ICAP-2002 Abstracts and Posters

ICAP 2002 Abstracts and Posters

New methods for the numerical solution of Maxwell's equations

Abstract

We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We discuss a family of unconditionally stable algorithms, based on the Suzuki product-formula approach. We show that the convential Yee algorithm can be viewed as a Suzuki product-formula and propose two variants that do not require the use of the staggered-in-time grid. We also consider a one-step algorithm, based on the Chebyshev polynomial expansion, and compare the computational efficiency of the the one-step, the Yee-type, and the unconditionally stable algorithms. For applications where the long-time behavior is of main interest, we find that the one-step algorithm may be orders of magnitude more efficient than present multiple time-step, finite-difference time-domain algorithms.

H.De Raedt,K.Michielsen,J.S.Kole,M.T.Figge

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