[petsc-users] Question about preconditioner

[Pierre Jolivet]

> On 16 Feb 2023, at 8:43 AM, user_gong Kim <ksi2443 at gmail.com> wrote:
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> Hello,
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> There are some questions about some preconditioners.
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> The questions are from problem Au=b. The global matrix A has zero value diagonal terms.
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> 1.     Which preconditioner is preferred for matrix A which has zero value in diagonal terms?
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This question has not a single answer. It all depends on where your A and b are coming from.

> The most frequently used basic 2 preconditioners are jacobi and SOR (gauss seidel).
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They are not the most frequently used. And rightfully so, as they very often can’t handle non-trivial systems.

> As people knows both methods should have non zero diagonal terms. Although the improved method is applied in PETSc, jacobi can also solve the case with zero diagonal term, but I ask because I know that it is not recommended.
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> 2.     Second question is about running code with the two command options below in a single process.
> 1st command : -ksp_type gmres -pc_type bjacobi -sub_pc_type jacobi
> 2nd command : -ksp_type gmres -pc_type hpddm -sub_pc_type jacobi
> When domain decomposition methods such as bjacobi or hpddm are parallel, the global matrix is divided for each process. As far as I know, running it in a single process should eventually produce the same result if the sub pc type is the same. However, in the second option, ksp did not converge.
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1st command: it’s pointless to couple PCBJACOBI with PCJABOCI, it’s equivalent to only using PCJABOBI.
2nd command: it’s pointless to use PCHPDDM if you don’t specify in some way how to coarsen your problem (either algebraically or via an auxiliary operator). You just have a single level (equivalent to PCBJACOBI), but its options are prefixed by -pc_hpddm_coarse_ instead of -sub_
Again, both sets of options do not make sense.
If you want, you could share your A and b (or tell us what you are discretizing) and we will be able to provide a better feedback.

Thanks,
Pierre

> In this case, I wonder how to analyze the situation.
> How can I monitor and see the difference between the two?
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> Thanks,
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> Hyung Kim
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