[SciPy-User] solving large sparse linear system with Laplacian matrix

Jonathan Guyer guyer@nist....
Fri Oct 30 16:35:50 CDT 2009

On Oct 30, 2009, at 2:35 PM, Gael Varoquaux wrote:

> The problem Emmanuelle has here really is solving an anistropic  
> diffusion
> equation on a big grid. This can be seen as a PDE problem.

Sure, that's what it sounded like.

> Do you have
> any suggestions on good linear algebra or iterative options to do this
> with Python?

The suggestions that have already been offered would be what I would  
try; either GMRES (although that's broken in PySparse) or PyAMG.  
Depending on the problem, PyTrilinos might offer some advantageous  
preconditioners, but at substantial up-front installation cost.

> We have not looked at FiPy so far, as it seems tedious to
> formulate the problem in PDE terms.

If you choose to, an anisotropic diffusion equation is no big deal  
(we've got an example in the manual). N=1e6 is also no challenge,  
although because FiPy is something of a memory hog, that would be  
pushing the capacity of a 2 gig machine. We don't have any facilities  
for multiple RHS vectors, though.

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