The Wiener–Hopf Technique in Computational Electromagnetics: Part 1: Fundamentals.

The Wiener-Hopf technique provides an essential analytical and semi-analytical methodology in applied mathematics and mathematical physics for solving boundary-value problems, formulated by means of partial differential equations and/or integral equations. By exploiting the properties of the formulation in spectral domain after the application of integral transformation, rigorous solutions can be obtained for computational physics problems. In electromagnetics the method allows effective analysis of problems involving diffraction phenomena, guided propagation with discontinuities, antenna radiation and modern applications. Recent advances have extended the capabilities of the method to the analysis of complex electromagnetic (and not only) problems involving different geometries and arbitrary media rather than rectangular objects in isotropic media. One of the best benefits of the method is that intrinsically allows physical interpretation by means of the spectral domain. Part 1 is devoted to fundamental mathematical concepts.