From: Langou, Julien
Date: Thu, 6 Jun 2013 12:17:06 -0600
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
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
I hope the hints are useful.
From: <Viebahn>, "J.P."
Date: Tuesday, June 4, 2013 2:42 PM
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,
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