Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique

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This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds.

It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green’s functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space.

The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types of materials. On any particular machine, it results in either a faster solution for a given problem or the ability to solve problems of greater complexity. The Clifford-Cauchy-Dirac technique offers very real and significant advantages in uniformity, complexity, speed, storage, stability, consistency and accuracy.