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Convergence results for non-overlap Schwarz waveform relaxation algorithm with changing transmission conditions

Abstract

In this paper, we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem. More precisely, we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions. Then we give a simple method to estimate the new value of parameters in each iteration. The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps. Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.

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Correspondence to Minh-Phuong Tran.

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Tran, MP., Nguyen, TN., Huynh, PT. et al. Convergence results for non-overlap Schwarz waveform relaxation algorithm with changing transmission conditions. Acta Math Sci 42, 105–126 (2022). https://doi.org/10.1007/s10473-022-0105-0

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  • DOI: https://doi.org/10.1007/s10473-022-0105-0

Key words

  • domain decomposition method
  • Schwarz waveform relaxation algorithm
  • advection reaction diffusion
  • changing transmission conditions

2010 MR Subject Classification

  • 65N55
  • 65M12
  • 65M60
  • 35K57