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. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110814/8ecdebc0/attachment.htm>
