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The Ultra Weak Variational Formulation Using Bessel Basis Functions

Published online by Cambridge University Press:  20 August 2015

Teemu Luostari ,
Tomi Huttunen  and
Peter Monk
Teemu Luostari*
Affiliation:
Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland
Tomi Huttunen*
Affiliation:
Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland
Peter Monk*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
*
Corresponding author.Email:teemu.luostari@uef.fi
Email address:tomi.huttunen@uef.fi
Email address:monk@math.udel.edu
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Abstract

We investigate the ultra weak variational formulation (UWVF) of the 2-D Helmholtz equation using a new choice of basis functions. Traditionally the UWVF basis functions are chosen to be plane waves. Here, we instead use first kind Bessel functions. We compare the performance of the two bases. Moreover, we show that it is possible to use coupled plane wave and Bessel bases in the same mesh. As test cases we shall consider propagating plane and evanescent waves in a rectangular domain and a singular 2-D Helmholtz problem in an L-shaped domain.

Keywords

02.60.Cb02.60.Lj02.70.Dh43.20.-fThe ultra weak variational formulationHelmholtz problemplane wave basisBessel basisnon-polynomial basis

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Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 400 - 414
Copyright
Copyright © Global Science Press Limited 2012

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