An efficient solver for the three-dimensional capacitance of the interconnects in high speed digital circuit by the multiresolution method of moments

The computation of the equivalent capacitances for three-dimensional (3-D) interconnects features large memory usage and long computing time. In this paper, a matrix sparsification approach based on multiresolution representation is applied with the method of moments (MoM) to calculate 3-D capacitances of interconnects in a layered media. Instead of direct expansion of the charge distribution by the orthogonal wavelet basis functions, the large full matrix resulting from discretization of the integral equations is taken as a discrete image and sparsified by two-dimensional (2-D) multiresolution representations. The inverse of the obtained sparse matrix is efficiently implemented by Schultz's iterative approach. Several numerical examples are given and the results obtained show that the proposed method significantly sparsifies the matrix equation and the capacitance parameters computed by the matrix equation with high sparsity agree well with the results of other reports and those computed by an established capacitance extractor FASTCAP.