A multiscale method for fast capacitance extraction

The many levels of metal used in aggressive deep submicron process technologies has made fast and accurate capacitance extraction of complicated 3D geometries of conductors essential, and many novel approaches have been recently developed. In this paper we present an accelerated boundary-element method, like the well-known FASTCAP program, but instead of using an adaptive fast multipole algorithm we use a numerically generated multiscale basis for constructing a sparse representation of the dense boundary-element matrix. Results are presented to demonstrate that the multiscale method can be applied to complicated geometries, generates a sparser boundary-element matrix than the adaptive fast multipole method and provides an inexpensive but effective preconditioner. Examples are used to show that the better sparsification and the effective preconditioner yield a method that can be 25 times faster than FASTCAP while still maintain accuracy in the smallest coupling capacitances