Energy complementarity featured hybrid discrete geometric method for capacitance extraction of integrated circuits

Abstract

The generalised discrete geometric method (DGM) derived from the discrete exterior calculus is an attractive method to solve partial differential equations. Moreover, the energy complementarity of corresponding dual formulations and dual meshes has been exploited to approximate the extra solutions efficiently. Based on the thinking of duality, this reported work investigated the geometrically projective transformations or mapping operations between the interlocked dual meshes, and combined the two sets of dual formulations or algebraic equation systems into a hybrid one through the mapping matrix, which leads to a hybrid DGM featured with energy complementarity. The proposed method offers an effective and elegant solution. In particular, there is only one matrix system to be solved instead of two in the dual methods. The example of capacitance extraction of the integrated circuit, which is a typical electrostatic system problem governed by the Poisson equation, is studied. The results show that the hybrid method is available, fast and robust. Considering that geometric computation and interpolation are broadly used in physical field analyses and computer graphics, the proposed hybrid method is expected to provide a rapid approach and to greatly benefit relevant applications.