[petsc-users] Slepc: Computing first 4 smallest eigenvalues and eigenvectors of a large graph Laplacian

[Bodhisatta Pramanik]

Hi,

I apologize for the slepc question. I could not find any user lists so I'm
hoping someone on here might be able to offer some guidance.

*Problem Definition:*
I am working on a graph partitioning problem. I have the laplacian of a
large graph(500,000 nodes) and am interested in extracting its global
information in order to find good partitioning. An approach is to compute
the first few(4-5) eigenvalues and use that information to formulate the
partition algorithm.

I am leveraging the EPS solvers of the Slepc library. It appears that the
Jacobi-davidson eigen solver gives me the eigenvalues in the shortest
period of time compared to others (Krylov-Schur, Rayleigh quotient,
Lanczos, etc). I use this eigensolver with the conjugate gradient linear
solver and the block-jacobi preconditioner. So this is what I am basically
passing through the command line:

./RunPart -eps_type jd -eps_nev 4 -st_ksp_type cg -st_ksp_rtol 0.001
-eps_tol 0.001 -st_pc_type bjacobi -eps_smallest_real

*Question:*
The time it takes to compute the first 4-5 eigenvectors of a matrix of size
(200k) is near about 60 seconds. CPU config: Intel Xeon 2GHz. I am using a
single processor to run my code. Is there any way I can gain major speedup
than what I am getting?

Is it possible to obtain the eigenvalues inside 10-15 seconds of such huge
matrices even if I do not use multiple processor??

Can someone provide me with some valuable guidance??

*Thanks,*
Bodhi
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