Mannually specify a diagonal matrix as a preconditioner?

[Shi Jin]

Hi there,

I am trying to solve a mass matrix linear system by KSPSolve. Right now, I am passing the mass matrix itself (let's call it M) to KSPSetOperators() as the Pmat argument. In order to speed up the convergence, I have constructed the lumped mass matrix (named lumpedM). For a linear finite element, this is simply a diagonal matrix with entries equal to the sum of the row on M. It is a common practice to replace M with lumpedM to have faster convergence without losing the order of accuracy.

What I want to do is to still solve the M matrix but use lumpedM to precondition it. This way hopefully the number of iterations would be greatly reduced. In Petsc code, I tried

 ierr = KSPSetOperators( solMP, M, lumpedM, SAME_PRECONDITIONER);

However, instead of giving faster convergence, it actually takes more iterations to convergence than the regular one. Therefore, I wonder if setting lumpedM as Pmat is the correct way to do it. Could you please advice? I think right now lumpedM is taken as the input to compute the preconditioning matrix, using whatever method is specified by -pc_type . What I really want to do is to simply set lumpedM as the precondition matrix, without spending time to compute anything.
Thank you very much.

Shi






--
Shi Jin, PhD




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