Dirichlet-Neumann Waveform Relaxation Method with Multiple Subdomains for Reaction-Diffusion Equation with a Time Delay

TL;DR

This paper investigates the Dirichlet-Neumann Waveform Relaxation method applied to reaction-diffusion equations with time delay, focusing on multiple subdomains and transmission condition arrangements to improve computational efficiency.

Contribution

It introduces a numerical study of the DNWR algorithm with multiple subdomains for delayed reaction-diffusion equations, exploring various transmission conditions.

Findings

Different transmission condition arrangements affect convergence efficiency.

Numerical experiments demonstrate the effectiveness of the proposed method.

The study provides insights into optimizing domain decomposition for delayed PDEs.

Abstract

In this study, we present the numerical investigation of the Dirichlet-Neumann Waveform Relaxation (DNWR) algorithm applied to multiple subdomains for the reaction-diffusion equation with time delay. Various arrangements of transmission conditions between subdomains are explored and a series of numerical experiments are conducted to evaluate and compare the efficiency and effectiveness of these configurations.