A fast hierarchical algorithm for 3-D capacitance extraction

We presen t a new algorithm for computing the capacitance of three-dimensional perfect electrical conductors of complex structures. The new algorithm is significantly faster and uses muc h less memory than previous best algorithms, and is kernel independent. The new algorithm is based on a hierarchical algorithm for the <italic>n</italic>-body problem, and is an acceleration of the boundary-element method for solving the integral equation associated with the capacitance extraction problem. The algorithm first adaptively subdivides the conductor surfaces into panels according to an estimation of the potential coefficients and a user-supplied error band. The algorithm stores the poten tial coefficient matrix in a hierarchical data structure of size <italic>O</italic>(<italic>n</italic>), although the matrix is size <italic>n</italic><supscrpt>2</supscrpt> if expanded explicitly, where<italic>n</italic> is the n umber of panels. The hierarchical data structure allows us to multiply the coefficient matrix with an y vector in <italic>O</italic>(<italic>n</italic>) time. Finally, w e use a generalized minimal residual algorithm to solve <italic>m</italic> linear systems each of size <italic>n</italic> × <italic>n</italic> in <italic>O</italic>(<italic>mn</italic>) time, where <italic>m</italic> is the n umber of conductors. The new algorithm is implemented and the performance is compared with previous best algorithms. F or the <italic>k</italic> × <italic>k</italic> bus example, our algorithm is 100 to 40 times faster than F astCap, and uses 1/100 to 1/60 of the memory used by F astCap. The results computed by the new algorithm are within 2.7% from that computed by FastCap.