2[k2][ixlp1][k3], ImV2[k2][ixlp1][k3], /* x_(l+1),ky,kz */
ElectrodedVHart_Grid_c[0][grid_l_ref(ix0,kk2,k3)], /* (x,ky,kz) */
ElectrodedVHart_Grid_c[1][grid_r_ref(ixlp1,kk2,k3) ],
rev, imv /* output */
);
for (k1=0;k1<Ngrid1;k1++) { ReV2[k2][k1][k3]=rev[k1]; ImV2[k2][k1][k3]=imv[k1]; }
}
}
}
free(imv);
free(rev);
#ifdef DEBUG
/*debug*/
{
char name[100];
sprintf(name,"ReV2b.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson, Ngrid3,Start_Grid2[myid], ReV2);
sprintf(name,"ImV2b.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson,Ngrid3,Start_Grid2[myid], ImV2);
}
#endif
/* overwrite ElectrodedVHart_Grid_c */
/* (ReV2,ImV2), z=[0:TRAN_grid_bound[0]], [TRAN_grid_bound[1]:Ngrid3-1] <= ElectrodedVHart_Grid_c */
/* global 0:Ngrid2-1 */
/* local 0:My_NGrid2_Poisson-1 */
/* local_to_global k2 = kk2 + Start_Grid2[myid] */
TRAN_Overwrite_V2(Ngrid1,Ngrid2,Ngrid3, TRAN_grid_bound,My_NGrid2_Poisson, Start_Grid2[myid],
ElectrodedVHart_Grid_c,
ReV2, ImV2 ); /* output */
#ifdef DEBUG
/*debug*/
{ char name[100];
sprintf(name,"ReV2c.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson,Ngrid3,Start_Grid2[myid], ReV2);
sprintf(name,"ImV2c.%d",myid);
TRAN_Print_Grid_Startv(name, Ngrid1,My_NGrid2_Poisson,Ngrid3,Start_Grid2[myid], ImV2);
}
#endif
/* now (ReV2, ImV2) is a smooth function */
/* (ReV2,ImV2)=Hartree potential(x,ky,kz) with effects of boundary condition */
{
/* (kx,ky,z) -> (kx,ky,kz) */
#ifdef fftw2
p = fftw_create_plan(Ngrid1, -1, FFTW_ESTIMATE);
#else
p = fftw_plan_dft_1d(Ngrid1,fftin,fftout,-1,FFTW_ESTIMATE);
#endif
tmp0=1.0/(double)Ngrid1;
for (k3=0;k3<Ngrid3;k3++) {
/* global k2 0:Ngrid2-1 */
/* local k2 0:My_NGrid2_Poisson-1 */
/* local_to_global k2 = k2+ Start_Grid2[myid] */
for (k2=0;k2<My_NGrid2_Poisson;k2++) {
for (k1=0;k1<Ngrid1;k1++) {
#ifdef fftw2
c_re(fftin[k1]) = ReV2[k2][k1][k3];
c_im(fftin[k1]) = ImV2[k2][k1][k3];
#else
fftin[k1][0]= ReV2[k2][k1][k3];
fftin[k1][1]= ImV2[k2][k1][k3];
#endif
}
#if 0
{
printf("fftin(%d)->", Ngrid1);
for (k1=0;k1<Ngrid2;k1++) { printf("%lf ",fftin[k1][0]); } printf("\n");
}
#endif
#ifdef fftw2
fftw_one(p, fftin, fftout);
#else
fftw_execute(p);
#endif
#if 0
{
printf("fftout(%d)->", Ngrid1);
for (k1=0;k1<Ngrid2;k1++) { printf("%lf ",fftout[k1][0]); } printf("\n");
}
#endif
for (k1=0;k1<Ngrid1;k1++) {
#ifdef fftw2
ReV2[k2][k1][k3]=c_re(fftout[k1])*tmp0;
ImV2[k2][k1][k3]=c_im(fftout[k1])*tmp0;
#else
ReV2[k2][k1][k3]=fftout[k1][0]*tmp0;
ImV2[k2][k1][k3]=fftout[k1][1]*tmp0;
#endif
}
}
}
fftw_destroy_plan(p);
}
/* (ReV2,ImV2)=Hartree potential(kx,ky,kz) with effects of boundary condition */
#if 0
/*debug*/
{ int i; double R[4]; for (i=1;i<=3;i++) R[i]=0.0;
TRAN_Print_Grid_v("ReV2d", Grid_Origin,gtv, Ngrid1,Ngrid2, 0,Ngrid3-1, R, ReV2);
TRAN_Print_Grid_v("ImV2d", Grid_Origin,gtv, Ngrid1,Ngrid2, 0,Ngrid3-1, R, ImV2);
}
#endif
#ifdef fftw2
free(fftout);
free(fftin);
#else
fftw_free(fftout);
fftw_free(fftin);
#endif
/****************************************************
find the Hartree potential in real space
****************************************************/
Get_Value_inReal(0,ReV2,ImV2,ReV1,ImV1,dVHart_Grid,dVHart_Grid);
#ifdef DEBUG
{
int i; double R[4]; for (i=1;i<=3;i++) R[i]=0.0;
TRAN_Print_Grid_Cell0( "dVHart_Grid", Grid_Origin,gtv, Ngrid1,Ngrid2, 0,Ngrid3-1, R,
My_Cell0, dVHart_Grid);
}
#endif
/* for time */
dtime(&TEtime);
time0 = TEtime - TStime;
return time0;
}
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