Thanks for your helpful comments, Jed, Matt, and Mark. They've given me some things to think about, so I'll work on those then open a new email thread when I have further questions. --Matt
-------------------------------------------------------------- Matthew Young Graduate Student Boston University Dept. of Astronomy -------------------------------------------------------------- ________________________________________ From: Jed Brown [[email protected]] Sent: Monday, June 08, 2015 1:10 PM To: Young, Matthew, Adam; Matthew Knepley Cc: petsc-users Subject: Re: [petsc-users] Guidance on GAMG preconditioning "Young, Matthew, Adam" <[email protected]> writes: > This is a problem from ionospheric plasma physics. The simulation > treats ions via a particle-in-cell method and electrons as an > inertialess fluid, the justification being that ionospheric ions are > 10^4 times more massive than electrons. We further assume that the > plasma is effectively neutral on the length scale of interest > (i.e. quasi-neutral) and those assumptions allows us to write an > elliptic equation for the electrostatic potential, phi: Div[n(x) T > Grad(phi)]. n(x) is the quasi-neutral plasma density, which is updated > via an ion gather at each time step, and T is a tensor of constant > coefficients that looks like {{1, kappa, 0},{-kappa, 1, 0},{0, 0, > 1+kappa^2}}, where kappa is the ratio of gyrofrequency to collision > frequency for electrons (~100 for our problem)*. It seems to me that the nonsymmetric part of T is not an elliptic contribution so with your large value of kappa, you should think of this problem as a singular perturbation. Consequently, there is no reason to believe that methods designed for elliptic problems will work for your problem (especially not "out of the box").
