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 hong December 28, 2000 09:00

ICCG convergence case

Hi,

Incomplete Cholesky Conjugate gradient (ICCG) is known as a powerful tool to solve the linear equations. I have used ICCG(0) to solve the pressure poisson eqiarions very successfully. But now I faced one problem in unstuctured grid, the conjugate gradient with Jacobi preconditioner converges successfully, but the ICCG(0) always diverges, I doubted that maybe one must use ICCG (1) or ICCG(2)in some special cases to get converged results due to the fact that the iterarion matrix is not well behaviored in some senses. Any commnets about this problem are appreciated.

Ps. ICCG(N) means the fill-in of entries in the incomplete cholesky decompositio by point.

Hong

 Sebastien Perron December 28, 2000 10:37

Re: ICCG convergence case

I had convergence problems with the conjugate gradient with Jacobi preconditioner for solving the poisson equation on 3D unstructered Grid. But I have never had such problems with these algorithms:

-GMRES -Orthomin(2)

Sorry, but I have no experience with ICCG

 Ghanshyam Singh December 28, 2000 14:28

Re: ICCG convergence case

How many inner iterations you are giving. Try reducing the number of inner iterations and tell me your experience.

GS

Re: ICCG convergence case

solution solution solution is solution

 hong December 29, 2000 06:38

Re: ICCG convergence case

Hi,

I don't get your points by 'inner iterarion'. firstly I suppose this is a linear problem, secondly, in ICCG the iteration procedure is well defined, there is nothing you can make change about the algorithm.

Hongliang

 hong December 29, 2000 06:41

Re: ICCG convergence case

Thanks a lot

Hongliang

 Doug December 29, 2000 12:51

Re: ICCG convergence case

Two thoughts:

(1) For a central differenced structured grid solution of the pressure equation your matrix will be symmetric and ICCG should work well.

Is your matrix still symmetric with an unstructured grid? If not, that may be your problem. Cholesky factorization and CG are designed for symmetric matrices. Other gradient-based solvers (GMRES, Orthomin, CGS, BiCG-Stab, etc.) are designed to handle nonsymmetric matrices and should work better as someone else suggested.

(2) If a gradient based method is failing, that can mean your preconditioner is not effectively reducing the condition number of the matrix (and may be making it worse). The fact that Jacobi preconditioning converges doesn't make it seem that your matrix is too stiff, however.

If you have a nonsymmetric matrix, you'll probably want to do an ILU(N) with GMRES, CGS, etc. Hopefully, that will do the trick.

 hong December 30, 2000 06:44

Re: ICCG convergence case

Hi,

I totally agree with what you have said. I have checked my code which has a bug leading to the unsymmetry of the matrix, after curing the bug, the ICCG works perfectly.

From this experience, I also learned that the conjugate gradient with Jacobi preconditioner can work in kind of slightly unsymmetric matrix. but this is almost uselss information because we don't in which kind of unsymmetry it will work.

Thanks a lot

Hongliang

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