121 lines
2.5 KiB
C
121 lines
2.5 KiB
C
#define _XOPEN_SOURCE 600
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#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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// Option to change numerical precision.
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typedef int64_t int_t;
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typedef double real_t;
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// Simulation parameters: size, step count, and how often to save the state.
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const int_t
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N = 1024,
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max_iteration = 4000,
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snapshot_freq = 10;
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// Wave equation parameters, time step is derived from the space step.
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const real_t
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c = 1.0,
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dx = 1.0;
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real_t
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dt;
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// Buffers for three time steps, indexed with 2 ghost points for the boundary.
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real_t
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*buffers[3] = { NULL, NULL, NULL };
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#define U_prv(i) buffers[0][(i) + 1]
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#define U(i) buffers[1][(i) + 1]
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#define U_nxt(i) buffers[2][(i) + 1]
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// Save the present time step in a numbered file under 'data/'.
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void domain_save(int_t step) {
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char filename[256];
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sprintf(filename, "data/%.5ld.dat", step);
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FILE *out = fopen(filename, "wb");
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fwrite(&U(0), sizeof(real_t), N, out);
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fclose(out);
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}
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// TASK: T1
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// Set up our three buffers, fill two with an initial cosine wave,
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// and set the time step.
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void domain_initialize(void) {
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// allocate memory
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for (int i = 0; i < 3; i++)
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buffers[i] = malloc((N + 2) * sizeof(real_t));
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// apply initial condition
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real_t x = 0.0f;
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for (int i = 0; i < N; i++) {
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U_prv(i) = cos(2 * M_PI * x);
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U(i) = U_prv(i);
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U_nxt(i) = 0.0f;
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x += (real_t)dx / (real_t)N;
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}
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// set the time-step dt according to CFL
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dt = dx / c;
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}
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// TASK T2:
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// Return the memory to the OS.
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void domain_finalize(void) {
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for (int i = 0; i < 3; i++) {
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free(buffers[i]);
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buffers[i] = NULL;
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}
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}
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// TASK: T3
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// Rotate the time step buffers.
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void rotate_buffers(void) {
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real_t *temp = buffers[0];
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buffers[0] = buffers[1];
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buffers[1] = buffers[2];
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buffers[2] = temp;
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}
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// TASK: T4
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// Derive step t+1 from steps t and t-1.
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void time_step(void) {
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for (int i = 0; i < N; i++) {
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U_nxt(i) = -U_prv(i) + 2 * U(i) + dt * dt * c * c / (dx * dx) * (U(i - 1) + U(i + 1) - 2 * U(i));
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}
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}
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// TASK: T5
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// Neumann (reflective) boundary condition.
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void boundary(void) {
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U_prv(-1) = U_prv(1);
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U(-1) = U(1);
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U_nxt(-1) = U_nxt(1);
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U_prv(N) = U_prv(N - 2);
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U(N) = U(N - 2);
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U_nxt(N) = U_nxt(N - 2);
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}
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// TASK: T6
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// Main time integration.
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void simulate(void) {
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int_t iteration = 0;
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while (iteration < max_iteration) {
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boundary();
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time_step();
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rotate_buffers();
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domain_save(iteration / snapshot_freq);
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iteration++;
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}
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}
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int main(void) {
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domain_initialize();
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simulate();
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domain_finalize();
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exit(EXIT_SUCCESS);
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}
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