• DOI:10.48550/arXiv.2301.12909
• Corpus ID: 256390456

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

@article{Sana2023DirichletNeumannWR,
  title={Dirichlet-Neumann Waveform Relaxation Algorithm for Time Fractional Diffusion Equation in Heterogeneous Media},
  author={Soura Sana and Bankim Chandra Mandal},
  journal={ArXiv},
  year={2023},
  volume={abs/2301.12909}
}

• Soura Sana, B. Mandal
• Published 30 January 2023
• Mathematics
• ArXiv

. In this article, we have studied the convergence behavior of the Dirichlet-Neumann waveform re- laxation 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 numeri- cal 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.