论文标题
对角清扫域分解方法，用于Helmholtz方程的源传输
A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation
论文作者
论文摘要
在本文中，我们提出并测试了一种新型的对角线扫描域分解方法（DDM），其源传输用于求解$ \ mathbb {r}^n $中的高频helmholtz方程。在该方法中，将计算域分区分为重叠的棋盘子域，用于使用完美匹配的层（PML）技术，然后专门设计了一组对角扫描，以有效地解决该系统。该方法通过采用更有效的子域求解顺序来改善添加剂重叠的DDM（W. Leng and L. Ju，2019）和L-S-扫描方法（M. Taus等，2019）。我们表明，该方法在恒定的中型情况下以$ 2^n $扫描实现了全局PML问题的确切解决方案。尽管扫描通常意味着顺序的子域求解，但是该方法中每个扫描所需的顺序步骤数仅与域分解相对于所有方向的准均匀均匀时的$ n $ th root成正比，因此，它非常适合通过PipeLeleseletsine PipeLeline Processing与Helmholtz Process and pipleansellessing sellally Computs。提出了两个维度和三个维度的广泛数值实验，以证明该方法的有效性和效率。
In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in $\mathbb{R}^n$. In the method the computational domain is partitioned into overlapping checkerboard subdomains for source transfer with the perfectly matched layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially designed to solve the system efficiently. The method improves the additive overlapping DDM (W. Leng and L. Ju, 2019) and the L-sweeps method (M. Taus, et al., 2019) by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global PML problem with $2^n$ sweeps in the constant medium case. Although the sweeping usually implies sequential subdomain solves, the number of sequential steps required for each sweep in the method is only proportional to the $n$-th root of the number of subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness and efficiency of the proposed method.
