From Circuit Theory, Simulation to SPICEDiego<\/sup>: A Matrix Exponential Approach for Time-Domain Analysis of Large-Scale Circuits

SPICE (Simulation Program with Integrated Circuit Emphasis) is a widely used circuit simulation framework for integrated circuit designs. The basic skeleton of SPICE time domain simulation was derived from the versions developed in UC Berkeley during the 1970s. In this paper, we report most recent numerical integration methods to improve traditional SPICE time integration schemes, which are based on linear multi-step and low order approximation for the circuit differential equation system. Recently, matrix exponential based time domain simulation algorithms are being developed to address long-term issues in the standard numerical integration methods. We review the related techniques in matrix exponential based approaches and state several distinguished features in challenging simulation problems, such as linear power network analysis and nonlinear circuit system simulation (SPICEDiego). We believe that the matrix exponential approaches can shed new light on the research and development of future circuit simulation algorithmic systems.