Nested Iteration and First-Order Systems Least Squares for a Two-Fluid Electromagnetic Darwin Model

Abstract

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 $\mathcal{H}^1$-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. $\mathcal{H}^1$ 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...