[petsc-users] incredibly good performance of scipy lgmres

Pierre Seize pierre.seize at onera.fr
Wed Dec 9 10:34:15 CST 2020

I think that `callback` is called once for each outer cycle, and the 
default inner number of iterations is 30, so 30 x 5 = 150 iterations, it 
seems more realistic.

Pierre Seize

On 09/12/20 17:25, Stefano Zampini wrote:
> Could it be that scipy lgmres is reporting the wrong number of 
> iterations?
> I would try to replicate the scipy code first 
> https://github.com/scipy/scipy/blob/master/scipy/sparse/linalg/isolve/lgmres.py
> Il Mer 9 Dic 2020, 19:17 Florian Bruckner <e0425375 at gmail.com 
> <mailto:e0425375 at gmail.com>> ha scritto:
>     Dear PETSc developers,
>     I am currently re-implementing our FEM-BEM code using Firedrake.
>     The original code we were using is based on FEniCS and uses scipy
>     sparse solvers for the solution of the coupled FEM / BEM system.
>     For some reason the scipy lgmres method seems to outperform all
>     other methods which we tried. E.g. for the strayfield-calculation
>     of a 10x10x10 unit cube scipy-lgmres needs 5 iterations (without
>     preconditioner), whereas scipy-gmres needs 167. The new
>     implementation uses petsc-gmres and petsc-lgmres, but both need
>     around 170 iterations.
>     If I understand lgmres correctly it only improves convergence if
>     gmres is restarted. Since it only needs 5 iterations i think this
>     cannot be the reason. But nevertheless since the method seems to
>     perform very good, it would be worth looking at the differences in
>     detail. I provide the dense data of the system-matrix and
>     right-hand-side vector that I used, as well as scripts for the
>     different considered methods.
>     Any ideas how scipy-lgmres could be that good? It would be nice if
>     someone could validate my results (lgmres solves within 5
>     iterations). For me the next step will be to wrap scipy-lgmres
>     using petsc4py. I know how to do it with petsc4py directly, but I
>     am not exactly sure how it works with the firedrake interface.
>     best wishes
>     Florian

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