Dissertation/Thesis Abstract

A fourth-order adaptive mesh refinement solver for Maxwell's Equations
by Chilton, Sven, Ph.D., University of California, Berkeley, 2013, 142; 3616542
Abstract (Summary)

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 Ampère-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.

Indexing (document details)
Advisor: Colella, Phillip, Morse, Edward
Commitee: Wurtele, Jonathan, van Bibber, Karl
School: University of California, Berkeley
Department: Nuclear Engineering
School Location: United States -- California
Source: DAI-B 75/08(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Nuclear engineering, Electromagnetics
Keywords: Advanced weather research and forecasting model, Finite volume approach, Fourth-order, Maxwell's equations, Mesh refinement solver, Runge kutta method
Publication Number: 3616542
ISBN: 978-1-303-83390-8
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