Higher Order Basis Based Integral Equation Solver (HOBBIES)

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ELECTROMAGNETIC MODELING OF COMPOSITE METALLIC AND DIELECTRIC STRUCTURES USING HIGHER ORDER BASIS FUNCTIONS

1.0 SUMMARY

The mathematical equations and the unique properties of the higher order basis functions involved in the simulation software HOBBIES (Higher Order Basis Based Integral Equation Solver) are presented in this chapter. The theory and the solution methodology of using Surface Integral Equations (SIEs) for analyzing the radiation and scattering from composite metallic and dielectric structures in the frequency domain is introduced first, followed by the unique properties of the higher order basis functions. The higher order basis functions involved in this case are nothing but simple polynomials of varying degrees. These basis functions are now used to describe the unknowns over electrically large subdomain patches, in contrast to the conventional piecewise linear basis functions, popularly known as the Rao–Wilton–Glisson (RWG) basis functions over sub wavelength triangular patches. Use of these higher order basis—namely use multiple basis functions over the same electrically large patch—in contrast to use of a single basis over an electrically small patch can lead to a significant reduction in the total number of unknowns in addition to several other interesting properties as described in this chapter. Typically, for a higher order basis, only 10–20 unknowns per wavelength squared of surface area are needed, leading to a reduction of an order of the magnitude of ...