2次元FDM用CG法NO.1(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
2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CG法で
反復解xを求める。
α=(p,r)/(p,Ap),β=-(r,Ap)/(p,Ap)を使用した、直交性に比較的強いバージョン
2. プログラム
#include <stdio.h>
#include <math.h>
// Global Define
#define NDX 301
#define NDY 301
#define A(i,j,l) A[l-1][j][i]
#define B(i,j) B[j][i]
#define X(i,j) X[j][i]
#define R(i,j) R[j][i]
#define P(i,j) P[j][i]
#define Q(i,j) Q[j][i]
extern double A[3][NDY][NDX], B[NDY][NDX], X[NDY][NDX] ;
extern double R[NDY][NDX], P[NDY][NDX], Q[NDY][NDX] ;
extern FILE *FT1 ;
//=================================================================C
int CG2D1(int NX, int NY, double EPS, int *ITER, double *ERR)
//=================================================================C
// Solve Ax=b by CG NO.1 with 2 dimensional FDM C
// Alpha=(P,R)/(P,AP), Beta=-(R,AP)/(P,AP) C
//-----------------------------------------------------------------C
// NX I*4, In, Grid Numbers on X-axis C
// NY I*4, In, Grid Numbers on Y-axis 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
// return 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, IERR ;
double BN, RN, C, Alpha, Beta ;
// P=R=B-A*X
IERR = 0 ;
BN = 0.0 ;
for (j=1; j<=NY-1; j++) {
for (i=1; i<=NX-1; i++) {
BN = BN + B(i,j)*B(i,j) ;
R(i,j) = B(i,j) - A(i,j,1)*X(i,j-1) - A(i,j,2)*X(i-1,j)
- A(i,j,3)*X(i,j) - A(i+1,j,2)*X(i+1,j)
- A(i,j+1,1)*X(i,j+1) ;
P(i,j) = R(i,j) ; }
}
// Main Loop
for (k=1; k<=*ITER; k++) {
// Q=A*P, C=(P,Q), Alpha=(P,R)/C
C = 0.0 ;
Alpha = 0.0 ;
for (j=1; j<=NY-1; j++) {
for (i=1; i<=NX-1; i++) {
Q(i,j) = A(i,j,1)*P(i,j-1) + A(i,j,2)*P(i-1,j)
+ A(i,j,3)*P(i,j) + A(i+1,j,2)*P(i+1,j)
+ A(i,j+1,1)*P(i,j+1) ;
C = C + P(i,j)*Q(i,j) ;
Alpha = Alpha + P(i,j)*R(i,j) ; }
}
Alpha = Alpha/C ;
// X=X+Alpha*P, R=R-Alpha*Q
RN = 0.0 ;
Beta = 0.0 ;
for (j=1; j<=NY-1; j++) {
for (i=1; i<=NX-1; i++) {
X(i,j) = X(i,j) + Alpha*P(i,j) ;
R(i,j) = R(i,j) - Alpha*Q(i,j) ;
RN = RN + R(i,j)*R(i,j) ;
Beta = Beta + R(i,j)*Q(i,j) ; }
}
// if(ERR <= EPS) Convergent, Beta=-(R,Q)/(P,Q)
*ERR = sqrt(RN/BN) ;
if(*ERR <= EPS) goto M100 ;
Beta = -Beta/C ;
// P=R+Beta*P
for (j=1; j<=NY-1; j++) {
for (i=1; i<=NX-1; i++) {
P(i,j) = R(i,j) + Beta*P(i,j) ; }
}
}
IERR = 1 ;
//
M100: *ITER = k ;
return (IERR) ; }