Dirichlet-Neumann Waveform Relaxation Algorithm for Time Fractional Diffusion Equation in Heterogeneous Media

2023/01/30 by Soura Sana, Sana, Soura, Bankim C. Mandal +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2301.12909

openalex publication_date 2023/01/30 · openalex created_date 2023/02/01 · openalex updated_date 2026/07/28

Abstract

In this article, we have studied the convergence behavior of the Dirichlet-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion wave equations in 1D & 2D for regular domains, where the dimensionless diffusion coefficient takes different constant values in different subdomains. From numerical experiments, we first capture the optimal relaxation parameters. Using these optimal relaxation parameters, our analysis estimates the rate of change of the convergence behavior against the fractional order and time. We have performed our analysis in multiple subdomain cases for both in 1D & 2D.

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