The recently introduced plane wave time-domain (PWTD) algorithm (A. A. Ergin, B. Shanker, and E. Michielssen, Journal of Computational Physics, vol. 146, no. 1, pp. 157-180, 1998) permits the efficient evaluation of linear wave fields due to bandlimited transient sources. In essence, PWTD schemes connstitute extensions of the frequency domain fast multipole method (Helmholtz equation) to the time domain (wave equation). PWTD algorithms already have been proven useful in the construction of fast time domain integral equation solvers and fast boundary kernels for finite difference/element grid truncation.
PWTD schemes developed to date target lossless 3D media. This presentation will outline their extension to dissipative media and two-dimensional geometries. PWTD schemes for such environmments, just like those for lossless 3D media, express wave fields as superpositions of plane waves. For lossy media, the Green function tail is efficiently modeled by evolving these plane waves through numerical solution of a 1D wave equations with dissipative term. In 2D environments, the Green function tail is accounted for by inserting a Hilbert transform in the plane wave expansions.
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