On the Construction of Diracs Delta Functions from Poissons and Maxwells Equations
- Progress in Electromagnetic Research Symposium…
Variational formulations, singular surface integral techniques, and conservative methods, invariably employ sophisticated functional analysis tools, the development of which precedes computational electromagnetics (EM). Examples include Dirac's delta functions, the concepts of standard-, Frechet-, and Gateaux derivatives, the notions of integration (Riemann, Cauchy, Lebesgue, and many others), basis- and weighting (dual) functions, renormalization techniques and regularization of singularities. In developing tools for accelerated computational electrodynamics several fundamental questions arise, which are answered in this presentation affirmatively. In particular it has been demonstrated that problem-tailored analysis-, synthesis-, and diagnosis tools can be constructed directly from the Maxwell's and Poisson's equations. In terms of a simple, yet fundamental example, the underlying ideas and concepts are made explicit. Discussions of open problems and future prospectives are dispersed in the paper, wherever deemed necessary or otherwise illuminating.