Identifying Common Properties of Coefficient Matrices Appearing in Conventional or Invariant Scheme of Method of Fundamental Solutions

Kohei Yaji

doi:10.1002/tee.24263

journal article Jan 14, 2025

Identifying Common Properties of Coefficient Matrices Appearing in Conventional or Invariant Scheme of Method of Fundamental Solutions

Kohei Yaji

IEEJ Transactions on Electrical and Electronic Engineering Vol. 20 No. 7 pp. 991-997 · Wiley

View at Publisher Save 10.1002/tee.24263

Abstract

In previous studies on the method of fundamental solutions applied to Dirichlet problems, the only method for verifying the regularity of coefficient matrix has been by calculating the determinant and checking if it is non‐zero directly. These verifications were carried out in some specific cases. This paper presents an identification of common properties of coefficient matrices within the method of fundamental solutions related to regularity. It establishes sufficient conditions for coefficient matrices to be regular and diagonally dominant in the two‐dimensional plane or the three‐dimensional space. However, when dealing with both the conventional scheme and the invariant scheme, we encounter issues where achieving a good arrangement of charges while maintaining diagonal dominance is challenging. One advantage of the invariant scheme over the conventional scheme is found to be based on the solvability of the shift of the boundary data. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

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Details

Published: Jan 14, 2025
Vol/Issue: 20(7)
Pages: 991-997
License: View

Authors

K

Kohei Yaji

National Institute of Technology Kagoshima College 1460‐1, Shinko, Hayato‐cho Kirishima City Kagoshima 899‐5193 Japan

Cite This Article

Kohei Yaji (2025). Identifying Common Properties of Coefficient Matrices Appearing in Conventional or Invariant Scheme of Method of Fundamental Solutions. IEEJ Transactions on Electrical and Electronic Engineering, 20(7), 991-997. https://doi.org/10.1002/tee.24263

Identifying Common Properties of Coefficient Matrices Appearing in Conventional or Invariant Scheme of Method of Fundamental Solutions

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