Quaternionic fundamental solutions for the numerical analysis of electromagnetic scattering problems
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Vladimir S., Rabinovich
TL;DR
This paper introduces quaternionic fundamental solutions for Maxwell equations, proving their completeness and demonstrating their effectiveness through numerical results in electromagnetic scattering analysis.
Contribution
The paper presents a novel quaternionic fundamental solution approach for Maxwell boundary problems, with proven completeness and validated numerical performance.
Findings
Fundamental solutions are complete in Sobolev spaces.
Numerical results support the approach's effectiveness.
New quaternionic methods improve electromagnetic scattering analysis.
Abstract
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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Taxonomy
TopicsAlgebraic and Geometric Analysis · Advanced Mathematical Modeling in Engineering · Mathematical Analysis and Transform Methods