An Efficient Numerical Solution Technique for VLSI Interconnect Equations on Many-Core Processors

Abstract

This paper presents a technique to accelerate transient simulations of analog circuits using an explicit integration method parallelised on a many-core computer. Usual methods used by SPICE-type simulators are based on Newton-Raphson iterations, which are reliable and numerically stable, but require long CPU processing times. However, although the integration time step in explicit methods is smaller than that used in implicit methods, this technique avoids the calculation of time-consuming computations due to the Jacobian matrix inversion. The proposed method uses an explicit integration scheme based on the fourth order Adams–Bashforth formula. The algorithm has been parallelised on a NVIDIA general purpose GPU using the CUDA programming model. As a case study, the RC ladder model of a VLSI interconnect is simulated on a general purpose graphic processing unit and the achieved performance is then evaluated against that of a multiprocessor CPU. The results show that the proposed technique achieves a speedup of one order of magnitude in comparison with implicit integration techniques executed on a CPU.