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Convergence analysis of Schwarz waveform relaxation method to compute coupled advection–diffusion–reaction equations

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  • Dong, W.B.
  • Tang, H.S.

Abstract

We study the computation of coupled advection–diffusion–reaction equations with the same or different coefficients by the Schwarz waveform relaxation method. The study starts with linear equations and analyzes the computation’s convergence with a Dirichlet condition, a Robin condition, and a combination of them as the transmission conditions. Then, it presents an optimized algorithm for the Dirichlet condition, and this algorithm leads to a substantial speedup in the convergence. Furthermore, the optimized algorithm extends to the computation of nonlinear equations, including the viscous Burgers equation, and the algorithm largely remains effective for convergence speedup. Finally, the study compares waveform relaxation and conventional methods. Numerical experiments indicate that the former tends to be much more expensive than the latter regarding the number of times to solve the involved linear systems.

Suggested Citation

  • Dong, W.B. & Tang, H.S., 2024. "Convergence analysis of Schwarz waveform relaxation method to compute coupled advection–diffusion–reaction equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 462-481.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:462-481
    DOI: 10.1016/j.matcom.2023.11.026
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