论文标题
Helmholtz方程式
A Block Jacobi Sweeping Preconditioner for the Helmholtz Equation
论文作者
论文摘要
在最近的研究中，通过脱离标准层型型域的分解并在Checkerboard-Type型域的分解上引入新的扫描策略，可以更灵活地进行扫描，从而改善了用于高频时谐波波浪问题的扫描型算法的平行性能。这些扫描可以通过一定数量的步骤来完成，每个步骤都提供了从当前迭代求解的子域到其下一个相邻子域的必要信息。尽管可以在每个步骤同时解决这些子域中的子问题，但是扫描方法过程的顺序性质仍然存在，这限制了它们的平行性潜力。我们提出了一个大块的雅各比扫描预处理，这是扫描型预处理的一种改进的变体。这些改进的变体的新功能可以解释为几个部分扫描，可以将其视为并行在子域子集上运行的扫描。我们提出了几个二维有限元元素结果，以研究和比较扫描的预处理和块雅各比盖的预先调节器。
In recent research, the parallel performances of sweeping-type algorithms for high-frequency time-harmonic wave problems have been improved by departing from standard layer-type domain decomposition and introducing a new sweeping strategy on a checkerboard-type domain decomposition, where sweeps can be performed more flexibly. These sweeps can be done by a certain number of steps, each of which provides the necessary information from subdomains solved at the current iteration to their next neighboring subdomains. Although, subproblems in these subdomains can be solved concurrently at each step, the sequential nature of the process of the sweeping approaches still exists, which limits their potential for parallelization. We propose a block Jacobi sweeping preconditioner, which is an improved variant of sweeping-type preconditioners. The new feature of these improved variants can be interpreted as several partial sweeps, which can be thought of as sweeps that operate on a subset of the subdomains in parallel. We present several two-dimensional finite element results to study and compare the sweeping preconditioner and the block Jacobi sweeping preconditioner.
