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

Document Type

Article

Publication Date

12-15-2017

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.

Identifier

85026213237 (Scopus)

Publication Title

Journal of Mathematical Analysis and Applications

External Full Text Location

https://doi.org/10.1016/j.jmaa.2017.07.047

e-ISSN

10960813

ISSN

0022247X

First Page

767

Last Page

786

Issue

2

Volume

456

Grant

DMS-1319720

Fund Ref

National Science Foundation

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