An Efficient ADI Method for Transient Thermal Simulation of Liquid-Cooled 3-D ICs

Abstract

In this article, an efficient approach based on the parallel alternating direction implicit (ADI) method is presented for the transient thermal simulation of liquid-cooled 3-D integrated circuits (ICs). To accurately characterize the thermal behaviors, a compact thermal model based on finite-difference approximation is established. The ADI method with linear time complexity is utilized to reduce computational cost, which can easily deal with large-scale problems. To suppress the oscillations of transient results in the case of large time steps, an effective technique using the exponentially expanding subtime steps is introduced, which improves the accuracy of results significantly. In addition, taking the advantage of parallel computing, the transient simulation is further accelerated by the parallel cyclic reduction (PCR) algorithm implemented on graphics processing units (GPUs). The accuracy and efficiency of the proposed method are demonstrated by several numerical examples.