[petsc-users] Poisson equation with CG and BoomerAMG

[Benjamin Sanderse]

Hello all,

I am solving a Poisson equation with Neumann BC on a structured grid (arising from an incompressible Navier-Stokes problem). Although my mesh is structured, the matrix is 'given' so I am using AMG instead of geometric multigrid, for the moment.
To solve the Poisson equation I use CG with preconditioning provided by BoomerAMG, using standard options. I have run my problem for different grid sizes and number of processors, but I am confused regarding the parallel scalability. Attached are some timing results that give the average time spent on solving the Poisson equation. As you can see, when going from 1 to 2 processors, the scaling is very good, even for the case of 200^3 grid points (8 million). For larger number of processors this quickly deteriorates. The cluster I am running on has 8 cores per node and 24GB memory per node. 
Can someone comment on these results? Is this what I should expect?

Some additional information:
- I set the NullSpace of the matrix explicitly with MatNullSpaceCreate
- The set-up of the problem is not included in the timing results. The set-up is not efficient yet (use of MatRow, for example), and there is some code cleanup to do (too many matrices and vectors), but I think this should not affect the performance of the Poisson solve.
- log_summary and ksp_monitor are attached. 

Thanks a lot,

Benjamin

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Ir. B. Sanderse
 
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