Computer Science Create a MPI version of the program below that uses a striped decomposition. Each process is responsible for some number of columns of the square and also maintains two columns of ghost cells to mirror the columns on the neighboring processes. The ghost cells are needed in order to update the cells along the process boundary. At each time step, a ghost cell exchange takes place, then the update takes place. #include #include #include "anim.h" const int n = 200; // number of discrete points including endpoints int nstep = 200000; // number of time steps int wstep = 400; // time between writes to file const double m = 100.0; // initial temperature of rod interior const int h0 = n/2 - 2, h1 = n/2 + 2; // endpoints of heat source const double k = 0.2; // diffusivity constant char * filename = "diff2d.anim"; // name of file to create double ** u, ** u_new; // two copies of the temperature function ANIM_File af; // output file double start_time; // time simulation starts static void setup(void) { start_time = ANIM_time(); printf("diff2d: n=%d nstep=%d wstep=%d\n", n, nstep, wstep); u = ANIM_allocate2d(n,n); u_new = ANIM_allocate2d(n,n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) u_new[i][j] = u[i][j] = 0.0; for (int i = h0; i < h1; i++) for (int j = h0; j < h1; j++) u_new[i][j] = u[i][j] = m; af = ANIM_Create_heat (2, (int[]){n, n}, (ANIM_range_t[]){{0, 1}, {0, 1}, {0, m}}, filename); } static void teardown(void) { ANIM_Close(af); ANIM_free2d(u); ANIM_free2d(u_new); printf("\nTime (s) = %lf\n", ANIM_time() - start_time); } static void update() { for (int i = 1; i < n-1; i++) for (int j = 1; j < n-1; j++) u_new[i][j] = u[i][j] + k*(u[i+1][j] + u[i-1][j] + u[i][j+1] + u[i][j-1] - 4*u[i][j]); for (int i = 0; i < n; i++) u_new[i][n-1] = u_new[i][n-2]; for (int i = 0; i < n; i++) u_new[i][0] = u_new[i][1]; for (int j = 1; j < n-1; j++) u_new[0][j] = u_new[1][j]; for (int j = 1; j < n-1; j++) u_new[n-1][j] = u_new[n-2][j]; for (int i = h0; i < h1; i++) for (int j = h0; j < h1; j++) u_new[i][j] = m; double ** const tmp = u_new; u_new = u; u = tmp; } int main() { int dots = 0; setup(); if (wstep != 0) ANIM_Write_frame(af, u[0]); for (int i = 1; i <= nstep; i++) { update(); ANIM_Status_update(stdout, nstep, i, &dots); if (wstep != 0 && i%wstep == 0) ANIM_Write_frame(af, u[0]); } teardown(); }
Computer Science
Create a MPI version of the program below that uses a striped decomposition. Each process is responsible for some number of columns of the square and also maintains two columns of ghost cells to mirror the columns on the neighboring processes. The ghost cells are needed in order to update the cells along the process boundary. At each time step, a ghost cell exchange takes place, then the update takes place.
#include <stdlib.h>
#include <assert.h>
#include "anim.h"
const int n = 200; // number of discrete points including endpoints
int nstep = 200000; // number of time steps
int wstep = 400; // time between writes to file
const double m = 100.0; // initial temperature of rod interior
const int h0 = n/2 - 2, h1 = n/2 + 2; // endpoints of heat source
const double k = 0.2; // diffusivity constant
char * filename = "diff2d.anim"; // name of file to create
double ** u, ** u_new; // two copies of the temperature function
ANIM_File af; // output file
double start_time; // time simulation starts
static void setup(void) {
start_time = ANIM_time();
printf("diff2d: n=%d nstep=%d wstep=%d\n", n, nstep, wstep);
u = ANIM_allocate2d(n,n);
u_new = ANIM_allocate2d(n,n);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
u_new[i][j] = u[i][j] = 0.0;
for (int i = h0; i < h1; i++)
for (int j = h0; j < h1; j++)
u_new[i][j] = u[i][j] = m;
af = ANIM_Create_heat
(2, (int[]){n, n}, (ANIM_range_t[]){{0, 1}, {0, 1}, {0, m}}, filename);
}
static void teardown(void) {
ANIM_Close(af);
ANIM_free2d(u);
ANIM_free2d(u_new);
printf("\nTime (s) = %lf\n", ANIM_time() - start_time);
}
static void update() {
for (int i = 1; i < n-1; i++)
for (int j = 1; j < n-1; j++)
u_new[i][j] = u[i][j] +
k*(u[i+1][j] + u[i-1][j] + u[i][j+1] + u[i][j-1] - 4*u[i][j]);
for (int i = 0; i < n; i++) u_new[i][n-1] = u_new[i][n-2];
for (int i = 0; i < n; i++) u_new[i][0] = u_new[i][1];
for (int j = 1; j < n-1; j++) u_new[0][j] = u_new[1][j];
for (int j = 1; j < n-1; j++) u_new[n-1][j] = u_new[n-2][j];
for (int i = h0; i < h1; i++)
for (int j = h0; j < h1; j++)
u_new[i][j] = m;
double ** const tmp = u_new; u_new = u; u = tmp;
}
int main() {
int dots = 0;
setup();
if (wstep != 0) ANIM_Write_frame(af, u[0]);
for (int i = 1; i <= nstep; i++) {
update();
ANIM_Status_update(stdout, nstep, i, &dots);
if (wstep != 0 && i%wstep == 0) ANIM_Write_frame(af, u[0]);
}
teardown();
}
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