Ex20.c

/*
  Large Scale Computing
  2D Heat/Mass Transfer
  Ex20.c : Numerical Analysis
  Solve for
  d2c/dx2 + d2c/dy2 + 1 = 0
  With the boundary conditions of c = 0 
  along lines of x=1,-1, and y=1, and -1
 
 */
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include"cg.h"
 
#define NUM 100  /* number of points for x and y*/
#define TOL 1.0e-12  /* convergence tolerance */
 
int index(int ii,int jj);
int main(void ){
  int i,j,k,n;
  double x,y,dx;
  double phi[NUM][NUM]; /* define 1D array of length NUM * NUM */
  double rhs[NUM * NUM]; /* define 1D array of length NUM * NUM */
  double sol[NUM * NUM]; /* define 1D array of length NUM * NUM */
  double nzval[5 * NUM * NUM]; /* non-zero elements of A */
  int colind[5 * NUM * NUM]; /* column indices of nonzeros */
  int rowptr[NUM * NUM + 1]; /**/
  int nnz;
  FILE *fp;
 
  /*assuming dx = dy : domain is 2x2 */
  dx = 2.0 / (double)(NUM - 1);
 
  /* initial & boundary conditions */
  for (j = 0 ; j < NUM  ; j++){
    for (i = 0 ; i < NUM ; i++){
      phi[i][j] = 0.0;
    }
  }
 
  /* Setup Matrix A and RHS */
  nnz = 0;
  for (j = 1 ; j < NUM - 1 ; j++){
    for (i = 1 ; i < NUM - 1 ; i++){
      /* initial guess */
      sol[index(i,j)] = phi[i][j];
 
      /* set general RHS */
      rhs[index(i,j)] = -dx * dx;
 
      /* set first nonzero column of row index(i,j) */
      rowptr[index(i,j)] = nnz;
 
      /* sounth */
      if (j == 1){
        rhs[index(i,j)] -= phi[i][0]; 
      }else{
        nzval[nnz] = 1.0;
        colind[nnz] = index(i,j-1);
        nnz++;
      } 
 
      /* west */
      if (i == 1){
        rhs[index(i,j)] -= phi[0][j]; 
      }else{
        nzval[nnz] = 1.0;
        colind[nnz] = index(i-1,j);
        nnz++;
      } 
 
      /* diagonal Element */
      nzval[nnz] = -4.0;
      colind[nnz] = index(i,j);
      nnz++;
 
      /* east */
      if (i == NUM - 2){
        rhs[index(i,j)] -= phi[NUM-1][j]; 
      }else{
        nzval[nnz] = 1.0;
        colind[nnz] = index(i+1,j);
        nnz++;
      } 
 
      /* north */
      if (j == NUM - 2){
        rhs[index(i,j)] -= phi[i][NUM - 1]; 
      }else{
        nzval[nnz] = 1.0;
        colind[nnz] = index(i,j+1);
        nnz++;
      } 
    }
  }
 
  /* last element of rowptr si nnz */
  rowptr[(NUM-2) * (NUM-2)] = nnz;
 
  /* solve with CG */
  k = solve_cg((NUM-2) * (NUM-2), nnz, nzval, colind, rowptr, sol, rhs, TOL);
  if (k < 0){
    printf("calculation failed\n");
    exit(-1);
  }
  printf("Number of Interation=%d\n",k);
 
  /* store solution to main aray */
  for (j = 1 ; j < NUM - 1 ; j++){
    for (i = 1 ; i < NUM - 1 ; i++){
      phi[i][j] = sol[index(i,j)];
    }
  }
 
  /* Output Result */
  fp = fopen("res.dat","w");
  if (fp == NULL){
    printf("File could not create\n");
    exit(-1);
  }
 
  for (i = 0 ;i < NUM ; i++){
    for (j = 0 ; j < NUM ; j++){
      x = -1.0 + 2.0 * (double)i / (double)(NUM - 1);
      y = -1.0 + 2.0 * (double)j / (double)(NUM - 1);
      fprintf(fp,"%e %e %e\n",x,y,phi[i][j]);
    }
  }
  fclose(fp);
 
  printf("Done\n");
}
 
/* index for interior Points */
int index(int ii,int jj){
  return ii - 1 + (NUM - 2) * (jj - 1);
}

cg.c