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This chapter, as a continuation of Chap.  7 , will present the fast multipole methods for wave source interaction in layered media. The key mathematical foundations include multipole expansion (ME) and local expansion (LE) for wave sources embedded in layered media, extending the ME/LE for free space based on the addition theory of Bessel functions discussed in Sect.  7.4 . For Green’s functions in layered media corresponding to wave interactions in a layered setting, a plane wave representation of the Green’s function is used to derive the ME/LE and their translation operators.

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Fast Multipole Methods for Wave Interactions in Layered Media

  • 章节

  • 发表日期：

    2025年

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  • Wei Cai

摘要

This chapter, as a continuation of Chap.  7 , will present the fast multipole methods for wave source interaction in layered media. The key mathematical foundations include multipole expansion (ME) and local expansion (LE) for wave sources embedded in layered media, extending the ME/LE for free space based on the addition theory of Bessel functions discussed in Sect.  7.4 . For Green’s functions in layered media corresponding to wave interactions in a layered setting, a plane wave representation of the Green’s function is used to derive the ME/LE and their translation operators.