An algorithmic framework for efficient large-scale circuit simulation using exponential integrators

Abstract

We propose an efficient algorithmic framework for time-domain circuit simulation using exponential integrators. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes it capable of simulating stiff nonlinear circuit system at a large scale. In this framework, the system's nonlinearity is treated with exponential Rosenbrock-Euler formulation. The matrix exponential and vector product is computed using invert Krylov subspace method. Our proposed method has several distinguished advantages over conventional formulations (e.g., the well-known backward Euler with Newton-Raphson method). The matrix factorization is performed only for the conductance/resistance matrix G, without being performed for the combinations of the capacitance/inductance matrix C and matrix G, which are used in traditional implicit formulations. Furthermore, due to the explicit nature of our formulation, we do not need to repeat LU decompositions when adjusting the length of time steps for error controls. Our algorithm is better suited to solving tightly coupled post-layout circuits in the pursuit for full-chip simulation. Our experimental results validate the advantages of our framework.