论文标题
波形松弛方法的收敛分析以计算耦合的对流扩散反应方程
Convergence Analysis of Waveform Relaxation Method to Compute Coupled Advection-Diffusion-Reaction Equations
论文作者
论文摘要
我们研究了通过Schwarz波形弛豫方法来研究耦合对流扩散反应方程的计算。该研究从线性方程开始，并分析计算与差异条件，罗宾条件以及它们作为传输条件的组合的收敛性。然后，提出了针对DIRICHLET条件的优化算法以加速收敛，数值示例显示了收敛性的大幅加速。此外，优化的算法扩展到包括粘性汉堡方程在内的非线性方程的计算，数值实验表明该算法可能在很大程度上在收敛的加速方面仍然有效。
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.
