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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 1, 2003, pp. 147–166
DOI: 10.4171/ZAA/1136

Published online: 2003-03-31

Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application

K. V. Khmelnytskaya[1], Vladislav V. Kravchenko[2] and Vladimir S. Rabinovich[3]

(1) Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico
(2) Cinvestav del IPN, Santiago De Querétaro, Mexico
(3) Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico

We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth boundary and support the relevancy of our approach by numerical results.

Keywords: Quaternionic analysis, fundamental solutions, Maxwell equations, Beltrami fields, force-free fields

Khmelnytskaya K. V., Kravchenko Vladislav, Rabinovich Vladimir S.: Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application. Z. Anal. Anwend. 22 (2003), 147-166. doi: 10.4171/ZAA/1136