Development of the fast multipole method for stratified medium

Rapid developments in very large scale integration (VLSI) technology heighten the need for fast and accurate calculation of the parasitic capacitance and inductance of the circuit layouts. The fast multipole method (FMM) is an O(N) algorithm capable of accurately modeling much larger circuit layouts than other methods. Using computers commonly available today, this method can be employed to solve real-world sized problems consisting of millions of unknowns. The main focus of this thesis is to develop a stratified medium FMM where conductor traces and vias are embedded in layers of dielectrics. Such structures are commonly found in integrated circuits (ICs) fabricated using planar processing technology. The new algorithm developed in this thesis makes efficient use of the image charge and the image multipole expansion to account for the effects of dielectrics. As a result, one of the novelties of the algorithm is that it is only marginally more expensive than the free-space FMM.; The second part of this thesis is devoted to developing a fast algorithm to calculate the scattering by a perfect electrically conducting (PEC) body embedded in a single layer of a layered medium. A symmetric form of the dyadic Green's function is derived. All image scalar Green's functions within the dyadic Green's function are factorized. The fast algorithm can be completed by implementing these factorized scalar Green's functions in the free-space fast inhomogeneous plane wave algorithm (FIPWA).