Parallel Transient Simulation of Package/Board Power Distribution Networks Based on a 2-D Overlapping Partitioning Methodology

Abstract

Typical SPICE models for characterization of package/board power distribution networks (PDNs) are based on a 2-D discretization of the Helmholtz wave equation and hence require high computational costs. In this paper, a novel waveform relaxation (WR) algorithm for the parallelizable simulation of PDNs is presented. The key feature of this paper is the development of a 2-D partitioning methodology with overlapping, which addresses the slow convergence of conventional nonoverlapping-based WR algorithms for PDNs. In addition, a hybrid iterative technique is proposed that can provide additional exchange of information between the overlapping subcircuits to further improve the convergence of traditional Gauss-Jacobi-based relaxation iterations. The overall algorithm is highly parallelizable and exhibits good scaling with both the size of the circuit matrices involved and the number of CPUs available. Numerical examples are presented to illustrate the validity and efficiency of the proposed paper.