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PM.cu
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#define GPU
#include <cstdio>
#include <cstdlib>
#include <cmath>
#ifdef GPU
#include <cufft.h>
#else
#include <fftw3.h>
#endif
#include <ctime>
#include <omp.h>
#include <mpi.h>
//-----------------------------------
// A Partilce Mesh Code
// ----------------------------------
// constants
const double L = 14; // length of the 3-D domain box
#define N 64 // number of grid in each direction
const double dx = L/N; // spatial resolution
const double dt = 12; // time step
#define ParN 600 // number of particles
#define G 8.9045e-10 // gravitational constant
const double end_time = 60000; // end time of the evolution
static double *ParM = NULL; // mass of each particle
const int NThread = 1; // numer of threads
// schemes
const int BC = 2; // boundary condition ( 1=Periodic, 2=Isolated )
const int Scheme_SG = 1; // scheme of self-gravity ( 1=PM, 2=DN )
const int Scheme_MD = 3; // scheme of mass deposition ( 1=NGP, 2=CIC, 3=TSC )
const int Scheme_PS = 1; // scheme of poisson solver ( 1=FFT )
const int Scheme_OI = 3; // scheme of orbit integration ( 1=KDK, 2=DKD, 3=RK4 )
// GPU parallelizaion
#define BLOCK_SIZE 256
#define GRID_SIZE ( (8*N*N*N+BLOCK_SIZE-1)/BLOCK_SIZE )
// FUNCTION Init: Set the initial condition
void Init( double *x, double *v, const int NRank, const int MyRank ){
srand(100*MyRank);
//DATA
//Mass of 8 planets
const double Mass_Sun=333400.0;
const double Mass_Mercury = 0.06;
const double Mass_Venus = 0.82;
const double Mass_Earth = 1.0;
const double Mass_Mars = 0.11;
const double Mass_Jupiter = 317.8*5;
//const double Mass_Saturn = 95.2;
//const double Mass_Uranus = 14.6;
//const double Mass_Neptune = 17.2;
//const double Mass_Ceres = 1.574e-4;//穀神星
//Distance
const double Radius_Mercury = 0.39;
const double Radius_Venus = 0.72;
const double Radius_Earth = 1.0;
const double Radius_Mars = 1.52;
const double Radius_Jupiter = 5.20;
//const double Radius_Saturn = 9.54;
//const double Radius_Uranus = 19.22;
//const double Radius_Neptune = 30.06;
//const double Radius_Ceres = 2.7675;//穀神星
/* To be modified for the test problem */
ParM = new double[ParN];
double *Radius = NULL;
Radius = new double[2];
//Mass of 8 planets
ParM[0] = Mass_Sun;
ParM[1] = Mass_Jupiter;
Radius[0] = 0.0;
Radius[1] = Radius_Jupiter;
if (MyRank==0){
double v_rel = pow(G*Mass_Sun/Radius[1],0.5);
x[0*3+0] = 0.5*L-Radius_Jupiter*(Mass_Jupiter/(Mass_Jupiter+Mass_Sun));
x[0*3+1] = 0.5*L;
x[0*3+2] = 0.5*L;
v[0*3+0] = 0.0;
v[0*3+1] = -v_rel*(Mass_Jupiter/(Mass_Jupiter+Mass_Sun));
v[0*3+2] = 0.0;
//8 Planets' Position and Velocity
//double Planet_phi[10] = {0.0, M_PI,M_PI/6.0, 2.0*M_PI*260.0/360.0 ,2.0*M_PI*120.0/360.0, 2.0*M_PI*260.0/360.0, 2.0*M_PI*290.0/360.0 ,M_PI/6.0,2.0*M_PI*345.0/360.0, 2.0*M_PI*250.0/360.0 };
double Planet_phi[2] = {0.0, 0.0};
for(int i=1;i<2;i++){
x[i*3+0] = 0.5*L + Radius_Jupiter*(Mass_Sun/(Mass_Jupiter+Mass_Sun));
x[i*3+1] = 0.5*L;
x[i*3+2] = 0.5*L;
v[i*3+0] = 0;
v[i*3+1] = v_rel*(Mass_Sun/(Mass_Jupiter+Mass_Sun));
v[i*3+2] = 0.0;
}
//biggest 10 Asteroid's mass
for(int i=2 ;i<12;i++){
ParM[i] = (double)rand()/(RAND_MAX)*2*1.189e-5;
}
// other asteroids' mass
for(int i=12;i<ParN/NRank;i++){
ParM[i] = (double)rand()/(RAND_MAX)*2*(2.763e-4/(ParN-13));
}
//define variable of Asteroid
for(int i=2;i<ParN/NRank;i++){
double Asteroid_Radius = 2.0+rand()/((double)RAND_MAX+1)*(3.5-2.0);
double THETA = M_PI*(10.0/180.0)*(rand()/(double)RAND_MAX+1);
double PHI = 2.0*M_PI*rand()/((double)RAND_MAX+1);
double phi = 2.0*M_PI*rand()/((double)RAND_MAX+1);
//Matrix_change coordinate
double Trans_Matrix[3][3]={0.0};
Trans_Matrix[0][0] = cos(PHI);
Trans_Matrix[0][1] =-sin(PHI)*cos(THETA);
Trans_Matrix[0][2] = sin(PHI)*sin(THETA);
Trans_Matrix[1][0] = sin(PHI);
Trans_Matrix[1][1] = cos(PHI)*cos(THETA);
Trans_Matrix[1][2] =-cos(PHI)*sin(THETA);
Trans_Matrix[2][0] = 0.0;
Trans_Matrix[2][1] = sin(THETA);
Trans_Matrix[2][2] = cos(THETA);
//position in axis's xyz coordinate
double x_count[3] = {Asteroid_Radius*cos(phi), Asteroid_Radius*sin(phi),0.0};
double v_count[3] = {-pow(G*Mass_Sun/Asteroid_Radius,0.5)*sin(phi) , pow(G*Mass_Sun/Asteroid_Radius,0.5)*cos(phi), 0.0};
//position
for(int j=0;j<3;j++){
for(int k=0;k<3;k++){
x[i*3+j]+= Trans_Matrix[j][k] * x_count[k];
v[i*3+j]+= Trans_Matrix[j][k] * v_count[k];
}
x[i*3+j] = x[i*3+j] + x[0*3+j];
v[i*3+j] = v[i*3+j] + v[0*3+j];
}
}
} //if (MyRank==0)
else{
// other asteroids' mass
for(int i=0;i<ParN/NRank;i++){
ParM[i] = (double)rand()/(RAND_MAX)*2*(2.763e-4/(ParN-13));
}
//define variable of Asteroid
for(int i=0;i<ParN/NRank;i++){
double Asteroid_Radius = 2.0+rand()/((double)RAND_MAX+1)*(3.2-2.0);
double THETA = M_PI*(10.0/180.0)*(rand()/(double)RAND_MAX+1);
double PHI = 2.0*M_PI*rand()/((double)RAND_MAX+1);
double phi = 2.0*M_PI*rand()/((double)RAND_MAX+1);
//Matrix_change coordinate
double Trans_Matrix[3][3]={0.0};
Trans_Matrix[0][0] = cos(PHI);
Trans_Matrix[0][1] =-sin(PHI)*cos(THETA);
Trans_Matrix[0][2] = sin(PHI)*sin(THETA);
Trans_Matrix[1][0] = sin(PHI);
Trans_Matrix[1][1] = cos(PHI)*cos(THETA);
Trans_Matrix[1][2] =-cos(PHI)*sin(THETA);
Trans_Matrix[2][0] = 0.0;
Trans_Matrix[2][1] = sin(THETA);
Trans_Matrix[2][2] = cos(THETA);
//position in axis's xyz coordinate
double x_count[3] = {Asteroid_Radius*cos(phi), Asteroid_Radius*sin(phi),0.0};
double v_count[3] = {-pow(G*Mass_Sun/Asteroid_Radius,0.5)*sin(phi) , pow(G*Mass_Sun/Asteroid_Radius,0.5)*cos(phi), 0.0};
//position
for(int j=0;j<3;j++){
for(int k=0;k<3;k++){
x[i*3+j]+= Trans_Matrix[j][k] * x_count[k];
v[i*3+j]+= Trans_Matrix[j][k] * v_count[k];
}
x[i*3+j] = x[i*3+j] + 0.5*L;
}
}
}
return;
}// FUNCTION Init
// FUNCTION timespec diff: Caltulate the time difference
struct timespec diff( struct timespec start, struct timespec end ){
struct timespec temp;
if( (end.tv_nsec-start.tv_nsec)<0 ){
temp.tv_sec = end.tv_sec-start.tv_sec-1;
temp.tv_nsec = 1000000000+end.tv_nsec-start.tv_nsec;
}
else{
temp.tv_sec = end.tv_sec-start.tv_sec;
temp.tv_nsec = end.tv_nsec-start.tv_nsec;
}
return temp;
}// FUNCTION timespec diff
// FUNCTION CheckBoundary: Deal with the particles outside the box
void CheckBoundary( double *x, double *v, const int NRank ){
# pragma omp parallel for num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
if( BC==1 ){ // Periodic Boundary Condition
int offset;
for(int d=0;d<3;d=d+1){
if( x[i*3+d]<0 ){
offset = (-x[i*3+d])/L;
x[i*3+d] += (offset+1)*L;
}
if( x[i*3+d]>L ){
offset = x[i*3+d]/L;
x[i*3+d] -= offset*L;
}
}
}
else if( BC==2 ){ // Isolated Boundary Condition
if( x[i*3+0]<0 || x[i*3+1]<0 || x[i*3+2]<0 || x[i*3+0]>L || x[i*3+1]>L || x[i*3+2]>L ){
x[i*3+0] = 1000*L;
x[i*3+1] = 1000*L;
x[i*3+2] = 1000*L;
v[i*3+0] = 0;
v[i*3+1] = 0;
v[i*3+2] = 0;
}
}
else{
printf("Wrong BC\n");
}
}
return;
}// FUNCTION CheckBoundary
// FUNCTION Index: Convert 3D index in N*N*N box into 1D index
int Index( int i, int j, int k ){
return k+N*(j+N*i);
}// FUNCTION Index
// FUNCTION MassDeposition: Deposit particle mass onto grids
void MassDeposition( double *x, double *rho, const int NRank, const int MyRank ){
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
for(int k=0;k<N;k++){
rho[Index( i, j, k )] = 0.0; // initialization as zero
}}}
if( Scheme_MD==1 ){ // Nearest-Grid-Point
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
if( x[n*3+0]>dx && x[n*3+0]<L-dx && x[n*3+1]>dx && x[n*3+1]<L-dx && x[n*3+2]>dx && x[n*3+2]<L-dx )
# pragma omp critical
rho[Index( (int)(x[n*3+0]/dx), (int)(x[n*3+1]/dx), (int)(x[n*3+2]/dx) )] += ParM[n+MyRank*ParN/NRank]/(dx*dx*dx);
}
}
else if( Scheme_MD==2 ){ // Cloud-In-Cell
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
double weighting[3][2];
if( x[n*3+0]>1.5*dx && x[n*3+0]<L-1.5*dx && x[n*3+1]>1.5*dx && x[n*3+1]<L-1.5*dx && x[n*3+2]>1.5*dx && x[n*3+2]<L-1.5*dx ){
for(int i=0;i<3;i++){ // weighting of distribution
weighting[i][1] = (x[n*3+i]/dx-0.5) - (int)(x[n*3+i]/dx-0.5);
weighting[i][0] = 1 - weighting[i][1];
}
for(int i=0;i<2;i++)
for(int j=0;j<2;j++)
for(int k=0;k<2;k++) // deposit density into 8 cells
# pragma omp critical
rho[Index( (int)(x[n*3+0]/dx-0.5)+i, (int)(x[n*3+1]/dx-0.5)+j, (int)(x[n*3+2]/dx-0.5)+k )] += weighting[0][i]*weighting[1][j]*weighting[2][k]*ParM[n+MyRank*ParN/NRank]/(dx*dx*dx);
}
}
}
else if( Scheme_MD==3 ){ // Triangular-Shaped-Cloud
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
double devide[3];
double weighting[3][3];
if( x[n*3+0]>2.0*dx && x[n*3+0]<L-2.0*dx && x[n*3+1]>2.0*dx && x[n*3+1]<L-2.0*dx && x[n*3+2]>2.0*dx && x[n*3+2]<L-2.0*dx ){
for(int i=0;i<3;i++){ // weighting of distribution
devide[i]= x[n*3+i]/dx - (int)(x[n*3+i]/dx);//find the distance between n grid and center of particle
weighting[i][0] = pow((1.0-devide[i]),2)*0.5;
weighting[i][1] = 0.5*(1.0 + 2.0*devide[i]-2.0*pow(devide[i],2));
weighting[i][2] = pow(devide[i],2)*0.5;
}
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
for(int k=0;k<3;k++) // deposit density into 27 cells
# pragma omp critical
rho[Index( (int)(x[n*3+0]/dx-1.0)+i, (int)(x[n*3+1]/dx-1.0)+j, (int)(x[n*3+2]/dx-1.0)+k )] += weighting[0][i]*weighting[1][j]*weighting[2][k]*ParM[n+MyRank*ParN/NRank]/(dx*dx*dx);
}
}
}
return;
}// FUNCTION MassDeposition
#ifdef GPU
// KERNEL PoissonEquationInK_PerBC_GPU: Calculate phi(k) in K-space for periodic BC by GPU
__global__
void PoissonEquationInK_PerBC_GPU( const cufftDoubleComplex *g_rho_K, cufftDoubleComplex *g_phi_K ){
const uint i = blockDim.x*blockIdx.x + threadIdx.x;
if( i==0 ){
g_phi_K[i].x = 0.0; // set DC to 0
g_phi_K[i].y = 0.0; // set DC to 0
}
else if( i<N*N*(N/2+1) ){
int nx = (i/(N/2+1))/N - (((i/(N/2+1))/N)/(N/2))*N;
int ny = (i/(N/2+1))%N - (((i/(N/2+1))%N)/(N/2))*N;
int nz = i%(N/2+1);
double KK = (nx*2*M_PI/L)*(nx*2*M_PI/L) + (ny*2*M_PI/L)*(ny*2*M_PI/L) + (nz*2*M_PI/L)*(nz*2*M_PI/L); // K*K = Kx*Kx + Ky*Ky + Kz*Kz
g_phi_K[i].x = g_rho_K[i].x/KK*4.0*M_PI*G*(-1.0/(N*N*N)); // real part phi(k) = -4*Pi*G*rho(k)/k^2 and normalize by 1/N^3
g_phi_K[i].y = g_rho_K[i].y/KK*4.0*M_PI*G*(-1.0/(N*N*N)); // imag part phi(k) = -4*Pi*G*rho(k)/k^2 and normalize by 1/N^3
}
}// KERNEL PoissonEquationInK_PerBC_GPU
// KERNEL PoissonEquationInK_IsoBC_GPU: Calculate phi(k) in K-space for isolated BC by GPU
__global__
void PoissonEquationInK_IsoBC_GPU( const cufftDoubleComplex *g_mas_0pad_K, const cufftDoubleComplex *g_greensfn_K, cufftDoubleComplex *g_phi_0pad_K ){
const uint i = blockDim.x*blockIdx.x + threadIdx.x;
if( i<(2*N)*(2*N)*(N+1) ){
g_phi_0pad_K[i].x = G*( g_mas_0pad_K[i].x*g_greensfn_K[i].x-g_mas_0pad_K[i].y*g_greensfn_K[i].y)*(1.0/(2*N*2*N*2*N));// real part phi(k) = G*mas(k)*gre(k) and normalize by 1/(2N)^3
g_phi_0pad_K[i].y = G*( g_mas_0pad_K[i].x*g_greensfn_K[i].y+g_mas_0pad_K[i].y*g_greensfn_K[i].x)*(1.0/(2*N*2*N*2*N));// imag part phi(k) = G*mas(k)*gre(k) and normalize by 1/(2N)^3
}
}// KERNEL PoissonEquationInK_IsoBC_GPU
#endif
// FUNCTION PoissonSolver: Solve the Poisson equation to get the potential
void PoissonSolver( double *rho, double *phi ){
if( BC==1 ){ // Periodic Boundary Condition
if( Scheme_PS==1 ){ // Fast Fourier Transform
# ifdef GPU
cufftDoubleReal *d_rho; // (device) density
cudaMalloc( &d_rho, sizeof(cufftDoubleReal)*N*N*N );
cufftDoubleReal *d_phi; // (device) potential
cudaMalloc( &d_phi, sizeof(cufftDoubleReal)*N*N*N );
cufftDoubleComplex *d_rho_K; // (device) density in K space
cudaMalloc( &d_rho_K, sizeof(cufftDoubleComplex)*N*N*(N/2+1) );
cufftDoubleComplex *d_phi_K; // (device) potential in K space
cudaMalloc( &d_phi_K, sizeof(cufftDoubleComplex)*N*N*(N/2+1) );
cufftHandle rhoXtorhoK, phiKtophiX;
cufftPlan3d( &rhoXtorhoK, N, N, N, CUFFT_D2Z ); // Fourier Transform from rho(x) to rho(k)
cufftPlan3d( &phiKtophiX, N, N, N, CUFFT_Z2D ); // Inverse Fourier Transform from phi(k) to phi(x)
cudaMemcpy( d_rho, rho, N*N*N*sizeof(double), cudaMemcpyHostToDevice );
cufftExecD2Z( rhoXtorhoK, d_rho, d_rho_K ); // Fourier Transform from rho(x) to rho(k)
PoissonEquationInK_PerBC_GPU <<< GRID_SIZE, BLOCK_SIZE >>>( d_rho_K, d_phi_K );
cufftExecZ2D( phiKtophiX, d_phi_K, d_phi ); // Inverse Fourier Transform from phi(k) to phi(x)
cudaMemcpy( phi, d_phi, N*N*N*sizeof(double), cudaMemcpyDeviceToHost );
cufftDestroy( rhoXtorhoK );
cufftDestroy( phiKtophiX );
cudaFree( d_rho );
cudaFree( d_phi );
cudaFree( d_rho_K );
cudaFree( d_phi_K );
# else
fftw_complex *rho_K; // density in K space
rho_K = (fftw_complex*) fftw_malloc( N*N*(N/2+1) * sizeof(fftw_complex) );
fftw_complex *phi_K; // potential in K space
phi_K = (fftw_complex*) fftw_malloc( N*N*(N/2+1) * sizeof(fftw_complex) );
fftw_plan rhoXtorhoK, phiKtophiX;
rhoXtorhoK = fftw_plan_dft_r2c_3d( N, N, N, rho, rho_K, FFTW_ESTIMATE ); // Fourier Transform from rho(x) to rho(k)
phiKtophiX = fftw_plan_dft_c2r_3d( N, N, N, phi_K, phi, FFTW_ESTIMATE ); // Inverse Fourier Transform from phi(k) to phi(x)
fftw_execute( rhoXtorhoK ); // Fourier Transform from rho(x) to rho(k)
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
for(int k=0;k<N/2+1;k++){
double KK; // K*K = Kx*Kx + Ky*Ky + Kz*Kz
int nx, ny;
if( i>N/2 ) nx=i-N; else nx=i;
if( j>N/2 ) ny=j-N; else ny=j;
KK = (nx*2*M_PI/L)*(nx*2*M_PI/L) + (ny*2*M_PI/L)*(ny*2*M_PI/L) + (k*2*M_PI/L)*(k*2*M_PI/L); // K*K = Kx*Kx + Ky*Ky + Kz*Kz
phi_K[k+(N/2+1)*(j+N*i)][0] = rho_K[k+(N/2+1)*(j+N*i)][0]/KK*4.0*M_PI*G*(-1.0/(N*N*N)); // real part phi(k) = -4*Pi*G*rho(k)/k^2 and normalize by 1/N^3
phi_K[k+(N/2+1)*(j+N*i)][1] = rho_K[k+(N/2+1)*(j+N*i)][1]/KK*4.0*M_PI*G*(-1.0/(N*N*N)); // imag part phi(k) = -4*Pi*G*rho(k)/k^2 and normalize by 1/N^3
}}}
phi_K[0][0] = 0.0; // set DC to 0
phi_K[0][1] = 0.0; // set DC to 0
fftw_execute( phiKtophiX ); // Inverse Fourier Transform from phi(k) to phi(x)
fftw_destroy_plan( rhoXtorhoK );
fftw_destroy_plan( phiKtophiX );
fftw_free( rho_K );
fftw_free( phi_K );
# endif
}
else printf("ERROR: Unsupported Scheme_PS!\n");
}
else if( BC==2 ){ // Isolated Boundary Condition
if( Scheme_PS==1 ){ // Fast Fourier Transform
# ifdef GPU
double *h_mas_0pad = new double[2*N*2*N*2*N]; // (host) zero padding on the mass array
double *h_greensfn = new double[2*N*2*N*2*N]; // (host) symmetric discrete Green's function -1/r
double *h_phi_0pad = new double[2*N*2*N*2*N]; // (host) zero padding ont eh potential array
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<2*N;i++){
for(int j=0;j<2*N;j++){
for(int k=0;k<2*N;k++){
int nx,ny,nz; // number of distance interval
if( i<N && j<N && k<N ) h_mas_0pad[k+(2*N)*(j+(2*N)*i)] = rho[Index( i, j, k )]*dx*dx*dx; // mass of cell = density * cell volume
else h_mas_0pad[k+(2*N)*(j+(2*N)*i)] = 0.0; // zero padding
if( i>=N ) nx=2*N-i; else nx=i; // symmetrization
if( j>=N ) ny=2*N-j; else ny=j; // symmetrization
if( k>=N ) nz=2*N-k; else nz=k; // symmetrization
if( i==0 && j==0 && k==0 ) h_greensfn[0] = 0.0; // ignore self force
else h_greensfn[k+(2*N)*(j+(2*N)*i)] = -1.0/(dx*sqrt( nx*nx + ny*ny + nz*nz )); // -1/r
}}}
cufftDoubleReal *d_mas_0pad; // (device) zero padding on the mass array
cudaMalloc( &d_mas_0pad, sizeof(cufftDoubleReal)*(2*N)*(2*N)*(2*N) );
cufftDoubleReal *d_greensfn; // (device) symmetric discrete Green's function -1/r
cudaMalloc( &d_greensfn, sizeof(cufftDoubleReal)*(2*N)*(2*N)*(2*N) );
cufftDoubleReal *d_phi_0pad; // (device) zero padding on the potential array
cudaMalloc( &d_phi_0pad, sizeof(cufftDoubleReal)*(2*N)*(2*N)*(2*N) );
cufftDoubleComplex *d_mas_0pad_K; // (device) mass in K space
cudaMalloc( &d_mas_0pad_K, sizeof(cufftDoubleComplex)*(2*N)*(2*N)*(N+1) );
cufftDoubleComplex *d_greensfn_K; // (device) Green's function in K space
cudaMalloc( &d_greensfn_K, sizeof(cufftDoubleComplex)*(2*N)*(2*N)*(N+1) );
cufftDoubleComplex *d_phi_0pad_K; // (device) potential in K space
cudaMalloc( &d_phi_0pad_K, sizeof(cufftDoubleComplex)*(2*N)*(2*N)*(N+1) );
cufftHandle masXtomasK, greXtogreK, phiKtophiX;
cufftPlan3d( &masXtomasK, 2*N, 2*N, 2*N, CUFFT_D2Z ); // Fourier Transform from mas(x) to mas(k)
cufftPlan3d( &greXtogreK, 2*N, 2*N, 2*N, CUFFT_D2Z ); // Fourier Transform from gre(x) to gre(k)
cufftPlan3d( &phiKtophiX, 2*N, 2*N, 2*N, CUFFT_Z2D ); // Inverse Fourier Transform from phi(k) to phi(x)
cudaMemcpy( d_mas_0pad, h_mas_0pad, 2*N*2*N*2*N*sizeof(double), cudaMemcpyHostToDevice );
cudaMemcpy( d_greensfn, h_greensfn, 2*N*2*N*2*N*sizeof(double), cudaMemcpyHostToDevice );
cufftExecD2Z( masXtomasK, d_mas_0pad, d_mas_0pad_K ); // Fourier Transform from mas(x) to mas(k)
cufftExecD2Z( greXtogreK, d_greensfn, d_greensfn_K ); // Fourier Transform from gre(x) to gre(k)
PoissonEquationInK_IsoBC_GPU <<< GRID_SIZE, BLOCK_SIZE >>> ( d_mas_0pad_K, d_greensfn_K, d_phi_0pad_K );
cufftExecZ2D( phiKtophiX, d_phi_0pad_K, d_phi_0pad ); // Inverse Fourier Transform from phi(k) to phi(x)
cudaMemcpy( h_phi_0pad, d_phi_0pad, 2*N*2*N*2*N*sizeof(double), cudaMemcpyDeviceToHost );
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<N;i++)
for(int j=0;j<N;j++)
for(int k=0;k<N;k++)
phi[Index( i, j, k )] = h_phi_0pad[k+(2*N)*(j+(2*N)*i)]; // remove the padding
cufftDestroy( masXtomasK );
cufftDestroy( greXtogreK );
cufftDestroy( phiKtophiX );
cudaFree( d_mas_0pad_K );
cudaFree( d_greensfn_K );
cudaFree( d_phi_0pad_K );
cudaFree( d_mas_0pad );
cudaFree( d_greensfn );
cudaFree( d_phi_0pad );
delete [] h_mas_0pad;
delete [] h_greensfn;
delete [] h_phi_0pad;
# else
double *mas_0pad; // zero padding on the mass array
mas_0pad = (double*) fftw_malloc( (2*N)*(2*N)*(2*N) * sizeof(double) );
double *greensfn; // symmetric discrete Green's function -1/r
greensfn = (double*) fftw_malloc( (2*N)*(2*N)*(2*N) * sizeof(double) );
double *phi_0pad; // zero padding on the potential array
phi_0pad = (double*) fftw_malloc( (2*N)*(2*N)*(2*N) * sizeof(double) );
fftw_complex *mas_0pad_K; // mass in K space
mas_0pad_K = (fftw_complex*) fftw_malloc( (2*N)*(2*N)*(N+1) * sizeof(fftw_complex) );
fftw_complex *greensfn_K; // Green's function in K space
greensfn_K = (fftw_complex*) fftw_malloc( (2*N)*(2*N)*(N+1) * sizeof(fftw_complex) );
fftw_complex *phi_0pad_K; // potential in K space
phi_0pad_K = (fftw_complex*) fftw_malloc( (2*N)*(2*N)*(N+1) * sizeof(fftw_complex) );
fftw_plan masXtomasK, greXtogreK, phiKtophiX;
masXtomasK = fftw_plan_dft_r2c_3d( 2*N, 2*N, 2*N, mas_0pad, mas_0pad_K, FFTW_ESTIMATE ); // Fourier Transform from mas(x) to mas(k)
greXtogreK = fftw_plan_dft_r2c_3d( 2*N, 2*N, 2*N, greensfn, greensfn_K, FFTW_ESTIMATE ); // Fourier Transform from gre(x) to gre(k)
phiKtophiX = fftw_plan_dft_c2r_3d( 2*N, 2*N, 2*N, phi_0pad_K, phi_0pad, FFTW_ESTIMATE ); // Inverse Fourier Transform from phi(k) to phi(x)
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<2*N;i++){
for(int j=0;j<2*N;j++){
for(int k=0;k<2*N;k++){
int nx,ny,nz; // number of distance interval
if( i<N && j<N && k<N ) mas_0pad[k+(2*N)*(j+(2*N)*i)] = rho[Index( i, j, k )]*dx*dx*dx; // mass of cell = density * cell volume
else mas_0pad[k+(2*N)*(j+(2*N)*i)] = 0.0; // zero padding
if( i>=N ) nx=2*N-i; else nx=i; // symmetrization
if( j>=N ) ny=2*N-j; else ny=j; // symmetrization
if( k>=N ) nz=2*N-k; else nz=k; // symmetrization
if( i==0 && j==0 && k==0 ) greensfn[0] = 0.0; // ignore self force
else greensfn[k+(2*N)*(j+(2*N)*i)] = -1.0/(dx*sqrt( nx*nx + ny*ny + nz*nz )); // -1/r
}}}
fftw_execute( masXtomasK ); // Fourier Transform from mas(x) to mas(k)
fftw_execute( greXtogreK ); // Fourier Transform from gre(x) to gre(k)
# pragma omp parallel for num_threads(NThread)
for(int i=0;i<2*N;i++){
for(int j=0;j<2*N;j++){
for(int k=0;k<N+1;k++){
phi_0pad_K[k+(N+1)*(j+(2*N)*i)][0] = G*( mas_0pad_K[k+(N+1)*(j+(2*N)*i)][0]*greensfn_K[k+(N+1)*(j+(2*N)*i)][0]-mas_0pad_K[k+(N+1)*(j+(2*N)*i)][1]*greensfn_K[k+(N+1)*(j+(2*N)*i)][1])*(1.0/(2*N*2*N*2*N));// real part phi(k) = G*mas(k)*gre(k) and normalize by 1/(2N)^3
phi_0pad_K[k+(N+1)*(j+(2*N)*i)][1] = G*( mas_0pad_K[k+(N+1)*(j+(2*N)*i)][0]*greensfn_K[k+(N+1)*(j+(2*N)*i)][1]+mas_0pad_K[k+(N+1)*(j+(2*N)*i)][1]*greensfn_K[k+(N+1)*(j+(2*N)*i)][0])*(1.0/(2*N*2*N*2*N));// imag part phi(k) = G*mas(k)*gre(k) and normalize by 1/(2N)^3
}}}
fftw_execute( phiKtophiX ); // Inverse Fourier Transform from phi(k) to phi(x)
# pragma omp parallel for collapse( 3 ) num_threads(NThread)
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
for(int k=0;k<N;k++){
phi[Index( i, j, k )] = phi_0pad[k+(2*N)*(j+(2*N)*i)]; // remove the padding
}}}
fftw_destroy_plan( masXtomasK );
fftw_destroy_plan( greXtogreK );
fftw_destroy_plan( phiKtophiX );
fftw_free( mas_0pad_K );
fftw_free( greensfn_K );
fftw_free( phi_0pad_K );
fftw_free( mas_0pad );
fftw_free( greensfn );
fftw_free( phi_0pad );
# endif
}
else printf("ERROR: Unsupported Scheme_PS!\n");
}
else printf("ERROR: Unsuppoted Boundary Condition!\n");
return;
}// FUNCTION PoissonSolver
#ifdef GPU
// KERNEL Acceleration_DN_GPU: Calculate the acceleration for Direct N-Body by GPU
__global__
void Acceleration_DN_GPU( const double *g_m, const double *g_x, double *g_a )
{
const uint i = blockDim.x*blockIdx.x + threadIdx.x;
if( i<ParN ){
// load data from global memory to the **per-thread** registers (much faster)
const double I_x = g_x[i*3+0];
const double I_y = g_x[i*3+1];
const double I_z = g_x[i*3+2];
// declared shared-memory arrays
__shared__ double sJ_x[BLOCK_SIZE];
__shared__ double sJ_y[BLOCK_SIZE];
__shared__ double sJ_z[BLOCK_SIZE];
__shared__ double sJ_m[BLOCK_SIZE];
double I_a[3] = { 0.0, 0.0, 0.0 };
double dx, dy, dz, r, r3;
uint j;
// calculate BLOCK_SIZE j particles at a time (because of the limited shared memory)
for(int J_Base=0;J_Base<ParN;J_Base+=BLOCK_SIZE){
j = J_Base + threadIdx.x;
sJ_x[threadIdx.x] = g_x[j*3+0];
sJ_y[threadIdx.x] = g_x[j*3+1];
sJ_z[threadIdx.x] = g_x[j*3+2];
sJ_m[threadIdx.x] = g_m[j];
// synchronize all threads to ensure that all shared-memory data have been loaded
__syncthreads();
// k : kth particle in the currently loaded j particles
for(int k=0;k<BLOCK_SIZE;k++){
// load data from the shared memory (for the j particle)
// and the per-thread registers (for the i particles)
dx = sJ_x[k] - I_x;
dy = sJ_y[k] - I_y;
dz = sJ_z[k] - I_z;
// accumulate the gravitational acceleration
r = sqrt( dx*dx + dy*dy + dz*dz );
r3 = r*r*r;
// store temporary data in the per-thread variable "Acc" instead of g_Acc (much faster)
I_a[0] += G*sJ_m[k]*dx/r3;
I_a[1] += G*sJ_m[k]*dy/r3;
I_a[2] += G*sJ_m[k]*dz/r3;
} // for (int k=0; k<GroupSize_J; k++)
// synchronize all threads again before reloading data into the shared memory
__syncthreads();
} // for (int J_Base=0; J_Base<n; J_Base+=BLOCK_SIZE)
// store data back to the global memory
g_a[i*3+0] = I_a[0];
g_a[i*3+1] = I_a[1];
g_a[i*3+2] = I_a[2];
}
}// KERNEL Acceleration_DN_GPU
#endif
// FUNCTION Acceleration: Calculate the acceleration of each particle
void Acceleration( double *x, double *a, const int NRank, const int MyRank ){
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i++)
for(int j=0;j<3;j++)
a[i*3+j] = 0.0; // initialization as zero
if( Scheme_SG==1 ){ // Particle Mesh
double *Rho = new double[N*N*N]; // density
double *Phi = new double[N*N*N]; // potential
struct timespec MD_start, MD_end, PS_start, PS_end;
double MD_time_used, PS_time_used;
clock_gettime(CLOCK_MONOTONIC, &MD_start);
/////////measure start
MassDeposition( x, Rho, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &MD_end);
struct timespec MD_temp = diff(MD_start, MD_end);
MD_time_used = MD_temp.tv_sec + (double) MD_temp.tv_nsec / 1000000000.0;
// printf("MD_Time = %f\n", MD_time_used);
clock_gettime(CLOCK_MONOTONIC, &PS_start);
/////////measure start
PoissonSolver( Rho, Phi );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &PS_end);
struct timespec PS_temp = diff(PS_start, PS_end);
PS_time_used = PS_temp.tv_sec + (double) PS_temp.tv_nsec / 1000000000.0;
// printf("PS_Time = %f\n", PS_time_used);
double *XSendBuf = new double[ParN/NRank*3]; // Buffer for sending x between MPI ranks
double *ASendBuf = new double[ParN/NRank*3]; // Buffer for sending a between MPI ranks
MPI_Request Request[2];
for(int rank=0;rank<NRank;rank++){
if( Scheme_MD==1 ){ // Nearest-Grid-Point
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
if( x[n*3+0]>dx && x[n*3+0]<L-dx && x[n*3+1]>dx && x[n*3+1]<L-dx && x[n*3+2]>dx && x[n*3+2]<L-dx ){
// x-direction
a[n*3+0] += -( Phi[Index( (int)(x[n*3+0]/dx)+1, (int)(x[n*3+1]/dx), (int)(x[n*3+2]/dx) )] - Phi[Index( (int)(x[n*3+0]/dx)-1, (int)(x[n*3+1]/dx), (int)(x[n*3+2]/dx) )] ) /(2.0*dx);
// y-direction
a[n*3+1] += -( Phi[Index( (int)(x[n*3+0]/dx), (int)(x[n*3+1]/dx)+1, (int)(x[n*3+2]/dx) )] - Phi[Index( (int)(x[n*3+0]/dx), (int)(x[n*3+1]/dx-1), (int)(x[n*3+2]/dx) )] ) /(2.0*dx);
// z-direction
a[n*3+2] += -( Phi[Index( (int)(x[n*3+0]/dx), (int)(x[n*3+1]/dx), (int)(x[n*3+2]/dx)+1 )] - Phi[Index( (int)(x[n*3+0]/dx), (int)(x[n*3+1]/dx), (int)(x[n*3+2]/dx)-1 )] ) /(2.0*dx);
}
}
}
else if( Scheme_MD==2 ){ // Cloud-In-Cell
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
double weighting[3][2];
if( x[n*3+0]>1.5*dx && x[n*3+0]<L-1.5*dx && x[n*3+1]>1.5*dx && x[n*3+1]<L-1.5*dx && x[n*3+2]>1.5*dx && x[n*3+2]<L-1.5*dx ){
for(int i=0;i<3;i++){ // weighting of distribution
weighting[i][1] = (x[n*3+i]/dx-0.5) - (int)(x[n*3+i]/dx-0.5);
weighting[i][0] = 1 - weighting[i][1];
}
for(int i=0;i<2;i++){
for(int j=0;j<2;j++){
for(int k=0;k<2;k++){ // get acceleration from 8 cells
// x-direction
a[n*3+0] += -( Phi[Index( (int)(x[n*3+0]/dx-0.5)+i+1, (int)(x[n*3+1]/dx-0.5)+j, (int)(x[n*3+2]/dx-0.5)+k )] - Phi[Index( (int)(x[n*3+0]/dx-0.5)+i-1, (int)(x[n*3+1]/dx-0.5)+j, (int)(x[n*3+2]/dx-0.5)+k) ] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
// y-direction
a[n*3+1] += -( Phi[Index( (int)(x[n*3+0]/dx-0.5)+i, (int)(x[n*3+1]/dx-0.5)+j+1, (int)(x[n*3+2]/dx-0.5)+k )] - Phi[Index( (int)(x[n*3+0]/dx-0.5)+i, (int)(x[n*3+1]/dx-0.5)+j-1, (int)(x[n*3+2]/dx-0.5)+k )] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
// z-direction
a[n*3+2] += -( Phi[Index( (int)(x[n*3+0]/dx-0.5)+i, (int)(x[n*3+1]/dx-0.5)+j, (int)(x[n*3+2]/dx-0.5)+k+1 )] - Phi[Index( (int)(x[n*3+0]/dx-0.5)+i, (int)(x[n*3+1]/dx-0.5)+j, (int)(x[n*3+2]/dx-0.5)+k-1 )] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
}}}
}
}
}
else if( Scheme_MD==3 ){ // Triangular-Shaped-Cloud
# pragma omp parallel for num_threads(NThread)
for(int n=0;n<ParN/NRank;n++){
double weighting[3][3];
double devide[3];
if( x[n*3+0]>2.0*dx && x[n*3+0]<L-2.0*dx && x[n*3+1]>2.0*dx && x[n*3+1]<L-2.0*dx && x[n*3+2]>2.0*dx && x[n*3+2]<L-2.0*dx ){
for(int i=0;i<3;i++){ // weighting of distribution
devide[i]= x[n*3+i]/dx - (int)(x[n*3+i]/dx);//find the distance between n grid and center of particle
weighting[i][0] = pow((1.0-devide[i]),2)*0.5;
weighting[i][1] = 0.5*(1.0 + 2.0*devide[i]-2.0*pow(devide[i],2));
weighting[i][2] = pow(devide[i],2)*0.5;
}
for(int i=0;i<3;i++){
for(int j=0;j<3;j++){
for(int k=0;k<3;k++){ // get acceleration from 27 cells
// x-direction
a[n*3+0] += -( Phi[Index( (int)(x[n*3+0]/dx-1.0)+i+1, (int)(x[n*3+1]/dx-1.0)+j, (int)(x[n*3+2]/dx-1.0)+k )] - Phi[Index( (int)(x[n*3+0]/dx-1.0)+i-1, (int)(x[n*3+1]/dx-1.0)+j, (int)(x[n*3+2]/dx-1.0)+k )] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
// y-direction
a[n*3+1] += -( Phi[Index( (int)(x[n*3+0]/dx-1.0)+i, (int)(x[n*3+1]/dx-1.0)+j+1, (int)(x[n*3+2]/dx-1.0)+k )] - Phi[Index( (int)(x[n*3+0]/dx-1.0)+i, (int)(x[n*3+1]/dx-1.0)+j-1, (int)(x[n*3+2]/dx-1.0)+k )] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
// z-direction
a[n*3+2] += -( Phi[Index( (int)(x[n*3+0]/dx-1.0)+i, (int)(x[n*3+1]/dx-1.0)+j, (int)(x[n*3+2]/dx-1.0)+k+1 )] - Phi[Index( (int)(x[n*3+0]/dx-1.0)+i, (int)(x[n*3+1]/dx-1.0)+j, (int)(x[n*3+2]/dx-1.0)+k-1 )] )/(2.0*dx)*weighting[0][i]*weighting[1][j]*weighting[2][k];
}}}
}
}
}
for(int i=0;i<ParN/NRank*3;i++){ // prepare buffers for MPI
XSendBuf[i] = x[i];
ASendBuf[i] = a[i];
}
MPI_Isend( XSendBuf, ParN/NRank*3, MPI_DOUBLE, (MyRank+NRank+1)%NRank, 123, MPI_COMM_WORLD, &Request[0] ); // send x to RHS Rank
MPI_Isend( ASendBuf, ParN/NRank*3, MPI_DOUBLE, (MyRank+NRank+1)%NRank, 456, MPI_COMM_WORLD, &Request[1] ); // send a to RHS Rank
MPI_Recv( x, ParN/NRank*3, MPI_DOUBLE, (MyRank+NRank-1)%NRank, 123, MPI_COMM_WORLD, MPI_STATUS_IGNORE ); // recv x from LHS Rank
MPI_Recv( a, ParN/NRank*3, MPI_DOUBLE, (MyRank+NRank-1)%NRank, 456, MPI_COMM_WORLD, MPI_STATUS_IGNORE ); // recv a from LHS Rank
}
delete [] XSendBuf;
delete [] ASendBuf;
delete [] Rho;
delete [] Phi;
}
else if( Scheme_SG==2 ){ // Direct N-body
if( NRank!=1 ){ printf( "ERROR: Direct N-body is not supported for NRank!=1\n" ); return;}
# ifdef GPU
// allocate device memory
double *d_x, *d_a, *d_m;
cudaMalloc( &d_x, ParN*3*sizeof(double) );
cudaMalloc( &d_a, ParN*3*sizeof(double) );
cudaMalloc( &d_m, ParN*sizeof(double) );
cudaMemcpy( d_x, x, ParN*3*sizeof(double), cudaMemcpyHostToDevice );
cudaMemcpy( d_m, ParM, ParN*sizeof(double), cudaMemcpyHostToDevice );
Acceleration_DN_GPU <<< GRID_SIZE, BLOCK_SIZE >>> ( d_m, d_x, d_a );
cudaMemcpy( a, d_a, ParN*3*sizeof(double), cudaMemcpyDeviceToHost );
cudaFree( d_x );
cudaFree( d_a );
# else
# pragma omp parallel for num_threads(NThread)
for(int i=0;i<ParN;i++){
if( x[i*3+0]>0 && x[i*3+0]<L && x[i*3+1]>0 && x[i*3+1]<L && x[i*3+2]>0 && x[i*3+2]<L ){
for(int j=0;j<ParN;j++){
double r; // distance between two particles
if( i!=j && x[j*3+0]>0 && x[j*3+0]<L && x[j*3+1]>0 && x[j*3+1]<L && x[j*3+2]>0 && x[j*3+2]<L ){
r = sqrt( (x[j*3+0]-x[i*3+0])*(x[j*3+0]-x[i*3+0]) + (x[j*3+1]-x[i*3+1])*(x[j*3+1]-x[i*3+1]) + (x[j*3+2]-x[i*3+2])*(x[j*3+2]-x[i*3+2]) );
# pragma omp critical
a[i*3+0] += G*ParM[j]/(r*r)*(x[j*3+0]-x[i*3+0])/r;
# pragma omp critical
a[i*3+1] += G*ParM[j]/(r*r)*(x[j*3+1]-x[i*3+1])/r;
# pragma omp critical
a[i*3+2] += G*ParM[j]/(r*r)*(x[j*3+2]-x[i*3+2])/r;
}
}
}
}
# endif
}
return;
}// FUNCTION Acceleration
// FUNCTION Update: Update the system by dt
void Update( double *x, double *v, const int NRank, const int MyRank ){
double *a= new double[ParN/NRank*3]; // acceleration of the particle
struct timespec AC1_start, AC1_end, AC2_start, AC2_end, AC3_start, AC3_end, AC4_start, AC4_end;
double AC1_time_used, AC2_time_used, AC3_time_used, AC4_time_used;
if( Scheme_OI==1 ){ // Kick-Drift-Kick
clock_gettime(CLOCK_MONOTONIC, &AC1_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC1_end);
struct timespec AC1_temp = diff(AC1_start, AC1_end);
AC1_time_used = AC1_temp.tv_sec + (double) AC1_temp.tv_nsec / 1000000000.0;
// printf("AC_Time = %f\n", AC1_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
v[i*3+d] += a[i*3+d]*dt/2;
}
} // Kick
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
x[i*3+d] += v[i*3+d]*dt;
}
} // Drift
clock_gettime(CLOCK_MONOTONIC, &AC2_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC2_end);
struct timespec AC2_temp = diff(AC2_start, AC2_end);
AC2_time_used = AC2_temp.tv_sec + (double) AC2_temp.tv_nsec / 1000000000.0;
// printf("AC2_Time = %f\n", AC2_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
v[i*3+d] += a[i*3+d]*dt/2;
}
} // Kick
}
else if( Scheme_OI==2 ){ // Drift-Kick-Drift
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
x[i*3+d] += v[i*3+d]*dt/2;
}
} // Drift
clock_gettime(CLOCK_MONOTONIC, &AC1_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC1_end);
struct timespec AC1_temp = diff(AC1_start, AC1_end);
AC1_time_used = AC1_temp.tv_sec + (double) AC1_temp.tv_nsec / 1000000000.0;
// printf("AC_Time = %f\n", AC1_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
v[i*3+d] += a[i*3+d]*dt;
}
} // Kick
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
x[i*3+d] += v[i*3+d]*dt/2;
}
} // Drift
}
else if( Scheme_OI==3 ){ // Runge-Kutta 4th
double *rk = new double[4*ParN/NRank*3*2]; // k_n, Par_ID, dim, pos/vel
clock_gettime(CLOCK_MONOTONIC, &AC1_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC1_end);
struct timespec AC1_temp = diff(AC1_start, AC1_end);
AC1_time_used = AC1_temp.tv_sec + (double) AC1_temp.tv_nsec / 1000000000.0;
// printf("AC_Time = %f\n", AC1_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
rk[((0*ParN/NRank+i)*3+d)*2+0] = v[i*3+d];
rk[((0*ParN/NRank+i)*3+d)*2+1] = a[i*3+d];
x[i*3+d] += (dt/2)* rk[((0*ParN/NRank+i)*3+d)*2+0];
v[i*3+d] += (dt/2)* rk[((0*ParN/NRank+i)*3+d)*2+1];
}
} // Step1
clock_gettime(CLOCK_MONOTONIC, &AC2_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC2_end);
struct timespec AC2_temp = diff(AC2_start, AC2_end);
AC2_time_used = AC2_temp.tv_sec + (double) AC2_temp.tv_nsec / 1000000000.0;
// printf("AC2_Time = %f\n", AC2_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
rk[((1*ParN/NRank+i)*3+d)*2+0] = v[i*3+d];
rk[((1*ParN/NRank+i)*3+d)*2+1] = a[i*3+d];
x[i*3+d] += (dt/2)* rk[((1*ParN/NRank+i)*3+d)*2+0] -(dt/2)* rk[((0*ParN/NRank+i)*3+d)*2+0];
v[i*3+d] += (dt/2)* rk[((1*ParN/NRank+i)*3+d)*2+1] -(dt/2)* rk[((0*ParN/NRank+i)*3+d)*2+1];
}
} // Step2
clock_gettime(CLOCK_MONOTONIC, &AC3_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC3_end);
struct timespec AC3_temp = diff(AC3_start, AC3_end);
AC3_time_used = AC3_temp.tv_sec + (double) AC3_temp.tv_nsec / 1000000000.0;
// printf("AC3_Time = %f\n", AC3_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
rk[((2*ParN/NRank+i)*3+d)*2+0] = v[i*3+d];
rk[((2*ParN/NRank+i)*3+d)*2+1] = a[i*3+d];
x[i*3+d] += (dt)* rk[((2*ParN/NRank+i)*3+d)*2+0] -(dt/2)* rk[((1*ParN/NRank+i)*3+d)*2+0];
v[i*3+d] += (dt)* rk[((2*ParN/NRank+i)*3+d)*2+1] -(dt/2)* rk[((1*ParN/NRank+i)*3+d)*2+1];
}
} // Step3
clock_gettime(CLOCK_MONOTONIC, &AC4_start);
/////////measure start
CheckBoundary( x, v, NRank );
Acceleration( x, a, NRank, MyRank );
/////////measure end
clock_gettime(CLOCK_MONOTONIC, &AC4_end);
struct timespec AC4_temp = diff(AC4_start, AC4_end);
AC4_time_used = AC4_temp.tv_sec + (double) AC4_temp.tv_nsec / 1000000000.0;
// printf("AC4_Time = %f\n", AC4_time_used);
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<ParN/NRank;i=i+1){
for(int d=0;d<3;d=d+1){
rk[((3*ParN/NRank+i)*3+d)*2+0] = v[i*3+d];
rk[((3*ParN/NRank+i)*3+d)*2+1] = a[i*3+d];
x[i*3+d] += (dt/6)*(rk[((0*ParN/NRank+i)*3+d)*2+0] + 2*rk[((1*ParN/NRank+i)*3+d)*2+0] +2*rk[((2*ParN/NRank+i)*3+d)*2+0] + rk[((3*ParN/NRank+i)*3+d)*2+0]) -(dt)* rk[((2*ParN/NRank+i)*3+d)*2+0];
v[i*3+d] += (dt/6)*(rk[((0*ParN/NRank+i)*3+d)*2+1] + 2*rk[((1*ParN/NRank+i)*3+d)*2+1] +2*rk[((2*ParN/NRank+i)*3+d)*2+1] + rk[((3*ParN/NRank+i)*3+d)*2+1]) -(dt)* rk[((2*ParN/NRank+i)*3+d)*2+1];
}
} // Step4
delete [] rk;
}
else{
printf("Wrong Scheme_OI Mode\n");
}
delete [] a;
return;
}// FUNCTION Update
// FUNCTION Energy: Calculate the total energy of the system
double Energy( double *x, double *v ){
double e; // total energy
double ekin = 0.0; // kinetic energy
double epot = 0.0; // potentail energy
// kineteic energy
# pragma omp parallel for reduction( +:ekin ) num_threads(NThread)
for(int i=0;i<ParN;i++){
ekin += 0.5*ParM[i]*( v[i*3+0]*v[i*3+0] + v[i*3+1]+v[i*3+1] + v[i*3+2]*v[i*3+2] );
}
// potential energy
double *Rho = new double[N*N*N]; // density
double *Phi = new double[N*N*N]; // potential
MassDeposition( x, Rho, 1, 0 ); // get density
PoissonSolver( Rho, Phi ); // get potential
# pragma omp parallel for collapse( 2 ) num_threads(NThread)
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
for(int k=0;k<N;k++){
# pragma omp critical
epot += 0.5*Rho[Index( i, j, k )]*Phi[Index( i, j, k )]*dx*dx*dx;
}}}
delete [] Rho;
delete [] Phi;
// total energy
e = ekin + epot;