Rapid solution of potential integral equations in complicated 3-dimensional geometries

Abstract : Analysis of many electromagnetic problems in engineering, such as electromagnetic interference (EMI) calculations or estimation of interconnected coupling capacitances and inductance's, is often performed via numerical methods based on integral equations. Analysis of the complicated three-dimensional geometries of modern engineering structures required efficient algorithms to solve the large, dense linear systems generated by integral equation techniques. This thesis develops and analyzes a grid-based, "precorrected-FFT" method which preserves the efficiency of recently developed fast-multipole techniques but is more easily generalizable to a variety of kernels, and may have substantial performance benefits for commonly encountered geometries. The proposed algorithm is intended to be particularly efficient for problems with Helmholtz kernels where the size of the problem domain is of the order of a few wavelengths, such as typically occurs in EMI calculations, and for problems with planar interfaces, such as integrated circuits or interconnect in layered media (dielectrics and groundplanes).

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