[petsc-users] FieldSplit and Biot's poroelasticity

[Lawrence Mitchell]

On 13/12/16 16:50, Karin&NiKo wrote:
> Dear Petsc-gurus,
> 
> I am solving Biot's poroelasticity problem :
>  Images intégrées 1
> 
> I am using a mixed P2-P1 finite element discretization.
> 
> I am using the fieldsplit framework to solve the linear systems. Here
> are the options I am using :
> -pc_type fieldsplit
> -pc_field_split_type schur
> -fieldsplit_0_pc_type gamg
> -fieldsplit_0_pc_gamg_threshold -1.0
> -fieldsplit_0_ksp_type gmres
> -fieldsplit_0_ksp_monitor
> -fieldsplit_1_pc_type sor
> -fieldsplit_1_ksp_type gmres
> -pc_fieldsplit_schur_factorization_type upper
> 
> 
> By increasing the mesh size, I get increasing numbers of outer
> iterations.
> 
> According to your own experience, among all the features of
> fieldsplit, was is the "best" set of preconditioners for this rather
> classical problem  in order to get an extensible solver (I would like
> to solve this problem on some tens millions of unknowns of some
> hundreds of procs)?

Here's a recent preprint that develops a three-field formulation of
the problem that gets reasonably mesh and parameter-independent
iteration counts using block-diagonal preconditioning.

https://arxiv.org/abs/1507.03199

(No need for schur complements)

If you can create the relevant blocks it should be implementable with
-pc_fieldsplit_type additive


Lawrence

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