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A meshless method for some inverse problems associated with the Helmholtz equation

Jin, B; Zheng, Y; (2006) A meshless method for some inverse problems associated with the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering , 195 (19-22) pp. 2270-2288. 10.1016/j.cma.2005.05.013. Green open access

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Abstract

In this paper, a new numerical scheme based on the method of fundamental solutions is proposed for the numerical solution of some inverse boundary value problems associated with the Helmholtz equation, including the Cauchy problem. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing truncated singular value decomposition, while the regularization parameter for the regularization method is provided by the L-curve method. Numerical results are presented for problems on smooth and piecewise smooth domains with both exact and noisy data, and the convergence and stability of the scheme are investigated. These results show that the proposed scheme is highly accurate, computationally efficient, stable with respect to the noise in the data and convergent with respect to decreasing the amount of data noise and increasing the distance between the physical and fictitious boundaries, and could be considered as a competitive alternative to existing methods for these problems.

Type: Article
Title: A meshless method for some inverse problems associated with the Helmholtz equation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.cma.2005.05.013
Publisher version: http://dx.doi.org/10.1016/j.cma.2005.05.013
Language: English
Additional information: © 2005 Elsevier B.V. This manuscript is made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at http://creativecommons.org/ licenses/by/4.0. Access may be initially restricted by the publisher.
Keywords: The method of fundamental solutions; Cauchy problem; Helmholtz equation; Truncated singular value decomposition; Inverse problem
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1443357
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