### Solving large sparse indefinite systems

Posted:

**Wed Feb 26, 2020 5:11 am**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

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