- Main
A fourth-order adaptive mesh refinement solver for Maxwell's Equations
- Chilton, Sven
- Advisor(s): Colella, Phillip;
- Morse, Edward
Abstract
We present a fourth-order accurate, multilevel Maxwell solver, discretized
in space with a finite volume approach and advanced in time with the
classical fourth-order Runge Kutta method (RK4). Electric fields are
decomposed into divergence-free and curl-free parts; we solve for the
divergence-free parts of Faraday's Law and the Amp\`ere-Maxwell Law
while imposing Gauss' Laws as initial conditions. We employ a damping
scheme inspired by the Advanced Weather Research and Forecasting
Model to eliminate non-physical waves reflected off of coarse-fine
grid boundaries, and Kreiss-Oliger artificial dissipation to remove standing
wave instabilities. Surprisingly, artificial dissipation appears to damp the
spuriously reflected waves at least as effectively as the atmospheric
community's damping scheme.
Main Content
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