Local Method Of Fundamental Solutions Formulations For Polyharmonic Bvps

Authors

• Andreas Karageorghis, University of Cyprus
• C. S. Chen, College of Arts and Sciences
• Malgorzata A. Jankowska, Politechnika Poznanska

Document Type

Article

Publication Date

1-1-2026

School

Mathematics and Natural Sciences

Abstract

We develop three local method of fundamental solutions (LMFS) formulations for solving two-dimensional boundary value problems (BVPs) governed by the polyharmonic equation (Formula presented), in (Formula presented). The efficacy of the proposed techniques is demonstrated by several numerical experiments in multi-connected domains. Using the local version of the MFS, the difficulty of selecting the source points in multi-connected domains, especially those containing tiny holes, can be alleviated. We also demonstrate the importance of selecting the appropriate formulation for solving higher order polyharmonic equations. In addition, we formulate matrix decomposition algorithms for the efficient solution of polyharmonic BVPs in radially symmetric domains.

Publication Title

Journal of Computational Science

Volume

93

Recommended Citation

Karageorghis, A., Chen, C., Jankowska, M. (2026). Local Method Of Fundamental Solutions Formulations For Polyharmonic Bvps. Journal of Computational Science, 93.
Available at: https://aquila.usm.edu/fac_pubs/22070