Fourier method for the Neumann problem on a torus-Reference-Cited by-同舟云学术

Fourier method for the Neumann problem on a torus

Published:2023-09-14 Issue:5 Volume:13 Page:
ISSN:1664-2368
Container-title:Analysis and Mathematical Physics
language:en
Short-container-title:Anal.Math.Phys.

Author:

Ashtab Z.,Morais J.,Porter R. Michael

Abstract

AbstractThe Fourier method approach to the Neumann problem for the Laplacian operator in the case of a solid torus contrasts in many respects with the much more straight forward situation of a ball in 3-space. Although the Dirichlet-to-Neumann map can be readily expressed in terms of series expansions with toroidal harmonics, we show that the resulting equations contain undetermined parameters which cannot be calculated algebraically. A method for rapidly computing numerical solutions of the Neumann problem is presented with numerical illustrations. The results for interior and exterior domains combine to provide a solution for the Neumann problem for the case of a shell between two tori.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s13324-023-00836-4.pdf

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