Waveform Transmission Method, a New Waveform-relaxation Based Algorithm to Solve Ordinary Differential Equations in Parallel

2009/11/06 by Fei Wei, Huazhong Yang, Wei, Fei +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Parallel #and Cluster Computing (cs.DC)

paper · pdf · doi:10.48550/arxiv.0911.1166

openalex publication_date 2009/11/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Waveform Relaxation method (WR) is a beautiful algorithm to solve Ordinary Differential Equations (ODEs). However, because of its poor convergence capability, it was rarely used. In this paper, we propose a new distributed algorithm, named Waveform Transmission Method (WTM), by virtually inserting waveform transmission lines into the dynamical system to achieve distributed computing of extremely large ODEs. WTM has better convergence capability than the traditional WR algorithms.

Related

• Waveform Relaxation with asynchronous time-integration
• Transmission Line Inspires A New Distributed Algorithm to Solve the Nonlinear Dynamical System of Physical Circuit
• A Non-iterative Overlapping Schwarz Waveform Relaxation Algorithm for Wave Equation
• A time adaptive multirate Quasi-Newton waveform iteration for coupled problems
• Multi-stage waveform Relaxation and Multisplitting Methods for Differential Algebraic Systems