Transient Simulations of Three-dimensional Integrated Circuit Interconnect Using a Mixed Surface-Volume approach

It has recently been shown that the boundary-element method can be used to perform accurate cross-talk simulations of three-dimensional integrated circuit interconnect. However, the computational complexity grows as N2, where N is the number of surface unknowns. Straightforward application of the fast-multipole algorithm reduces the computational complexity to order N, but produces magnified errors due to the ill-conditioning of the steady-state problem. We present a mixed surface-volume approach and prove that the formulation results in the exact steady-state solution, independent of the multipole approximations. Numerical experiments are presented to demonstrate the accuracy and efficiency of this technique. On a realistic example, the new method runs fifteen times faster than using dense-matrix iterative methods.