FastCap: A Multipole Accelerated 3D Capacitance Extraction Program

In this paper a fast algorithm for computing the capacitance of a complicated 3-D geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. Boundary-element methods become slow when a large number of elements are used because they lead to dense matrix problems, which are typically solved with some form of Gaussian elimination. This implies that the computation grows as n ³, where n is the number of panels or tiles needed to accurately discretize the conductor surface charges. In this paper we present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian elimination based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy.