An unconditional stable general operator splitting method for transistor level transient analysis

Abstract

Abstract-In this paper, we introduce a general operator splitting method for transient simulation of VLSI circuits. The proposed approach generates special partitions of the circuits and alternates the explicit and implicit integrations between the partitions. We prove that the method is unconditionally stable independent of the step size. The splitting scheme greatly reduces the nonzero fill-ins generated in direct methods like LU decomposition. Orders of magnitude speedup over Berkeley SPICE3 is observed for sets of circuits.

Transient Linear Circuit Analysis Using Finite Element Technique

“…[27,28]. To perform the assembling procedure, local systems (11) in the case of the ϑ-method time integration scheme and (32) in the case of Heun's method time integration scheme, each FE has to be set in the following form:…”

“…Most of the circuit simulators such as SPICE [1] apply the well-known backward differentiation formulae (BDF) integration method to the system of differential-algebraic equations (DAEs) that is defined after applying the well-known modified nodal analysis (MNA) to the considered linear circuit/network. To provide a fast and accurate circuit/network analysis, many efforts have been made to improve integration algorithms [2][3][4][5][6][7][8][9][10][11]. The most used methods in modern circuit simulators for time integration of the DAEs are the BDF methods [12,13], improved BDF method (yields less damping) in combination with the Trapezoidal Rule [14], Implicit Runge-Kutta methods such as the Radau [15] and Choral methods [16], and Modified Extended BDF methods [17].…”