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

W.B. Dong and H.S. Tang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 218, issue C, 462-481

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.

Keywords: Advection–diffusion–reaction equation; Schwarz waveform relaxation method; Conventional schwarz method; Dirichlet condition; Robin condition; Dirichlet–Robin condition; Optimized transmission algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:218:y:2024:i:c:p:462-481

DOI: 10.1016/j.matcom.2023.11.026

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