Solving Helmholtz equation at high wave numbers in exterior domains

Kun Wang, Yau Shu Wong and Jizu Huang

Applied Mathematics and Computation, 2017, vol. 298, issue C, 221-235

Abstract: This paper presents effective difference schemes for solving the Helmholtz equation at high wave numbers. Considering the problems in the polar and spherical coordinates, we show that pollution-free difference schemes can be constructed for annulus and hollow sphere domains, but the “pollution effect” cannot be avoided in the neighborhood of the origin of the coordinate. Using the fact that the “pollution effect” appears in a small neighborhood of the origin of the coordinate, we propose a local mesh refinement approach so that a fine grid is applied only for a small region near the origin of the coordinate and a much larger grid size is employed in the remaining domain. The most attractive feature of this approach is that the computational storage can be significantly reduced while keeping almost the same numerical accuracy. Moreover, by applying a two-level local refinement technique, we can further enhance the performance of the proposed scheme. Numerical simulations are reported to verify the effectiveness of the proposed schemes for the Helmholtz problem in exterior domains.

Keywords: Helmholtz equation; High wave number; Local refinement; Polar and spherical coordinates; Pollution-free scheme (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031630683X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:298:y:2017:i:c:p:221-235

DOI: 10.1016/j.amc.2016.11.015

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().