Transmission Line Inspires A New Distributed Algorithm to Solve the Nonlinear Dynamical System of Physical Circuit

TL;DR

This paper introduces the Mimic Transmission Method (MTM), a novel distributed algorithm inspired by transmission lines in physical circuits, enabling efficient and accurate simulation of nonlinear dynamical systems in a distributed manner without convergence issues.

Contribution

The paper presents MTM, a new black-box distributed algorithm that mimics transmission line behavior to solve nonlinear dynamical systems in physical circuits efficiently.

Findings

MTM effectively solves nonlinear ODEs from physical circuits.

MTM avoids convergence issues common in parallel nonlinear system solutions.

MTM requires only one distributed computation per time window.

Abstract

As known, physical circuits, e.g. integrated circuits or power system, work in a distributed manner, but these circuits could not be easily simulated in a distributed way. This is mainly because that the dynamical system of physical circuits is nonlinear and the linearized system of physical circuits is nonsymmetrical. This paper proposes a simple and natural strategy to mimic the distributed behavior of the physical circuit by mimicking the distributed behavior of the internal wires inside this circuit. Mimic Transmission Method (MTM) is a new distributed algorithm to solve the nonlinear ordinary differential equations extracted from physical circuits. It maps the transmission delay of interconnects between subcircuits to the communication delay of digital data link between processors. MTM is a black-box algorithm. By mimicking the transmission lines, MTM seals the nonlinear dynamical system within the subcircuit. As the result, we do not need to pay attention on how to solve the nonlinear dynamic system or nonsymmetrical linear system in parallel. MTM is a global direct algorithm, and it does only one distributed computation at each time window to obtain accurate result, so unconvergence issues do not need to be worried about.