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.
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Vladislav V. Kravchenko, Vladimir S. Rabinovich, K. V. Khmelnytskaya, Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application. Z. Anal. Anwend. 22 (2003), no. 1, pp. 147–166DOI 10.4171/ZAA/1136