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<p>We show that the acoustic Green’s function for a half-space impedance problem in arbitrary spatial dimension <i>d</i> can be written as a sum of three terms, each of which is the product of an exponential function with the <i>eikonal</i> in the argument and a <i>slowly varying</i> function. We introduce the notion of families of slowly varying functions to formulate this statement as a theorem and present its proof.</p>

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Factorization of the Green’s function of high-frequency acoustic half-space impedance problems

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • C. Lin,
  • J. M. Melenk,
  • S. Sauter

摘要

We show that the acoustic Green’s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of three terms, each of which is the product of an exponential function with the eikonal in the argument and a slowly varying function. We introduce the notion of families of slowly varying functions to formulate this statement as a theorem and present its proof.