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[Lapack] Poisson solver

Dear Jan,

However, you may want to give a shot to the LAPACK banded solver DPBSV. (The 
Poisson equation leads to a banded symmetric positive definite operator.)
You will need to allocate a data structure of size ( 256 * 256 * 256 ), this is 
not that bad. But this'll never scale. (I.e. When the size of the matrix gets 
larger, the
cost and memory requirement grows much faster.)

LAPACK does not support sparse matrices. The solution of choice for sparse 
matrices and direct solver would be to use a sparse direct solver like:
UMFPACK, MUMPS or superLU. There are more choices.

You can also use iterative methods. Multigrid methods work great for Poisson 
equation. You can google "Fast Poisson Solver" and see the related literature. 
DPBSV is general purpose. It'll decently work but cannot compete with a fast 
solver.

I hope the hints are useful.

Cheers,
Julien.


From: <Viebahn>, "J.P." 
<J.P.Viebahn@Domain.Removed<mailto:J.P.Viebahn@Domain.Removed>>
Date: Tuesday, June 4, 2013 2:42 PM
To: "lapack@Domain.Removed<mailto:lapack@Domain.Removed>" 
<lapack@Domain.Removed<mailto:lapack@Domain.Removed>>
Subject: [Lapack] Poisson solver

Dear LAPACK team,

I would like to solve a (2D) Poisson equation on a uniform grid of about 256 by 
256 points with a Dirichlet boundary condition.

That is, I want to solve a linear system with a sparse matrix that has size of 
about (256*256) by (256*256).

Could you tell which Lapack routine would be optimal (fast and precise) in this 
respect? Or where I can find documentation on that? That would be great.

Thanks in advance and best regards,

Jan Viebahn
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