[petsc-users] CG fails to converge in parallel

[Pierre Jolivet]

> On 20 Apr 2023, at 7:53 AM, Bojan Niceno <bojan.niceno.scientist at gmail.com> wrote:
> 
> Dear all,
> 
> 
> I am solving a Laplace equation with finite volume method on an unstructured grid with a Fortran code I have developed, and PETSc 3.19 library.
> 
> I first used cg solver with asm preconditioner, which converges nicely when executed sequentially, but fails for MPI parallel version.  I believed that there must be an error in which I set up and assemble parallel matrices for PETSc, but I soon noticed that if I use bicg with asm, everything works fine, the parallel bicg/asm shows almost the same convergence as sequential version.

KSPCG requires a symmetric PC.
By default, PCASMType is PC_ASM_RESTRICT, which yields a non-symmetric preconditioner.
With a single process, this does not matter, but with more than one process, it does.
If you switch to -pc_asm_type basic, KSPCG should converge.
That being said, for Laplace equation, there are much faster alternatives than PCASM, e.g., PCGAMG.

Thanks,
Pierre

> I could carry on with bicg, but I am still worried a little bit.  To my knowledge of Krylov solvers, which is admittedly basic since I am a physicist only using linear algebra, the convergence of bicg should be very similar to that of cg when symmetric systems are solved.  When I run my cases sequentially, I see that's indeed the case.  But in parallel, bicg converges and cg fails.
> 
> Do you see the above issues as an anomaly and if so, could you advise how to search for a cause?  
> 
> 
>     Kind regards,
> 
> 
>     Bojan
> 
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