Asymmetric matrix solving on parallel incompressible computation

songyi719 · March 7, 2023, 07:17

Hello, I am trying several matrix solvers on incompressible steady-state flow, and currently using GAMG

I found this thread saying that for parallel computation, PBiCGstab with DILU as preconditioner performs best for pressure

How to choose solvers

However, when I try to implement by myself, according to log, error occurs because my matrix is symmetric while DILU is for asymmetric.

I guess this error occurs because decomposePar seperates mesh into several parts and each processor runs n x n matrix where n is # of cell, while what thread wanted is decomposed N x N matrix into many asymmetric matrix calculation.

How can I change my matrix solver work so? Or is it best to just replace it with DIC preconditioner?

dlahaye · March 7, 2023, 15:02

The post you refer to does distinguish between the incompressible and compressible case.

In the incompressible case, the pressure matrix is symmetric and positive definite in both the sequential and parallel decomposed case.

The advice is to use CG as Krylov solver in both the sequential and parallel decomposed case. The preconditioner should be adapted with the number of subdomains becomes large.

The advice is to use GAMG as preconditioner in case of one or a small number of processors. The advice is to replace GAMG by a preconditioner for symmetric matrices such as DIC (as you suggest) in case that the number of subdomains is large.

More precise statements depend on the version of GAMG used (PETSC4FOAM or AMGX).

songyi719 · March 7, 2023, 20:48

Thanks for the reply!

Is there reference paper about matrix solvers? I would like to know

dlahaye · March 8, 2023, 03:41

https://netlib.org/templates/templates.pdf

https://www-users.cse.umn.edu/~saad/...Book_2ndEd.pdf

and references cited therein

March 7, 2023, 07:17	Asymmetric matrix solving on parallel incompressible computation	#1
songyi719 Member Song Young Ik Join Date: Apr 2022 Location: South Korea Posts: 59 Rep Power: 4	Hello, I am trying several matrix solvers on incompressible steady-state flow, and currently using GAMG I found this thread saying that for parallel computation, PBiCGstab with DILU as preconditioner performs best for pressure How to choose solvers However, when I try to implement by myself, according to log, error occurs because my matrix is symmetric while DILU is for asymmetric. I guess this error occurs because decomposePar seperates mesh into several parts and each processor runs n x n matrix where n is # of cell, while what thread wanted is decomposed N x N matrix into many asymmetric matrix calculation. How can I change my matrix solver work so? Or is it best to just replace it with DIC preconditioner?

March 7, 2023, 15:02		#2
dlahaye Senior Member Domenico Lahaye Join Date: Dec 2013 Posts: 798 Blog Entries: 1 Rep Power: 17	The post you refer to does distinguish between the incompressible and compressible case. In the incompressible case, the pressure matrix is symmetric and positive definite in both the sequential and parallel decomposed case. The advice is to use CG as Krylov solver in both the sequential and parallel decomposed case. The preconditioner should be adapted with the number of subdomains becomes large. The advice is to use GAMG as preconditioner in case of one or a small number of processors. The advice is to replace GAMG by a preconditioner for symmetric matrices such as DIC (as you suggest) in case that the number of subdomains is large. More precise statements depend on the version of GAMG used (PETSC4FOAM or AMGX). songyi719 likes this. Last edited by dlahaye; March 7, 2023 at 15:03. Reason: improved

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March 7, 2023, 20:48		#3
songyi719 Member Song Young Ik Join Date: Apr 2022 Location: South Korea Posts: 59 Rep Power: 4	Thanks for the reply! Is there reference paper about matrix solvers? I would like to know

March 8, 2023, 03:41		#4
dlahaye Senior Member Domenico Lahaye Join Date: Dec 2013 Posts: 798 Blog Entries: 1 Rep Power: 17	https://netlib.org/templates/templates.pdf https://www-users.cse.umn.edu/~saad/...Book_2ndEd.pdf and references cited therein