Efficient capacitance extraction computations in wavelet domain

A new approach is presented for efficient capacitance extraction. This technique utilizes wavelet bases and is kernel independent. The main benefits of the proposed technique are as follows: (1) it takes a full advantage of the multiresolution analysis and gives accurate total charge on a conductor without obtaining an accurate solution for the charge density per se; (2) the method employs an extremely aggressive thresholding algorithm and compresses the stiffness matrix to an almost diagonal sparse matrix; and (3) construction of the stiffness matrix is performed iteratively, which facilitates easy and simple control of convergence and provides means of trading accuracy for speed. The proposed method has computational cost of O(N), versus O(N³) for conventional methods. The proposed algorithm has a major impact on the speed and accuracy of physical interconnect parameter extraction with speedup reaching 10³ for even moderately sized problems