| 1 | = Ex17.c = |
| 2 | {{{#!C |
| 3 | /* |
| 4 | Large Scale Computing |
| 5 | 2D Heat/Mass Transfer |
| 6 | ex17.c : Numerical Analysis |
| 7 | Solve for |
| 8 | d2c/dx2 + d2c/dy2 + 1 = 0 |
| 9 | With the boundary conditions of c = 0 |
| 10 | along lines of x=1,-1, and y=1, and -1 |
| 11 | */ |
| 12 | #include<stdio.h> |
| 13 | #include<stdlib.h> |
| 14 | #include<math.h> |
| 15 | |
| 16 | #define NUM 20 /* number of points for x and y*/ |
| 17 | #define TOL 1.0e-12 /* convergence tolerance */ |
| 18 | |
| 19 | int main(void ){ |
| 20 | int i,j,k,n,ie,iw,in,is; |
| 21 | double x,y,dx,w,err; |
| 22 | double cnc[NUM * NUM]; /* define 1D array of length NUM * NUM */ |
| 23 | FILE *fp; |
| 24 | |
| 25 | /*assuming dx = dy : domain is 2x2 */ |
| 26 | dx = 2.0 / (double)(NUM - 1); |
| 27 | |
| 28 | /* Initialize */ |
| 29 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 30 | cnc[n] = 0.0; |
| 31 | } |
| 32 | |
| 33 | /* computing for C with Gauss-Seidel */ |
| 34 | k = 0; |
| 35 | while(1){ |
| 36 | err = 0.0; |
| 37 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 38 | i = n % NUM; /* i is residual */ |
| 39 | j = n / NUM; /* j is division */ |
| 40 | if (i == 0) continue; /*skip left end*/ |
| 41 | if (i == NUM-1) continue; /*skip right end*/ |
| 42 | if (j == 0) continue; /*skip bottom end*/ |
| 43 | if (j == NUM-1) continue; /*skip top end*/ |
| 44 | |
| 45 | ie = n + 1; |
| 46 | iw = n - 1; |
| 47 | in = n + NUM; |
| 48 | is = n - NUM; |
| 49 | w = 0.25 * (dx * dx + cnc[ie] + cnc[iw] + cnc[in] + cnc[is]); |
| 50 | err += (w - cnc[n]) * (w - cnc[n]); |
| 51 | cnc[n] = w; |
| 52 | } |
| 53 | k++; |
| 54 | if (err < TOL) break; |
| 55 | } |
| 56 | printf("# of Iteration=%d\n",k); |
| 57 | |
| 58 | /* Output Result */ |
| 59 | fp = fopen("res.dat","w"); |
| 60 | if (fp == NULL){ |
| 61 | printf("File could not create\n"); |
| 62 | exit(-1); |
| 63 | } |
| 64 | |
| 65 | for (i = 0 ;i < NUM ; i++){ |
| 66 | for (j = 0 ; j < NUM ; j++){ |
| 67 | x = -1.0 + 2.0 * (double)i / (double)(NUM - 1); |
| 68 | y = -1.0 + 2.0 * (double)j / (double)(NUM - 1); |
| 69 | fprintf(fp,"%e %e %e\n",x,y,cnc[i + NUM * j]); |
| 70 | } |
| 71 | } |
| 72 | fclose(fp); |
| 73 | |
| 74 | printf("Done\n"); |
| 75 | } |
| 76 | }}} |