Commun. Comput. Phys., 11 (2012), pp. 400-414.


The Ultra Weak Variational Formulation Using Bessel Basis Functions

Teemu Luostari 1*, Tomi Huttunen 1, Peter Monk 2

1 Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland.
2 Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA.

Received 12 December 2009; Accepted (in revised version) 4 January 2011
Available online 24 October 2011
doi:10.4208/cicp.121209.040111s

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.


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PACS: 02.60.Cb, 02.60.Lj, 02.70.Dh, 43.20.-f
Key words: The ultra weak variational formulation, Helmholtz problem, plane wave basis, Bessel basis, non-polynomial basis.

*Corresponding author.
Email: teemu.luostari@uef.fi (T. Luostari), tomi.huttunen@uef.fi (T. Huttunen), monk@math.udel.edu (P. Monk)
 

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