论文标题
Dirichlet-Neumann和Neumann-Neumann-Neumann波形松弛算法，用于时间分数子扩散和扩散波方程
Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time fractional sub-diffusion and diffusion-wave equations
论文作者
论文摘要
在本文中，我们研究了Dirichlet-Neumann和Neumann-Neumann波形弛豫算法的收敛行为，用于定期域中的时间分数子扩散和扩散波的扩散波方程，其中尺寸的无扩散系数在不同子域中具有不同的常数。我们首先观察到不同的扩散系数导致不同的弛豫参数以获得最佳收敛。使用这些最佳弛豫参数，我们的分析估计算法的慢速超线性收敛时，当时间衍生物的分数顺序接近零时，当阶接近两个阶时几乎有限的步骤收敛，并且在两者之间，随着分数的增加，超线性收敛变得更快。因此，我们已经成功地捕获了收敛速率的过渡，并在估计值中随时间导数的分数顺序变化，并通过数值实验对其进行了验证。
In this article, we have studied the convergence behavior of the Dirichlet-Neumann and Neumann- Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations in 1D & 2D for regular domains, where the dimensionless diffusion coefficient takes different constant values in different subdomains. We first observe that different diffusion coefficients lead to different relaxation parameters for optimal convergence. Using these optimal relaxation parameters, our analysis estimates the slow superlinear convergence of the algorithms when the fractional order of the time derivative is close to zero, almost finite step convergence when the order is close to two, and in between, the superlinear convergence becomes faster as fractional order increases. So, we have successfully caught the transition of convergence rate with the change of fractional order of the time derivative in estimates and verified them with numerical experiments.
