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Sample Usage

In this section, several examples using NSPCG to solve a sample matrix problem are given.

Example 1:

In this example, NSPCG was used to solve the linear system Ax=bwhich resulted from discretizing the problem

$\begin{displaymath}\left\{\begin{array}{cc} u_{xx} + 2u_{yy} = 0 & \mbox{on S $... ... \\ u = 1 + xy & \mbox{on boundary of S} \end{array} \right. \end{displaymath}$

using the standard 5-point central finite difference formula with a mesh size of $h = \frac{1}{11}$ . The finite difference stencil at node (i,j) is thus

6u_i,j-u_i-1,j-u_i+1,j-2u_i,j+1-2u_i,j-1 = 0

This resulted in a symmetric and positive definite matrix of order 100 with five nonzero diagonals. Symmetric diagonal storage was used to represent the matrix. Thus, only the main diagonal and the two nonzero super-diagonals were stored so MAXNZ =3. Also, the JCOEF vector was (0,1,10). The iterative method used was the Modified Incomplete Cholesky (MIC) method with conjugate gradient acceleration. The computer used to run the program was a Cyber 170/750 and the compiler used was FTN5. The program to generate the matrix data and the output resulting from this call to NSPCG is given below:

      PROGRAM MAIN (OUTPUT,TAPE6=OUTPUT)
C
C ... ARRAY DECLARATIONS.
C
      REAL COEF(120,4), RHS(100), U(100), WKSP(600), UBAR(1),
     A     RPARM(30)
      INTEGER JCOEF(4), IWKSP(300), IPARM(30), P(1), IP(1)
      EXTERNAL CG, MIC2
C
      NDIM = 120
      MDIM = 4
      NW = 600
      INW = 300
C
C ... GENERATE COEF, JCOEF, AND RHS.
C
      NX = 10
      NY = 10
      N = NX*NY
      H = 1.0/FLOAT(NX + 1)
      MAXNZ = 3
      DO 10 I = 1,N 
         COEF(I,1) = 6.0
         COEF(I,2) = -1.0
         COEF(I,3) = -2.0
         RHS(I) = 0.0
 10   CONTINUE
      K = 0
      DO 30 J = 1,NY
         Y = FLOAT(J)*H
         DO 25 I = 1,NX
            X = FLOAT(I)*H
            K = K + 1
            IF (J .EQ. 1) THEN
               RHS(K) = RHS(K) + 2.0
            ENDIF
            IF (J .EQ. NY) THEN
               RHS(K) = RHS(K) + 2.0*(1.0 + X)
               COEF(K,3) = 0.0
            ENDIF
            IF (I .EQ. 1) THEN
               RHS(K) = RHS(K) + 1.0
            ENDIF
            IF (I .EQ. NX) THEN
               RHS(K) = RHS(K) + 1.0 + Y
               COEF(K,2) = 0.0
            ENDIF
 25      CONTINUE
 30   CONTINUE
      JCOEF(1) = 0
      JCOEF(2) = 1
      JCOEF(3) = NX 
      CALL DFAULT (IPARM,RPARM)
C
C ... NOW, RESET SOME DEFAULT VALUES.
C
      IPARM(2) = 50 
      IPARM(3) = 3
      RPARM(1) = 1.0E-8
C
C ... GENERATE AN INITIAL GUESS FOR U AND CALL NSPCG.
C
      CALL VFILL (N,U,0.0)
C
      CALL NSPCG (MIC2,CG,NDIM,MDIM,N,MAXNZ,COEF,JCOEF,P,IP,
     A            U,UBAR,RHS,WKSP,IWKSP,NW,INW,IPARM,RPARM,IER)
      STOP
      END

INITIAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 2 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 0 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 2 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 2 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .00000000E+00 (TIMFAC) RPARM(14) = .00000000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF ) INITIAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 50 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-07 (ZETA ) RPARM( 2) = .20000000E+01 (EMAX ) RPARM( 3) = .10000000E+01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .00000000E+00 (TIMIT ) RPARM( 7) = .00000000E+00 (DIGIT1) RPARM( 8) = .00000000E+00 (DIGIT2) RPARM( 9) = .10000000E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .00000000E+00 (SPECR )
CG INTERMEDIATE OUTPUT AFTER EACH ITERATION ITERATION CONVERGENCE EMAX EMIN N S TEST 0 0 .99366E+01 .20000E+01 .10000E+01 1 1 .46168E-01 .10010E+01 .10010E+01 2 2 .57189E-02 .20232E+01 .10002E+01 3 3 .12255E-02 .24807E+01 .10001E+01 4 4 .23770E-03 .27522E+01 .10000E+01 5 5 .49325E-04 .28711E+01 .10000E+01 6 6 .87776E-05 .29024E+01 .10000E+01 7 7 .16811E-05 .29071E+01 .10000E+01 8 8 .42316E-06 .29074E+01 .10000E+01 9 9 .15339E-06 .29075E+01 .10000E+01 10 10 .38502E-07 .29075E+01 .10000E+01 11 11 .71532E-08 .29076E+01 .10000E+01 CG HAS CONVERGED IN 11 ITERATIONS
FINAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 11 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-07 (ZETA ) RPARM( 2) = .29076287E+01 (EMAX ) RPARM( 3) = .10000004E+01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .34800000E+00 (TIMIT ) RPARM( 7) = .81454998E+01 (DIGIT1) RPARM( 8) = .78457903E+01 (DIGIT2) RPARM( 9) = .10000000E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .00000000E+00 (SPECR ) FINAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 2 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 0 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 1 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 2 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .22000000E-01 (TIMFAC) RPARM(14) = .51200000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF )
Example 2:

In this example, the same problem was solved but primary storage format was used. Thus all five nonzero diagonals were stored. The iterative method used was the Reduced System (RS) method with conjugate gradient acceleration. To use this method, a red-black coloring was applied to the mesh with the REDBLK facility. Since NSPCG must permute the matrix, the P and IP vectors had to be dimensioned to the problem size. The program to generate the matrix data and the output resulting from this call to NSPCG is given below:

PROGRAM MAIN (OUTPUT,TAPE6=OUTPUT) C C ... ARRAY DECLARATIONS. C REAL COEF(120,5), RHS(100), U(100), WKSP(600), UBAR(1), A RPARM(30) INTEGER JCOEF(120,5), IWKSP(300), IPARM(30), P(100), IP(100) EXTERNAL CG, RS6 C NDIM = 120 MDIM = 5 NW = 600 INW = 300 C C ... GENERATE COEF, JCOEF, AND RHS. C NX = 10 NY = 10 N = NX*NY H = 1.0/FLOAT(NX + 1) MAXNZ = 5 DO 10 I = 1,N COEF(I,1) = 6.0 COEF(I,2) = -1.0 COEF(I,3) = -2.0 COEF(I,4) = -1.0 COEF(I,5) = -2.0 JCOEF(I,1) = I JCOEF(I,2) = I + 1 JCOEF(I,3) = I + NX JCOEF(I,4) = I - 1 JCOEF(I,5) = I - NX RHS(I) = 0.0 10 CONTINUE K = 0 DO 40 J = 1,NY Y = FLOAT(J)*H DO 35 I = 1,NX X = FLOAT(I)*H K = K + 1 IF (J .EQ. 1) THEN RHS(K) = RHS(K) + 2.0 COEF(K,5) = 0.0 JCOEF(K,5) = 0 ENDIF IF (J .EQ. NY) THEN RHS(K) = RHS(K) + 2.0*(1.0 + X) COEF(K,3) = 0.0 JCOEF(K,3) = 0 ENDIF IF (I .EQ. 1) THEN RHS(K) = RHS(K) + 1.0 COEF(K,4) = 0.0 JCOEF(K,4) = 0 ENDIF IF (I .EQ. NX) THEN RHS(K) = RHS(K) + 1.0 + Y COEF(K,2) = 0.0 JCOEF(K,2) = 0 ENDIF 35 CONTINUE 40 CONTINUE CALL DFAULT (IPARM,RPARM) C C ... NOW, RESET SOME DEFAULT VALUES. C IPARM(3) = 3 IPARM(12) = 1 IPARM(14) = 1 IPARM(23) = 0 C C ... GENERATE AN INITIAL GUESS FOR U AND CALL NSPCG. C CALL VFILL (N,U,0.0) C CALL REDBLK (NDIM,N,MAXNZ,COEF,JCOEF,P,IP,1,IWKSP,IER) CALL NSPCG (RS6,CG,NDIM,MDIM,N,MAXNZ,COEF,JCOEF,P,IP, A U,UBAR,RHS,WKSP,IWKSP,NW,INW,IPARM,RPARM,IER) STOP END
INITIAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 1 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 1 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 2 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 0 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .00000000E+00 (TIMFAC) RPARM(14) = .00000000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF ) INITIAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 100 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-05 (ZETA ) RPARM( 2) = .20000000E+01 (EMAX ) RPARM( 3) = .10000000E+01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .00000000E+00 (TIMIT ) RPARM( 7) = .00000000E+00 (DIGIT1) RPARM( 8) = .00000000E+00 (DIGIT2) RPARM( 9) = .10000000E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .00000000E+00 (SPECR )
CG INTERMEDIATE OUTPUT AFTER EACH ITERATION ITERATION CONVERGENCE EMAX EMIN N S TEST 0 0 .58026E+01 .20000E+01 .10000E+01 1 1 .43389E+00 .63392E+00 .63392E+00 2 2 .39789E+00 .86043E+00 .29993E+00 3 3 .52881E+00 .92756E+00 .15453E+00 4 4 .36826E+00 .97104E+00 .98805E-01 5 5 .20966E+00 .98764E+00 .83754E-01 6 6 .80236E-01 .99236E+00 .80254E-01 7 7 .26052E-01 .99496E+00 .79652E-01 8 8 .16576E-01 .99605E+00 .79530E-01 9 9 .70079E-02 .99698E+00 .79406E-01 10 10 .23601E-02 .99731E+00 .79383E-01 11 11 .12251E-02 .99754E+00 .79377E-01 12 12 .41032E-03 .99777E+00 .79374E-01 13 13 .14115E-03 .99785E+00 .79374E-01 14 14 .44531E-04 .99795E+00 .79374E-01 15 15 .13200E-04 .99802E+00 .79374E-01 16 16 .51949E-05 .99804E+00 .79374E-01 17 17 .12208E-05 .99806E+00 .79374E-01 18 18 .24719E-06 .99807E+00 .79374E-01 CG HAS CONVERGED IN 18 ITERATIONS
FINAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 18 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-05 (ZETA ) RPARM( 2) = .99806941E+00 (EMAX ) RPARM( 3) = .79373655E-01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .31900000E+00 (TIMIT ) RPARM( 7) = .66069656E+01 (DIGIT1) RPARM( 8) = .71292805E+01 (DIGIT2) RPARM( 9) = .10000000E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .00000000E+00 (SPECR ) FINAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 1 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 1 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 2 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 0 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .00000000E+00 (TIMFAC) RPARM(14) = .53800000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF )
Example 3:

In this example, the same problem was solved using the Line SOR method with line red-black ordering. To use this method, a line red-black coloring was applied to the mesh with the COLOR facility. Since NSPCG must permute the matrix, the P and IP vectors had to be dimensioned to the problem size. The matrix was stored in the symmetric diagonal storage format. Note that even though only three nonzero diagonals were stored, it was necessary to dimension the COEF and JCOEF arrays to be large enough to store the permuted matrix. The program to generate the matrix data and the output resulting from this call to NSPCG is given below:

PROGRAM MAIN (OUTPUT,TAPE6=OUTPUT) C C ... ARRAY DECLARATIONS. C REAL COEF(120,5), RHS(100), U(100), WKSP(600), UBAR(1), A RPARM(30) INTEGER JCOEF(5), IWKSP(300), IPARM(30), P(100), IP(100) INTEGER PATT(2) EXTERNAL SOR, SOR7 C NDIM = 120 MDIM = 5 NW = 600 INW = 300 C C ... GENERATE COEF, JCOEF, AND RHS. C NX = 10 NY = 10 NZ = 1 N = NX*NY H = 1.0/FLOAT(NX + 1) MAXNZ = 3 DO 10 I = 1,N COEF(I,1) = 6.0 COEF(I,2) = -1.0 COEF(I,3) = -2.0 RHS(I) = 0.0 10 CONTINUE K = 0 DO 30 J = 1,NY Y = FLOAT(J)*H DO 25 I = 1,NX X = FLOAT(I)*H K = K + 1 IF (J .EQ. 1) THEN RHS(K) = RHS(K) + 2.0 ENDIF IF (J .EQ. NY) THEN RHS(K) = RHS(K) + 2.0*(1.0 + X) COEF(K,3) = 0.0 ENDIF IF (I .EQ. 1) THEN RHS(K) = RHS(K) + 1.0 ENDIF IF (I .EQ. NX) THEN RHS(K) = RHS(K) + 1.0 + Y COEF(K,2) = 0.0 ENDIF 25 CONTINUE 30 CONTINUE JCOEF(1) = 0 JCOEF(2) = 1 JCOEF(3) = NX CALL DFAULT (IPARM,RPARM) C C ... NOW, RESET SOME DEFAULT VALUES. C IPARM(3) = 3 IPARM(14) = 1 C C ... GENERATE AN INITIAL GUESS FOR U AND CALL NSPCG. C CALL VFILL (N,U,0.0) C NXP = 1 NYP = 2 NZP = 1 PATT(1) = 1 PATT(2) = 2 CALL COLOR (NXP,NYP,NZP,NX,NY,NZ,PATT,P) CALL NSPCG (SOR7,SOR,NDIM,MDIM,N,MAXNZ,COEF,JCOEF,P,IP, A U,UBAR,RHS,WKSP,IWKSP,NW,INW,IPARM,RPARM,IER) STOP END
INITIAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 2 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 1 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 2 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 2 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .00000000E+00 (TIMFAC) RPARM(14) = .00000000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF ) INITIAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 100 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-05 (ZETA ) RPARM( 2) = .20000000E+01 (EMAX ) RPARM( 3) = .10000000E+01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .00000000E+00 (TIMIT ) RPARM( 7) = .00000000E+00 (DIGIT1) RPARM( 8) = .00000000E+00 (DIGIT2) RPARM( 9) = .10000000E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .00000000E+00 (SPECR )
SOR INTERMEDIATE OUTPUT AFTER EACH ITERATION NUMBER OF CONVERGENCE EMAX OMEGA SPECTRAL ITERATIONS TEST RADIUS 0 0 .10000E+04 .20000E+01 .10000E+01 .00000E+00 1 0 .10000E+04 .20000E+01 .10000E+01 .61609E+00 2 0 .60559E+00 .20000E+01 .10000E+01 .63475E+00 3 0 .65576E+00 .20000E+01 .10000E+01 .77061E+00 4 0 .67933E+00 .91212E+00 .10000E+01 .83197E+00 5 1 .67933E+00 .91212E+00 .14185E+01 .14752E+01 6 1 .67933E+00 .91212E+00 .14185E+01 .10876E+01 7 1 .67933E+00 .91212E+00 .14185E+01 .77707E+00 8 1 .36291E+00 .91212E+00 .14185E+01 .71832E+00 9 1 .23778E+00 .91212E+00 .14185E+01 .69934E+00 10 1 .10202E+00 .91212E+00 .14185E+01 .69195E+00 11 1 .69782E-01 .91212E+00 .14185E+01 .68947E+00 12 1 .47922E-01 .91212E+00 .14185E+01 .68862E+00 13 1 .32945E-01 .91212E+00 .14185E+01 .68826E+00 14 1 .22660E-01 .91212E+00 .14185E+01 .68813E+00 15 1 .14844E-01 .94045E+00 .14185E+01 .68808E+00 16 2 .14844E-01 .94045E+00 .14926E+01 .74939E+00 17 2 .14844E-01 .94045E+00 .14926E+01 .74302E+00 18 2 .14844E-01 .94045E+00 .14926E+01 .65901E+00 19 2 .27382E-02 .94045E+00 .14926E+01 .61710E+00 20 2 .15091E-02 .94045E+00 .14926E+01 .59201E+00 21 2 .83411E-03 .94045E+00 .14926E+01 .57533E+00 22 2 .45715E-03 .94045E+00 .14926E+01 .56343E+00 23 2 .24843E-03 .94045E+00 .14926E+01 .55452E+00 24 2 .13395E-03 .94045E+00 .14926E+01 .54759E+00 25 2 .71687E-04 .94045E+00 .14926E+01 .54206E+00 26 2 .38156E-04 .94045E+00 .14926E+01 .53753E+00 27 2 .20202E-04 .94045E+00 .14926E+01 .53376E+00 28 2 .10645E-04 .94045E+00 .14926E+01 .53057E+00 29 2 .55865E-05 .94045E+00 .14926E+01 .52784E+00 30 2 .29208E-05 .94045E+00 .14926E+01 .52547E+00 31 2 .15221E-05 .94045E+00 .14926E+01 .52339E+00 32 2 .79083E-06 .94045E+00 .14926E+01 .52156E+00 SOR HAS CONVERGED IN 32 ITERATIONS
FINAL ITERATIVE PARAMETERS GENERAL AND ACCELERATION PARAMETERS IPARM( 1) = 2 (NTEST ) IPARM( 2) = 32 (ITMAX ) IPARM( 3) = 3 (LEVEL ) IPARM( 4) = 6 (NOUT ) IPARM( 5) = 0 (IDGTS ) IPARM( 6) = 1 (MAXADP) IPARM( 7) = 1 (MINADP) IPARM( 8) = 1 (IOMGAD) IPARM( 9) = 5 (NS1 ) IPARM(10) = 100000 (NS2 ) IPARM(11) = 0 (NS3 ) RPARM( 1) = .10000000E-05 (ZETA ) RPARM( 2) = .94045018E+00 (EMAX ) RPARM( 3) = .10000000E+01 (EMIN ) RPARM( 4) = .75000000E+00 (FF ) RPARM( 5) = .75000000E+00 (FFF ) RPARM( 6) = .52100000E+00 (TIMIT ) RPARM( 7) = .61019185E+01 (DIGIT1) RPARM( 8) = .63177121E+01 (DIGIT2) RPARM( 9) = .14926136E+01 (OMEGA ) RPARM(10) = .00000000E+00 (ALPHAB) RPARM(11) = .25000000E+00 (BETAB ) RPARM(12) = .52156493E+00 (SPECR ) FINAL ITERATIVE PARAMETERS PREPROCESSOR AND PRECONDITIONER PARAMETERS IPARM(12) = 2 (NSTORE) IPARM(13) = 0 (ISCALE) IPARM(14) = 1 (IPERM ) IPARM(15) = 1 (IFACT ) IPARM(16) = 0 (LVFILL) IPARM(17) = 0 (LTRUNC) IPARM(18) = 1 (IPROPA) IPARM(19) = -1 (KBLSZ ) IPARM(20) = -1 (NBL2D ) IPARM(21) = 1 (IFCTV ) IPARM(22) = 1 (IQLR ) IPARM(23) = 2 (ISYMM ) IPARM(24) = 0 (IELIM ) IPARM(25) = 1 (NDEG ) RPARM(13) = .50000000E-02 (TIMFAC) RPARM(14) = .75100000E+00 (TIMTOT) RPARM(15) = .35500000E-11 (TOL ) RPARM(16) = .00000000E+00 (AINF )

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