On improving the conditioning of the method of fundamental solutions for biharmonic BVPs in 2D domains

Pedro R.S. Antunes, Hernani Calunga and Pedro Serranho

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 243, issue C, 237-250

Abstract: The MFS-SVD approach introduced in [1], which combines the method of fundamental solutions (MFS) with singular value decomposition (SVD), is a potential alternative to existing methods for improving the conditioning of MFS linear systems. However, until now, the feasibility of this approach for boundary value problems (BVPs) defined on planar domains, has only been illustrated for two problems involving second order partial differential equations: The Laplace equation in [1] and the homogeneous Helmholtz equation in [2]. These papers suggest that SVD should be applied to the ill-conditioned factor of the MFS linear systems decomposition, which does not apply to higher order problems. In this work, we bring more clarity to this point, contributing to the establishment of a complete procedure to follow when solving problems using the MFS-SVD approach. We use the biharmonic boundary value problem, a fourth order PDE, to illustrate this procedure. This is done by approaching the numerical solution of the problem using two different ansatz, which means two different addition theorems and two different decompositions, with the aim of reinforcing the idea about the robustness of the MFS-SVD, regardless of the numerical formulation being considered. As expected, the MFS-SVD performs similarly in both cases.

Keywords: Biharmonic BVP; Method of fundamental solutions; MFS-SVD; Addition theorem; Ill-conditioning (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425004987
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:243:y:2026:i:c:p:237-250

DOI: 10.1016/j.matcom.2025.11.033

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().