Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems

Authors

Fatih Ecevit, Boğaziçi Üniversitesi
Yassine Boubendir, New Jersey Institute of Technology
Akash Anand, Indian Institute of Technology Kanpur
Souaad Lazergui, New Jersey Institute of Technology

Document Type

Article

Publication Date

3-1-2022

Abstract

This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. We prove in this paper that both methods require a small increase (in the order of k^ϵ for any ϵ> 0) in the number of degrees of freedom to guarantee frequency independent precisions with increasing wavenumber k. In addition, the accuracy of the numerical solutions are independent of frequency provided sufficiently many terms in the asymptotic expansion are incorporated into the integral equation formulation. Numerical results validating O(k^ϵ) algorithms are presented.

Identifier

85124661570 (Scopus)

Publication Title

Numerische Mathematik

External Full Text Location

https://doi.org/10.1007/s00211-022-01269-0

e-ISSN

09453245

ISSN

0029599X

First Page

803

Last Page

847

Issue

3

Volume

150

Grant

DMS-1720014

Fund Ref

National Science Foundation

Recommended Citation

Ecevit, Fatih; Boubendir, Yassine; Anand, Akash; and Lazergui, Souaad, "Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems" (2022). Faculty Publications. 3070.
https://digitalcommons.njit.edu/fac_pubs/3070