Fast capacitance extraction using inexact factorization

Most capacitance extraction algorithms based on boundary element method (BEM) use iterative solvers, which is favorable for solving large systems. Different from the common practice, we present an approach that solves a small system for capacitance using the direct solver. Our study is based on the sparse formulation proposed in. With proper ordering of the rows and columns, the sparse system can be approximated by its inexact factorization. Furthermore, with the proper ordering, the part of the solution vector, which contributes to capacitance, can be solved using the sub-matrix of the inexact factors. The dimension of the sub-matrix is O(m), where m is the number of conductors. To our knowledge, this is the first BEM style method to solve capacitance extraction problem without using iterative solver. Experimental results show that the new algorithm is up to 100 times faster than FastCap and is also much faster than the method in (we call it PHiCap). The error of the new method with respect to FastCap is within 2%.