On Oct 24, 2013, at 3:09 PM, Jon Alm Eriksen <jon.alm.erik...@gmail.com> wrote:
> Bad news I guess, in the end I need to scale up my system. So close! > Anyways, if I try your suggestion, will it matter if I formulate a > vector equation with four components, rather that a coupled set of > four equations, for the issue you mention. Or is there any distinction > in the implementation of vector equation vs. coupled equation? Thanks for asking that. I had forgotten, but I believe the vector formulation works fine, whereas a pair of scalars does not. This is confusing because the two implementations should be doing the same thing. > I understand that iterations are necessary for a non-linear equation. > But if I solve a linear equation, is there any reason for iterating > with the LinearLUSolver? Or is there a newtons method algorithm in the > solver that converges on the first step for linear problems with the > solve method? At the end of the day, I only care about residuals for > my application, but I would like to know what goes on behind the > curtains. Hopefully Wheeler can weigh in. The non-linearities are really a question of sweeping, not iterating, and that applies equally to all solvers. At the moment, I can't remember what it was about the LU that benefited from iterating, but it does matter and I'm not confident anymore that it has anything to do with non-linearities. I vaguely recall that it may be more to do with normalization of the matrix, where large coefficients will dominate the direct solve, but iteration picks up the effect of the small matrix entries. I'm probably just making things up at this point, though. _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
