Yes, My problem is originally dense. That's why I used LAPACK to solve the equation. After some sparsifications, when the problem becomes sparse, I use sparse solvers. As I wrote, I have successfully used direct sparse solvers using other packages and now I am moving to iterative solvers using PETSc. I expected ILU preconditioner to be inappropriate for my needs and that explains slow convergence. I printed out number of iterations and also normalized residual and in slowest case the number of iterations was ~470 and the residual was 6.04524e-5. I experienced faster convergence but with higher residual 0.0005. The solution is also quite inaccurate in most cases and I guess the residual is still high. That's what I guess and the remedy can be using a better preconditioner. As I said, my problem is badly conditioned and this can be observed by plotting eigenvalues spectrum which is not clustered at all and therefore results to a high condition number.
Thanks, D. On Mon, 2011-05-09 at 19:57 +0200, Jed Brown wrote: > On Mon, May 9, 2011 at 19:06, Danesh Daroui <danesh.daroui at ltu.se> > wrote: > Thanks for the tip, but I already have two different version > of my > solver with PARDISO and MUMPS. Sparse Direct Solvers gave us a > great > contribution but I need to move to O(n^2) time complexity, So > I really > need to employ iterative solvers! :) > > I'm confused. Is your problem dense? If so, then it doesn't make sense > to use sparse solvers. If it is sparse, then the asymptotics for a > direct solver are O(n^{3/2}) flops and O(n log n) space in two > dimensions and O(n^2) flops and O(n^{4/3}) spare in three dimensions. > > > You can still use PETSc, but sparse preconditioners won't help you. In > particular, ILU is just a really crappy direct solver if you use it on > a dense matrix. Are there preconditioners for your problem in the > literature? Can it be done with a hierarchical method like FMM?