Mixing electromagnetic and electrical circuit simulations

As clock rates in computers become faster, EM effects become more important in computer board and chip simulations. Hence, efficient computer simulations with the correct physics exploiting best CEM methods are imperative for the design of the next generation computers. The recently developed fast methods, MLFMA (multilevel fast multipole algorithm) and low-frequency MLFMA (LF-MLFMA), and low-frequency fast inhomogeneous plane wave algorithm (LF-FIPWA), can accelerate high-accuracy electromagnetic simulations by orders of magnitude. Such methods are integral equation methods such as MOM and low-frequency MOM (LF-MOM). LF-MLFMA/LF-MOM and LF-FIPWA/LF-MOM can be used to characterize blocks of circuits with S parameters when those parts of circuits are linear. Then we interface the nonlinear part of the circuits with the linear part with a fast convolution scheme with reduced complexity. In this manner, general circuits can be modeled by fully exploiting advances in fast electromagnetic solvers. Also, the characterization with S parameters over a broad range of frequencies can be done in parallel for different blocks of the circuit, and these parameters can be computed and stored for later simulations.