[petsc-users] Linear system solvers for unsymmetrical matrix

[Smith, Barry F.]

  Normally for pressure Poisson's with standard discretizations such as finite differences, finite elements/volumes multigrid (either geometric or algebraic depending on the circumstances) is absolutely the go to method and it is rare to have a reason to use something else.

  For SPH you will need to do a literature search to see what is viable for solving the pressure Poisson. Intuitively for very large problems you will need a hierarchical solver (like multigrid) that takes advantage of the elliptic nature of the problem. Simple arguments about communication of information seem to indicate that solvers such as conjugate gradient with Jacobi preconditioner will not scale for large problems.

   Barry




> On Dec 25, 2017, at 8:11 AM, 我 <dayedut123 at 163.com> wrote:
> 
> Thanks for your reply. My research is focused on the in-compressible SPH which is kind of particle method in CFD and I want to solve the pressure Poisson's equation during the computation. I think the PDE is an elliptic one. The matrix size is as large as possible. For now, the problem is just 2 dimension and the number of unknowns is about 250,000. But in the future, it will expand to 3D and the number of unknowns will be millions. In addition, choosing the suitable preconditioner should be another key factor for the iterative algorithm, would you mind providing me some suggestions about it ?
> Thank you again!
> Daye
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> At 2017-12-25 19:56:31, "Smith, Barry F." <bsmith at mcs.anl.gov> wrote:
> >
> >  Most of the linear solvers in PETSc are suitable for non symmetric problems. You should not use KSPCG, KSPCR or PCCHOLESKY since they are only for symmetric problems.
> >
> >   Finding the best solver for your problem depends on your problem and how large a problem you want to solve. Please tell use as much as possible 
> >
> >1) where the comes from, for example CFD, structural mechanics, etc
> >
> >2) if it comes from an elliptic, parabolic, or hyperbolic PDE
> >
> >and 
> >
> >3) how large a problem you need to solve, 100,000 unknowns, 10 million, a billion?
> >
> >   Barry
> >
> >
> >> On Dec 25, 2017, at 12:17 AM, 我 <dayedut123 at 163.com> wrote:
> >> 
> >> Hello,
> >> I want to use PETSC to solve an unsymmetrical matrix. I find many linear system solvers in PETSC. But I don't know which one is suitable for the unsymmetrical matrix. I want to choose the best solver for my problem. Would you mind give me some alternative solvers for the unsymmetrical matrix in PETSC?
> >> Thank you very much!
> >> Daye
> >> 
> >> 
> >>  
> >
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