NESTED ITERATION AND FIRST-ORDER SYSTEMS LEAST SQUARES FOR A TWO-FLUID ELECTROMAGNETIC DARWIN MODEL

摘要

In this paper, a two-fluid plasma (TFP) model is presented. The model couples the conservation of momentum and conservation of number density of both ions and electrons to Maxwell's equations. A Darwin approximation of Maxwell is used to eliminate spurious light waves from the model. After scaling and modification, the TFP-Darwin model yields a nonlinear, first-order system of equations whose Frechet derivative is shown to be uniformly H-1-elliptic in a neighborhood of the exact solution. This system is addressed numerically by nested iteration (NI) and a first-order system least squares discretization. An important goal of NI is to produce an approximation that is within the basin of attraction for Newton's method on a relatively coarse mesh and, thus, on all subsequent meshes. H-1 ellipticity yields optimal finite element performance and linear systems amenable to solution with algebraic multigrid. Numerical tests demonstrate the efficacy of this approach, yielding an approximate solution within discretization error in a relatively small number of computational work units.