2022/05/03 by Wenbin Dong, Dong, Wenbin, Hansong Tang +1
Computer Science · Mathematics · #65M55 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #G.1.8 #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2205.01708
openalex publication_date 2022/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a Robin condition, and a combination of them as the transmission conditions. Then, an optimized algorithm for the Dirichlet condition is presented to accelerate the convergence, and numerical examples show a substantial speedup in the convergence. Furthermore, the optimized algorithm is extended to the computation of nonlinear equations, including the viscous Burgers equation, and numerical experiments indicate the algorithm may largely remain effective in the speedup of convergence.