Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for heterogeneous sub-diffusion and diffusion-wave equations

This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 150; pp. 102 - 124
Main Authors: Sana, Soura, Mandal, Bankim C.
Format: Journal Article
Language:English
Published: Elsevier Ltd 15.11.2023
Subjects:
Diffusion-wave
Dirichlet-Neumann
Domain decomposition
Neumann-Neumann
Sub-diffusion
Waveform relaxation
Sub-diffusion
Neumann-Neumann
Dirichlet-Neumann
Waveform relaxation
Diffusion-wave
Domain decomposition
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different constant values of the generalized diffusion coefficient on the algorithms' convergence is analyzed. The convergence rate of the algorithms is analyzed as the fractional order of the time derivative changes. The paper demonstrates that the algorithms exhibit slow superlinear convergence when the fractional order is close to zero, almost finite step convergence (exact finite step convergence for wave case) when the order approaches two, and faster superlinear convergence as the fractional order increases in between. The transitional nature of the algorithms' behavior is effectively captured through estimates with changes in the fractional order, and the results are verified by numerical experiments.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2023.09.013