Chebyshev method to solve the time-dependent Maxwell equations.

De Raedt H, Michielsen K, Kole JS, Figge MT (2003) Chebyshev method to solve the time-dependent Maxwell equations. In: Computer simulation studies in condensed-matter physics XV, pp. 211-215.Springer-Verlag Berlin Heidelberg.

Abstract

We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from unconditionally stable algorithms and demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite- difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.

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doi: 10.1007/978-3-642-55522-0_26