[petsc-users] BiCGSTAB for general use

[Jed Brown]

On Sun, Aug 14, 2011 at 06:18, Paul Anton Letnes <
paul.anton.letnes at gmail.com> wrote:

> I believe of the first kind - there is. Our approach is to discretize the
> integral equation. The equations we are "really solving" are the Maxwell
> equations.
>

Is this the sort of system you're working with?

http://link.aps.org/doi/10.1103/PhysRevLett.104.223904

Note that the system has the form

J_H(x_\parallel | \omega) = J_H(x_\parallel | \omega)_{inc} + \int (...) G(x
| x') J_H(x_\parallel' | \omega) + \int (...) G(x | x') J_E(x_\parallel' |
\omega)

which is the form of a second order integral equation. I assume the incident
field J_H(...)_{inc} is known in this equation. If you dropped the term on
the left hand side in this equation, you would have a Fredholm integral
equation of the first kind to "solve", which is problematic at a
mathematical level due to ill-posedness.


>
> I have downloaded and attempted to use a different BiCGSTAB code. It
> converges, but only after several hundred (about 400) for a very small (not
> physically interesting) problem. It would appear that if we are to get good
> performance, some form of preconditioning is necessary.
>

Do the eigenvalues decay quickly? Can you plot some eigenvalues? They should
decay rapidly to a positive value like (with appropriate scaling) 1.
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