64
Views
0
CrossRef citations to date
0
Altmetric
Articles

Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances

ORCID Icon
Pages 3841-3857 | Received 11 Jan 2022, Accepted 09 Feb 2022, Published online: 03 Mar 2022
 

Abstract

The 2D canonical case of a semi-circular canyon is addressed via two types of boundary-integral equations (BIE) methods which are shown, via Galerkin procedures, to lead to matrix equations with kernels that vanish at two different sets of (what appear as resonant) frequencies. This physically impossible result is interpreted as being the sign that the two BIE methods are generally defective and that the resonances are ‘spurious’. This ‘disease’ is cured by combining two BIE's into one which gives rise to a closed-form solution identical to the exact separation-of-variables solution devoid of resonances.

2020 Mathematics Subject Classification:

Disclosure statement

No potential conflict of interest by the author.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.