Low Energy Solutions to the Helmholtz Equation on a Torus

Raffaelli, Jacopo (2022) Low Energy Solutions to the Helmholtz Equation on a Torus. Bachelor's Thesis, Mathematics.

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Abstract

This Bachelor Project focuses on the low energy solution to the Helmholtz Equation on a torus, in particular it focuses on its relation to the solution to the same equation on the surface of a sphere. The first two chapters provide background information on the field of scattering and control theory, the Helmholtz Equation (as well as the Maxwell Equations) and toroidal coordinates. Then a review of topics from partial differential equations is carried out, with information concerning harmonics functions, the maximum principle, Poisson’s Formula, and the Sommerfeld Radiation Condition. Finally, the solution on the torus is carried out by means of an approximation through the Laplacian Equation for the specific case of a compactly supported solution, and the results show that the first power term of the solution is non-zero and analogous to that of the solution to the spherical case.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Waters, A.M.S. and Seri, M.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	19 Jul 2022 07:44
Last Modified:	19 Jul 2022 07:44
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/27972

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