Spectral Boundary Integral Equation Methods for Electromagnetic Research with Different Geometrical Configurations

Electromagnetic research with different geometrical configurations requires application of numerical simulation methods. In most of cases geometry of scatterers is simple, including circles or ellipses. Such shapes may be investigated by generalized Mie theory. However, investigation of other shapes requires the application of other methods. While domain discretization methods such as Finite Difference Time Domain method as we as Finite Element Method require the discretization of whole space, Boundary Integral Equation methods including classical Boundary Element Method require discretization of boundaries. Thus, conformal mapping approach to generate the parametrization of boundaries in combination with spectral Boundary Integral Equation method improved by analytical regularization based on singularity subtraction technique enhanced by Fast Fourier Transform is ideal to solve boundary value problem on polygonal structures with various configurations, while multiple multipole program and Method of Auxiliary Sources are also applicable to solve similar problems. Rewire of structures and corresponding techniques to make electromagnetic research on them is done in this work. Summary of techniques is used to solve full three-dimensional problem generating three-dimensional analog of specified two-dimensional Spectral Boundary Integral Equation method.