[petsc-users] Code performance for solving multiple RHS

[Barry Smith]

  Effectively utilizing multiple right hand sides with the same system can result in roughly 2 or at absolute most  3 times  improvement in solve time. A great improvement but when you have a million right hand sides not a giant improvement. 

  The first step is to get the best (most efficient) preconditioner for you problem. Since you have many right hand sides it obviously pays to spend more time building the preconditioner so that each solve is faster. If you provide more information on your linear system we might have suggestions.  CFD so is your linear system a Poisson problem? Are you using geometric or algebraic multigrid with PETSc? It not a Poisson problem how can you describe the linear system?

  Barry



> On Aug 10, 2016, at 9:54 PM, Harshad Ranadive <harshadranadive at gmail.com> wrote:
> 
> Hi All,
> 
> I have currently added the PETSc library with our CFD solver. 
> 
> In this I need to use KSPSolve(...) multiple time for the same matrix A. I have read that PETSc does not support passing multiple RHS vectors in the form of a matrix and the only solution to this is calling KSPSolve multiple times as in example given here:
> http://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/examples/tutorials/ex16.c.html
> 
> I have followed this technique, but I find that the performance of the code is very slow now. I basically have a mesh size of 8-10 Million and I need to solve the matrix A very large number of times. I have checked that the statement KSPSolve(..) is taking close to 90% of my computation time.
> 
> I am setting up the matrix A, KSPCreate, KSPSetup etc just once at the start. Only the following statements are executed in a repeated loop
> 
> Loop begin: (say million times !!)
> 
>    loop over vector length
>        VecSetValues( ....)
>    end
> 
>    VecAssemblyBegin( ... )
>    VecAssemblyEnd (...)
> 
>     KSPSolve (...)
> 
>     VecGetValues
> 
> Loop end.
> 
> Is there an efficient way of doing this rather than using KSPSolve multiple times?
> 
> Please note my matrix A never changes during the time steps or across the mesh ... So essentially if I can get the inverse once would it be good enough?  It has been recommended in the FAQ that matrix inverse should be avoided but would it be okay to use in my case?
> 
> Also could someone please provide an example of how to use MatLUFactor and MatCholeskyFactor() to find the matrix inverse... the arguments below were not clear to me.
> IS row 
> IS col
> const MatFactorInfo *info
> 
> Apologies for a long email and thanks to anyone for help.
> 
> Regards
> Harshad
> 
> 
> 
> 
>