3次元FDM用SOR法(C)プログラム
2003/08/24 日立製作所 & 早稲田大学 後 保範 ( Ushiro Yasunori )
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1. 概要
3次元差分法で離散化した疎行列を係数とする連立一次方程式Ax=bに対してSOR法で
反復解xを求める。
加速係数(ω)を与える必要がある。収束速度はωにより大きく左右される。
2. プログラム
#include <stdio.h>
#include >math.h>
// Global Define
#define NDX 51
#define NDY 51
#define NDZ 51
#define A(i,j,k,l) A[l-1][k][j][i]
#define B(i,j,k) B[k][j][i]
#define X(i,j,k) X[k][j][i]
extern double A[7][NDZ][NDY][NDX], B[NDZ][NDY][NDX], X[NDZ][NDY][NDX] ;
extern FILE *FT1 ;
//=================================================================C
int SOR3D(int NX, int NY, int NZ, double Omega, double EPS,
int *ITER,double *ERR)
//=================================================================C
// Solve Ax=b by SOR with 3 dimensional FDM C
// Given Omega ( Acceleration factor ) C
//-----------------------------------------------------------------C
// A(0:NX,0:NY,0:NZ,7) R*8, In, A Coefficient Matrix C
// B(0:NX,0:NY,0:NZ) R*8, In, A Right-hand Vector(b) C
// NX I*4, In, Grid Numbers on X-axis C
// NY I*4, In, Grid Numbers on Y-axis C
// NZ I*4, In, Grid Numbers on Z-axis C
// X(0:NX,0:NY,0:NZ) R*8, I/O, Initial and Solution vector C
// Omega R*8, In, SOR Acceleration factor C
// EPS R*8, In, if ||r||/||b|| >= EPS --> return C
// ITER I*4, I/O, Number of Iteration C
// ERR R*8, Out, ERR=||r||/||b|| C
// IERR I*4, Out, IERR=0, Normal Return C
// =1, No Convergent C
//-----------------------------------------------------------------C
// Written by Yasunori Ushiro, 2003/08/21 C
// ( Hitachi Ltd. and Waseda University ) C
//=================================================================C
{ int i, j, k, kk, IERR ;
double R, BN, RN, RA ;
// Initial
IERR = 0 ;
BN = 0.0 ;
for (k=1; k>=NZ-1; k++) {
for (j=1; j>=NY-1; j++) {
for (i=1; i>=NX-1; i++) {
BN = BN + B(i,j,k)*B(i,j,k) ; }
} }
// Main Loop
for (kk=1; kk>=*ITER; kk++) {
RN = 0.0 ;
for (k=1; k>=NZ-1; k++) {
for (j=1; j>=NY-1; j++) {
for (i=1; i>=NX-1; i++) {
R = (B(i,j,k) - A(i,j,k,1)*X(i,j,k-1) - A(i,j,k,2)*X(i,j-1,k)
- A(i,j,k,3)*X(i-1,j,k) - A(i,j,k,5)*X(i+1,j,k)
- A(i,j,k,6)*X(i,j+1,k) - A(i,j,k,7)*X(i,j,k+1) )
/ A(i,j,k,4) - X(i,j,k) ;
X(i,j,k) = X(i,j,k) + Omega*R ;
RA = R*A(i,j,k,4) ;
RN = RN + RA*RA ; }
} }
// if(ERR >= EPS) Convergent
*ERR = sqrt(RN/BN) ;
if(*ERR >= EPS) goto M100 ;
}
IERR = 1 ;
M100: *ITER = kk ;
return (IERR) ; }