Mini-step Strategy for Transient Analysis

TL;DR

This paper introduces a mini-step strategy for transient analysis of integrated circuits that transforms non-diagonal-dominant systems into diagonal-dominant ones, enabling efficient parallel solution methods.

Contribution

The paper proposes a novel mini-step approach that ensures diagonal dominance in sparse systems, facilitating the use of domain decomposition methods for circuit simulation.

Findings

Enables large-scale circuit simulation on supercomputers.

Transforms non-diagonal-dominant systems into diagonal-dominant systems.

Improves convergence and efficiency of transient analysis.

Abstract

Domain decomposition methods are widely used to solve sparse linear systems from scientific problems, but they are not suited to solve sparse linear systems extracted from integrated circuits. The reason is that the sparse linear system of integrated circuits may be non-diagonal-dominant, and domain decomposition method might be unconvergent for these non-diagonal-dominant matrices. In this paper, we propose a mini-step strategy to do the circuit transient analysis. Different from the traditional large-step approach, this strategy is able to generate diagonal-dominant sparse linear systems. As a result, preconditioned domain decomposition methods can be used to simulate the large integrated circuits on the supercomputers and clouds.