[petsc-users] Guidance on GAMG preconditioning

Young, Matthew, Adam may at bu.edu
Mon Jun 8 12:25:34 CDT 2015

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.

Matthew Young
Graduate Student
Boston University Dept. of Astronomy

From: Jed Brown [jed at jedbrown.org]
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" <may at bu.edu> 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").

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