Subroutine FASTSOLVE2

Solves the matrix equation AX = B using the iterative biconjugate gradient method, where X is the output vector. The matrix A is created from the contents of arrays icd and cond.

Calling convention:

call fastsolv(icd,cond,icond,itype,isink,par,ierr,x,b)
Arguments Data type Input/Output Description
icd Integer array (2,icond) Call

Input array of length icond that contains the connected element numbers of the conductances specified in cond.

  • icd(1,n) is the first element of the I'th conductance.
  • icd(2,n) is the second element of the I'th conductance.
cond Real array (icond) Call Conductance value.
itype Integer array (icond) Call

Specifies conductances type.

A value of –1 indictaes that it is a 1-way conductance (only the first element is affected).

A value > 0 implies a regular conductance.
icond Integer Call The number of conductances in cond.
isink Integer array (icond) Call If isink(i)=1 then elementiis a boundary condition and takes on the value b(i).
ierr Integer Return Error flag. Set to 1 on error, else set to 0.
par Real array (20) Both Parameters related to solution. For more information, see the parameter table.
x Real array Return The output vector. The array must be greater than the highest element number in array icd.
b Real array Call The right side input vector. The array must be greater than the highest element number in array icd. Contains sink values on input.

Parameter table

Parameter number Parameter description
1 The input initial fill-in value estimate for the preconditioning matrix.

The ILUT preconditioning method is used.

  • apr(1) = 0 defaults to 7. If convergence is not achieved, the fill-in value is updated in increments of 10 until convergence is achieved.
  • par(1) = -1 uses the Jacobi preconditioner, where the preconditioning matrix consists of the inverse of the diagonal of the matrix A.
2 The input tolerance value specified for eliminating small terms in the

preconditioning matrix. par(2) = 0 defaults to .0001.
3 The input convergence criterion. The solution is considered

converged if norm(AX-B)/norm(B)< par (3), or if the par (10) convergence criterion is fulfilled.

par (3) = 0 defaults to 1.E-8.
4 The input maximum number of iterations. par(4) = 0 defaults to 200.
5 The input flag that prints the convergence residual value to the verbose log file and to the screen. par(5) = 0 defaults to no residuals printed.
6 Reserved.
7 On return contains the value of the convergence residual.
8 On return contains the number of iterations completed.
9 An input flag to re-use the previously created preconditioning matrix on exit.

par(9) = 0 creates the preconditioning matrix.

par(9) = 1 uses the previously created preconditioning matrix in order to save CPU time.
10 Maximum number of outer loop iterations calling the Conjugate Gradient solver.
11 Input flag to increase performance for repeated re-entry.

par(11) = 1 improves performance by saving all temporary arrays (but not the matrix A) created internally for subsequent re-use.

par(11) = 0 does not save the arrays.
12 An input flag to increase performance for reported re-entry with the same matrix but different B.

par(12) = 1 saves all matrices, including the input matrix A created from icd, for subsequent calculations with another B vector.
13 Reserved.
14 Reserved.
15 Reserved.
16 Reserved.
17 Reserved.
18 Reserved.
19 Reserved.
20 Reserved.

The following example solves the matrix AX = B, where the matrices A and B are the following:

The matrix is entered as a sum of 3 conductances: G21 = 1, G12 = 1, and G11 = -1. The second conductance is specified as a 1-way conductance with ITYPE(2) = -1, such that only row 1 is affected, not row 2.

Example:

subroutine user1(gg,t,c,q,qd,r,time,dt,it,
+kode,nocon,maxno,iconv,dum1,dum2,dtp,tf)
dimension t(*),x(4),b(4),par(20),icd(2,2)
dimension cond(2), isink(2),itype(3)
save
data par,x,b,isink,itype/24*0.0,5*0/
icond=3
icd(1,1)=2
icd(2,1)=1
cond(1)=1
icd(1,2)=1
icd(2,2)=2
cond(2)=1
itype(2)=-1
icd(1,3)=1
icd(2,3)=1
cond(3)=-1
b(1)=100
call fastsolve2(icd,cond,icond,itype,isink,par,ierr,x,b)
t(1)=x(1)
t(2)=x(2)
return
end