| 1 | = Ex19.c = |
| 2 | {{{#!C |
| 3 | /* |
| 4 | Large Scale Computing |
| 5 | 2D Heat/Mass Transfer |
| 6 | ex19.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 | Conjugate Gradient Method |
| 13 | */ |
| 14 | #include<stdio.h> |
| 15 | #include<stdlib.h> |
| 16 | #include<math.h> |
| 17 | |
| 18 | #define NUM 100 /* number of points for x and y*/ |
| 19 | #define TOL 1.0e-12 /* convergence tolerance */ |
| 20 | |
| 21 | int main(void ){ |
| 22 | int i,j,n; |
| 23 | double x,y,dx; |
| 24 | double cnc[NUM * NUM]; /* define 1D array of length NUM * NUM */ |
| 25 | double r[NUM * NUM]; |
| 26 | double p[NUM * NUM]; |
| 27 | double Ap[NUM * NUM]; |
| 28 | double rr,pAp,rr1,alpha,beta; |
| 29 | int k; |
| 30 | FILE *fp; |
| 31 | |
| 32 | /*assuming dx = dy : domain is 2x2 */ |
| 33 | dx = 2.0 / (double)(NUM - 1); |
| 34 | |
| 35 | /* Initialize */ |
| 36 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 37 | cnc[n] = 0.0; |
| 38 | r[n] = 0.0; |
| 39 | } |
| 40 | |
| 41 | /* computing for C with Conjugate Gradient Method */ |
| 42 | /* r0 = b - Ax0 */ |
| 43 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 44 | i = n % NUM; /* i is residual */ |
| 45 | j = n / NUM; /* j is division */ |
| 46 | if (i == 0) continue; /*skip left end*/ |
| 47 | if (i == NUM-1) continue; /*skip right end*/ |
| 48 | if (j == 0) continue; /*skip bottom end*/ |
| 49 | if (j == NUM-1) continue; /*skip top end*/ |
| 50 | r[n] = -dx * dx; |
| 51 | r[n] -= -4.0 * cnc[n]; |
| 52 | r[n] -= cnc[n + 1]; |
| 53 | r[n] -= cnc[n + NUM]; |
| 54 | r[n] -= cnc[n - 1]; |
| 55 | r[n] -= cnc[n - NUM]; |
| 56 | } |
| 57 | |
| 58 | rr = 0.0; |
| 59 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 60 | p[n] = r[n]; /* p = r */ |
| 61 | rr += r[n] * r[n]; /* rr = r.r */ |
| 62 | } |
| 63 | |
| 64 | k = 0; |
| 65 | while(rr > TOL){ |
| 66 | // Ap = A*p |
| 67 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 68 | Ap[n] = 0.0; |
| 69 | i = n % NUM; /* i is residual */ |
| 70 | j = n / NUM; /* j is division */ |
| 71 | if (i == 0) continue; /*skip left end*/ |
| 72 | if (i == NUM-1) continue; /*skip right end*/ |
| 73 | if (j == 0) continue; /*skip bottom end*/ |
| 74 | if (j == NUM-1) continue; /*skip top end*/ |
| 75 | |
| 76 | /* computing A*p */ |
| 77 | Ap[n] = -4.0 * p[n]; |
| 78 | Ap[n] += p[n + 1]; |
| 79 | Ap[n] += p[n + NUM]; |
| 80 | Ap[n] += p[n - 1]; |
| 81 | Ap[n] += p[n - NUM]; |
| 82 | } |
| 83 | |
| 84 | // alpha = r.r / p.Ap |
| 85 | pAp = 0.0; |
| 86 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 87 | pAp += p[n] * Ap[n]; |
| 88 | } |
| 89 | alpha = rr / pAp; |
| 90 | |
| 91 | //Beta |
| 92 | rr1 = 0.0; |
| 93 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 94 | cnc[n] += alpha * p[n]; |
| 95 | r[n] -= alpha * Ap[n]; |
| 96 | rr1 += r[n] * r[n]; |
| 97 | } |
| 98 | |
| 99 | beta = rr1 / rr; |
| 100 | |
| 101 | for (n = 0 ; n < NUM * NUM ; n++){ |
| 102 | p[n] = r[n] + beta * p[n]; |
| 103 | } |
| 104 | |
| 105 | rr = rr1; |
| 106 | k++; |
| 107 | } |
| 108 | |
| 109 | printf("# of Iteration=%d\n",k); |
| 110 | |
| 111 | /* Output Result */ |
| 112 | fp = fopen("res.dat","w"); |
| 113 | if (fp == NULL){ |
| 114 | printf("File could not create\n"); |
| 115 | exit(-1); |
| 116 | } |
| 117 | |
| 118 | for (i = 0 ;i < NUM ; i++){ |
| 119 | for (j = 0 ; j < NUM ; j++){ |
| 120 | x = -1.0 + 2.0 * (double)i / (double)(NUM - 1); |
| 121 | y = -1.0 + 2.0 * (double)j / (double)(NUM - 1); |
| 122 | fprintf(fp,"%e %e %e\n",x,y,cnc[i + NUM * j]); |
| 123 | } |
| 124 | } |
| 125 | fclose(fp); |
| 126 | |
| 127 | printf("Done\n"); |
| 128 | } |
| 129 | }}} |