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yf yap February 3, 2001 06:31

advice needed in solving linear system
 
dear sirs:

in solving a 2 dimensional poisson equation, i obtained a set of linear equations in the following form:

C1*phi[i,j] + C2*phi[i+1,j] + C3*phi[i-1,j] + C4*phi[i,j+1] + C5*phi[i,j-1] = B[i,j] -[1]

C1 is always the largest. for all the equations,

C1 = C2 + C3 + C4 + C5 ----------- [2]

when this set of equations is solved using SOR, it is found that the solutions diverge slowly.

Questions: 1) how to avoid divergent in solving all those equations?

2) does [2] still imply strongly diagonally dominance ?

any advice would be greatly appreciated, thanks.

regards, yfyap

John C. Chien February 3, 2001 20:16

Re: advice needed in solving linear system
 
(1). First of all, the coefficients C1, C2, C3, C4 and C5 will all have effect on the results. (2). I would just create a five-point template problem, and check out the SOR result. You could do the hand calculations to look at the result of each iteration. Naturally, with the appropriate boundary conditions applied. (3). If the phi values are known at the boundary, then you should be able to get the solution quickly. If gradient type of b.C.'s is used, it will take longer to converge. But I guess, you can try different under-relaxation parameter values. But you still need to know the behavior of the coefficients.

John C. Chien (Alter Ego) February 4, 2001 19:24

Re: advice needed in solving linear system
 
Check out the book:

Templates for the Solution of Linear Systems in the resource section. I found it useful. You might also try some different solvers like CGSTAB, maybe even start with a brute force algorithm which always converges to see if you have set up your problem correctly.

Abhijit Tilak February 4, 2001 23:32

Re: advice needed in solving linear system
 
hi,

u will run in to trouble if C1,C2,... turn out to be negative(there are caes where they may go negative). just check that. Consider using Line Sor(LSOR) or ADI that will acclerate convergence. BTW from ur past postings looks like ur posting ur classroom course assignment questions on this forum eh? u may also consider under-relaxing as jhon said (SUR) hope that helps abhijit

yf yap February 5, 2001 00:21

Re: advice needed in solving linear system
 
thanks, John. regards, yfyap

yf yap February 5, 2001 00:21

Re: advice needed in solving linear system
 
dear abhijit, your valuable advice is greatly appreciated. please note that i'm not posting my assignments in this forum. for the previous postings, i feel that it is necessary for me to decribe my situations properly so that experts like your guys can have a better view of the situation. thanks. regards, yfyap


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