[petsc-users] incredibly good performance of scipy lgmres

[Florian Bruckner]

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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