A fast multipole method based calculation of the capacitance matrix in a stratified medium

An efficient, static fast multipole method (FMM) based algorithm is presented for the evaluation of the parasitic capacitance of 3-D microstrip signal lines in stratified dielectric media. The effect of dielectric interfaces on the capacitance matrix is included in the stage of the FMM when multipole expansions are used to form local multipole expansions, by the use of interpolated multipole-to-local translation functions. The increase in computational complexity and memory usage due to the presence of stratified media is therefore very small. The algorithm retains the structure and the O(N) computational cost and memory use of the free-space FMM, where N is the number of conductor patches.