Volume 11, Issue 2
The Ultra Weak Variational Formulation Using Bessel Basis Functions

Teemu Luostari, Tomi Huttunen & Peter Monk

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

Published online: 2012-12

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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.


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@Article{CiCP-11-400, author = {}, title = {The Ultra Weak Variational Formulation Using Bessel Basis Functions}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {400--414}, 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.121209.040111s}, url = {http://global-sci.org/intro/article_detail/cicp/7369.html} }
TY - JOUR T1 - The Ultra Weak Variational Formulation Using Bessel Basis Functions JO - Communications in Computational Physics VL - 2 SP - 400 EP - 414 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.121209.040111s UR - https://global-sci.org/intro/article_detail/cicp/7369.html KW - AB -

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.


Teemu Luostari, Tomi Huttunen & Peter Monk. (2020). The Ultra Weak Variational Formulation Using Bessel Basis Functions. Communications in Computational Physics. 11 (2). 400-414. doi:10.4208/cicp.121209.040111s
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