Parallel Gauss-Jordan Elimination and System Reduction for Efficient Circuit Simulation

TL;DR

This paper introduces two novel methods—parallel Gauss-Jordan elimination and partial system reduction—to improve the efficiency of solving linear systems in electric circuit simulation, demonstrating enhanced performance on various matrices.

Contribution

It presents a new parallel GJE algorithm and an innovative partial system reduction approach, both tailored for efficient circuit simulation.

Findings

Parallel GJE improves computational speed.

Partial system reduction enhances efficiency before iterations.

Combined methods maintain or improve parallel efficiency.

Abstract

For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we propose two independent novel approaches: a parallel GJE algorithm and partial system reduction prior to the start of iterations. The former is based on a well-known strategy applied for the first time in this context, whereas the latter, to the best of our knowledge, proposes an entirely new system reduction approach. To evaluate performance, we implement these algorithms in C++ using OpenMP and run them on various input matrices. Our analyses of the individual methods show improved performance, whilst combining them maintains parallel efficiency after partial reduction on medium-sized matrices and even improves efficiency on the largest matrices on the tested machine.