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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Lazergui, Souaad^1,2  Boubendir, Yassine¹ 

[1] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

[2] Univ Mostaghanem, Dept Pure & Appl Math, BP 188, Mostaganem 27000, Algeria

关键词: Wave equation;    Dirichlet to Neumann operator;    Asymptotic analysis;   

DOI  :  10.1016/j.jmaa.2017.07.047

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free