Re: [Libmesh-users] Repeatedly solving a linear system

[Vikram G. <vik...@ma...>]

Hey Vetter,
                  There is an example of reusing the preconditioner in
example 26. The steps are as follows:

1) Get the linear solver object:
LinearSolver<Number> *linear_solver = system.get_linear_solver();

2) Set the reuse preconditioner flag:
linear_solver->reuse_preconditioner(bool flag_value);

Hope that speeds things up a bit.

Thanks.

On Tue, Nov 29, 2011 at 11:51 AM, Vetter Roman <vet...@et...> wrote:
>
> Hi folks
>
> I'm using NewmarkSystem with PetscLinearSolver to solve M*a(t) + C*v(t) + K(t)*u(t) = f(t) in each time step. M and C are fixed, and the changes in K are very small (only 0-3 element contributions change between consecutive time steps). So, since I'm solving this millions of times for large systems in parallel, and the performance seems to be pretty bad when compared to other FEM software solving similar problems, I'm looking for a way to speed things up. The time dependence of K (and f for that matter) is absolutely minor, so I would like to reuse as many precomputed data as possible in the linear solver. Reusing the preconditioner and the current solution seems a good start. But there is probably lots of other work that can be skipped when almost the same system is solved again.
>
> What of the following is supported by libMesh, and how can I enable it?
> - Reusing the same preconditioner
> - Starting from the solution in the previous time step instead of zeros
> - Reusing other data in the solver, like decomposition matrices, etc.
> - Avoiding making copies of matrices, vectors, and destroying them again after the solve
> - Further optimizations for small changes?
>
> I'm using PETSc 3.2-p5 and libMesh 0.7.2 (both in optimized mode, in case turning off debug mode for better performance comes to mind).
>
> I've been looking at PetscLinearSolver::solve() a bit and some of the mentioned optimizations seem at least possible, but it's also somewhat messy to get to understand what exactly is copied where and which preconditioner is used by default etc. from the various nested function calls. I'm hoping somebody who's more experienced with the interplay between libMesh and PETSc can give me a hint. I'm not using any fancy stuff like boundary conditions, subset solving or the like, just a plain bulk with slightly evolving stiffnesses and forces, that needs to be solved many many times.
>
> Any advice is much appreciated!
>
> Roman
>
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--
Vikram Garg
PhD Candidate
Institute for Computational and Engineering Sciences
The University of Texas at Austin
http://users.ices.utexas.edu/~vikram/
http://www.runforindia.org/runners/vikramg