[petsc-users] Matrix Construction Question

[Jack Poulson]

On Tue, Jun 28, 2011 at 5:20 PM, Adam Byrd <adam1.byrd at gmail.com> wrote:

> Jack,
>
> I'm a summer intern just getting started with this project, so I don't know
> all the details yet (I can ask though). I know I need to find the Green's
> function which will involve the trace of the inverted Hamiltonian, as well
> as the rest of the matrix. I have inquired about avoiding the inversion
> altogether, but my instructor doesn't believe there is a way around it. Once
> I've worked through the math I want to explore other options though.
>
> Respectfully,
> Adam
>
>

Ah, it's not a discretized Hamiltonian, not a Hamiltonian matrix (
http://en.wikipedia.org/wiki/Hamiltonian_matrix).  For 2d problems, there is
a nice approach for efficiently computing the trace of the inverse here:
http://www.ma.utexas.edu/users/lexing/publications/siscpar.pdf. For 3d
problems it is more difficult and I'm not sure what the best approach is.

Jack
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