Matrix representation of the Neumann-Poincar\'e operator for a torus
Functional Analysis
2024-10-29 v1
Abstract
We represent a matrix representation of the Neumann-Poincar\'e operator defined on the boundaries of a torus. A torus is a doubly connected domain in three dimensions. There is a well-known parametrization for the shape of the torus, the toroidal coordinate system. Based on the coordinate system, we use toroidal harmonics to get an expansion of the NP operator for the torus. Along with proper bases, the Neumann-Poincar\'e operator can be explicitly represented by an infinite matrix.
Keywords
Cite
@article{arxiv.2410.20033,
title = {Matrix representation of the Neumann-Poincar\'e operator for a torus},
author = {Doosung Choi},
journal= {arXiv preprint arXiv:2410.20033},
year = {2024}
}