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

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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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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam

    Minh-Phuong Tran

  2. Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam

    Thanh-Nhan Nguyen & Phuoc-Toan Huynh

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam

    Nhu-Binh Ly, Minh-Dang Nguyen & Quoc-Anh Ho

Authors
  1. Minh-Phuong Tran
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  2. Thanh-Nhan Nguyen
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  3. Phuoc-Toan Huynh
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  4. Nhu-Binh Ly
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  5. Minh-Dang Nguyen
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  6. Quoc-Anh Ho
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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

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