Transmission line inspires a new distributed algorithm to solve linear system of circuit

TL;DR

This paper introduces the Virtual Transmission Method (VTM), a novel distributed iterative algorithm inspired by transmission lines, designed to efficiently solve linear systems from circuits with proven convergence for SPD systems and improved performance for unsymmetrical systems.

Contribution

The paper presents VTM, a new distributed algorithm inspired by transmission lines, with proven convergence for SPD systems and enhanced convergence for unsymmetrical systems.

Findings

VTM is convergent for symmetric positive definite systems.

Numerical experiments show VTM outperforms traditional stationary algorithms.

Preconditioning accelerates VTM's convergence when properly chosen.

Abstract

Transmission line, or wire, is always troublesome to integrated circuits designers, but it could be helpful to parallel computing researchers. This paper proposes the Virtual Transmission Method (VTM), which is a new distributed and stationary iterative algorithm to solve the linear system extracted from circuit. It tears the circuit by virtual transmission lines to achieve distributed computing. For the symmetric positive definite (SPD) linear system, VTM is proved to be convergent. For the unsymmetrical linear system, numerical experiments show that VTM is possible to achieve better convergence property than the traditional stationary algorithms. VTM could be accelerated by some preconditioning techniques, and the convergence speed of VTM is fast when its preconditioner is properly chosen.