Exact surface impedance/admittance boundary conditions for complex geometries: theory and applications

A methodology useful to derive exact and higher order surface impedance/admittance boundary conditions (HOI/ABC's) for complex geometries is presented. It is shown that exact surface boundary conditions are always expressed through dyadic integral operators involving the tangential magnetic and electric fields all over the surface of the body. Quasi-local surface boundary conditions that include curvature effects are shown to be computable through an asymptotic approximation of the integral operators. Finally, an example of a surface admittance boundary condition useful to analyze a structure exhibiting discontinuities along its surface boundary is presented. Practical examples to demonstrate the feasibility of the proposed methodology, as well as the accuracy of the resulting surface boundary conditions are also presented.