Efficient circuit simulation via adaptive moment matching and matrix exponential techniques

Abstract

This dissertation presents two efficient circuit simulation techniques for very large scale integrated (VLSI) circuits. Model order reduction (MOR) plays a significant role in VLSI circuit simulation as nowadays the system model may contain millions of equations or variables. MOR is needed to reduce the order of the original system to allow the simulation to be performed with an acceptable amount of time, reasonable storage and reliable accuracy. Multi-point moment matching is one of the state-of-the-art methods for MOR. However, the moment order and expansion points are usually selected in a heuristic way, which cannot guarantee the global accuracy of the reduced-order model (ROM). Therefore, it is important to utilize an adaptive algorithm in exercising multi-point moment matching. In this regard, we propose a novel automatic adaptive multi-point moment matching algorithm for MOR of linear descriptor systems. The algorithm implements both adaptive frequency expansion point selection and automatic moment order control guided by a transfer function-based error metric. Without a priori information of the system response, the proposed algorithm leads to a much higher global accuracy compared with standard multipoint moment matching without adaptation. The moments are computed via a generalized Sylvester equation which is subsequently solved by a newly proposed generalized alternating direction implicit (GADI) method.

Another technique for circuit simulation proposed in this thesis is the matrix exponential (MEXP) method. MEXP method has been demonstrated to be a competitive candidate for transient simulation of VLSI circuits. Nevertheless, the performance of MEXP based on ordinary Krylov subspace is unsatisfactory for stiff circuits, because the underlying Arnoldi process tends to oversample the high magnitude part of the system spectrum while under-sampling the low magnitude part that is important to the final accuracy. In this thesis, we explore the use of extended Krylov subspace to generate more accurate and efficient approximation for MEXP.We also develop a formulation, called generalized extended Krylov subspace, that allows unequal positive and negative dimensions in the subspace for better performance, and propose an adaptive scheme based on the generalized extended Krylov subspace to select the ratio between the positive and negative dimensions.