[petsc-users] Advise on choice of iterative solver

[Klaus Zimmermann]

On 06/08/2011 02:51 PM, Matthew Knepley wrote:
> On Wed, Jun 8, 2011 at 7:34 AM, Klaus Zimmermann
> <klaus.zimmermann at physik.uni-freiburg.de
> <mailto:klaus.zimmermann at physik.uni-freiburg.de>> wrote:
>
>     Hi Jed, Hi Matthew,
>
>     thanks for your quick responses!
>
>     On 06/08/2011 02:23 PM, Jed Brown wrote:
>      > On Wed, Jun 8, 2011 at 14:17, Matthew Knepley <knepley at gmail.com
>     <mailto:knepley at gmail.com>
>      > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>>> wrote:
>      >
>      >     However, you might look at Elemental
>      >     (http://code.google.com/p/elemental/) which solves the complex
>      >     symmetric eigenproblem and is very scalable.
>      >
>      >
>      > Note that Elemental is for dense systems.
>      >
>      >
>      > To solve your problem, it's important to know where it came from. The
>      > average number of nonzeros per row doesn't tell us anything about
>     it's
>      > mathematical structure which is needed to design a good solver.
>
>     We are doing quantum mechanical ab initio calculations. The Matrix
>     stems from a two particle Hamiltonian in a product basis. Thus we
>     have basis vectors S_{nm}. The sparseness is now due to the fact
>     that the matrix element <S_{nm}|H|S_{n'm'}> can only be non-zero if
>     |n-n'|<4 and |m-m'|<4.
>
>     Does this help or do you need more information? Like the matrix
>     construction code?
>
>
> This does not just sound sparse, it sounds banded. Is this true? If so,
> you can use dense, banded solvers instead.

Well, yes. Actually this is how it was done initially. However due to 
the product structure and another extension we want to do later this 
proved prohibitive in terms of memory usage.

Klaus