Efficient capacitance computation for structures with non-uniform adaptive surface meshes

Abstract

Circuit parasitic extraction problems are typically formulated using discretized integral equations that use basis functions defined over tesselated surface meshes. The fast multipole method (FMM) accelerates the solution process by rapidly evaluating potentials and fields due to these basis functions. Unfortunately, the FMM suffers from the drawback that its efficiency degrades if the surface mesh has disparately-sized elements in close proximity to each other. Closely-spaced non-uniformly sized elements can appear in realistic situations for a variety of reasons: owing to mesh refinement, due to accurate modeling requirements for fine structural features, and because of the presence of thin doubly-walled structures. In this paper, modifications to the standard multilevel FMM are presented that permit efficient potential and field evaluation over specific non-uniform meshes. The efficiency of the new technique is demonstrated through examples involving large surface meshes with nonuniformly sized elements in close proximity.