 Improving the conditioning of the Method of Fundamental Solutions for the Helmholtz equation on domains in polar or elliptic coordinatesPedro R.S. Antunes, Hernani Calunga and Pedro Serranho Applied Mathematics and Computation, 2024, vol. 482, issue C Abstract: A new approach to overcome the ill-conditioning of the Method of Fundamental Solutions (MFS) combining Singular Value Decomposition (SVD) and an adequate change of basis was introduced in [1] as MFS-SVD. The original formulation considered polar coordinates and harmonic polynomials as basis functions and is restricted to the Laplace equation in 2D. In this work, we start by adapting the approach to the Helmholtz equation in 2D and later extending it to elliptic coordinates. As in the Laplace case, the approach in polar coordinates has very good numerical results both in terms of conditioning and accuracy for domains close to a disk but does not perform so well for other domains, such as an eccentric ellipse. We therefore consider the MFS-SVD approach in elliptic coordinates with Mathieu functions as basis functions for the latter. We illustrate the feasibility of the approach by numerical examples in both cases. Keywords: Method of fundamental solutions; Helmholtz equation; MFS-SVD; Addition theorem; Ill-conditioning; Mathieu functions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:482:y:2024:i:c:s0096300324004302 DOI: 10.1016/j.amc.2024.128969 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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