[petsc-users] Guidance on GAMG preconditioning

[Jed Brown]

"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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