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Solving large sparse indefinite systems

Posted: Wed Feb 26, 2020 5:11 am
by berktaftali
Hi!

I’ve been testing GPU accelerated iterative solvers in Magma (2.5.1), but ran into a problem. A couple large sparse indefinite systems I picked from SuiteSparse matrix collection failed to converge to a solution (using unit RHS) no matter what solver & preconditioner I used. I had no issues solving similar but positive definite matrices from the same suite.

The main goal here is to figure out the best solver & preconditioner for direct integration time history analyses on finite element models of buildings/bridges etc. Such problems can easily lead to indefinite/ill conditioned systems in presence of geometric/material nonlinearity, hence the need for an indefinite solver.

A simple example successfully solving the following matrix would be deeply appreciated:

https://sparse.tamu.edu/Schenk_AFE/af_shell10

Thanks!

Berk

Re: Solving large sparse indefinite systems

Posted: Mon Aug 17, 2020 4:29 pm
by Stan Tomov
Hello,
Just checking if you found a solution to this proble.
MAGMA uses a default initial guess of 0, i.e., the RHS.
I checked this particular matrix with matlab and looks like the rank of the Krylov space starting with ones remain 2, so the space ramains limited and non of the Krylov methods converge (with this starting vector).
You can try to change the initial guess or the RHS.
Thanks,
Stan