Asymptotic expansions of the Helmholtz equation solutions using approximations of the Dirichlet to Neumann operator

Souaad Lazergui, Yassine Boubendir

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This work uses first and second order approximations of this operator to derive new asymptotic expressions of the normal derivative of the total field. The resulting expansions can be used to appropriately choose the ansatz in the design of high-frequency numerical solvers, such as those based on integral equations, in order to produce more accurate approximation of the solutions around the shadow and the deep shadow regions than the ones based on the usual ansatz.

Original languageEnglish (US)
Pages (from-to)767-786
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume456
Issue number2
DOIs
StatePublished - Dec 15 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Asymptotic analysis
  • Dirichlet to Neumann operator
  • Wave equation

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