The University of Southampton
University of Southampton Institutional Repository

Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation

Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation
Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation
Numerical solutions of the Helmholtz equation suffer from pollution effect especially for higher wavenumbers. The major cause for this is the dispersion error which is defined as the relative phase difference between the numerical solution of the wave and the exact wave. The dispersion error for the meshless methods can be a priori determined at an interior source node assuming that the potential field obeys a harmonic evolution with the numerical wavenumber.

In this paper, the dispersion errors, in the solution of 2D Helmholtz equation, for two different meshless methods are investigated, the local boundary integral equation method and the radial basis integral equation method. Radial basis functions, with second order polynomials and frequency-dependent polynomial basis vectors are used for the interpolation of the potential field in both methods. The results have been found to be of comparable accuracy with other meshless approaches reported in the literature
helmholtz equation, eshless methods, dispersion error, pollution effect, LBIE, RBIE
0955-7997
360-371
Dogan, Hakan
a1e136a9-aab8-4942-a977-0ae3440758cc
Popov, Viktor
e4c470fd-8a77-43ee-84d4-8a3c95e4f4f3
Ooi, Ean Hin
63ebcf57-32be-471a-af96-57e3f01e5fe2
Dogan, Hakan
a1e136a9-aab8-4942-a977-0ae3440758cc
Popov, Viktor
e4c470fd-8a77-43ee-84d4-8a3c95e4f4f3
Ooi, Ean Hin
63ebcf57-32be-471a-af96-57e3f01e5fe2

Dogan, Hakan, Popov, Viktor and Ooi, Ean Hin (2015) Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation. Engineering Analysis with Boundary Elements, 50, 360-371. (doi:10.1016/j.enganabound.2014.09.009).

Record type: Article

Abstract

Numerical solutions of the Helmholtz equation suffer from pollution effect especially for higher wavenumbers. The major cause for this is the dispersion error which is defined as the relative phase difference between the numerical solution of the wave and the exact wave. The dispersion error for the meshless methods can be a priori determined at an interior source node assuming that the potential field obeys a harmonic evolution with the numerical wavenumber.

In this paper, the dispersion errors, in the solution of 2D Helmholtz equation, for two different meshless methods are investigated, the local boundary integral equation method and the radial basis integral equation method. Radial basis functions, with second order polynomials and frequency-dependent polynomial basis vectors are used for the interpolation of the potential field in both methods. The results have been found to be of comparable accuracy with other meshless approaches reported in the literature

This record has no associated files available for download.

More information

Accepted/In Press date: 17 September 2014
Published date: January 2015
Keywords: helmholtz equation, eshless methods, dispersion error, pollution effect, LBIE, RBIE
Organisations: Inst. Sound & Vibration Research

Identifiers

Local EPrints ID: 376827
URI: http://eprints.soton.ac.uk/id/eprint/376827
ISSN: 0955-7997
PURE UUID: ed6cf548-b156-44df-8d6e-05c93044e810

Catalogue record

Date deposited: 07 May 2015 09:01
Last modified: 14 Mar 2024 19:50

Export record

Altmetrics

Contributors

Author: Hakan Dogan
Author: Viktor Popov
Author: Ean Hin Ooi

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×