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.

翻译：摘要：在近期研究中，通过脱离标准的分层区域分解并引入一种基于棋盘型区域分解的新扫掠策略，高频时谐波动问题的扫掠型算法并行性能得到提升，该策略可更灵活地执行扫掠。这些扫掠可通过若干步骤完成，每一步骤将当前迭代求解的子域中的必要信息传递至其相邻的下一个子域。尽管每个步骤中各子域的子问题可并行求解，但扫掠方法过程固有的顺序性仍然存在，这限制了其并行化潜力。本文提出了一种块雅可比扫掠预处理器，它是扫掠型预处理器的改进变体。这些改进变体的新特性可被解释为多个部分扫掠，可视为并行作用于部分子域的扫掠。我们展示了若干二维有限元结果，以研究并比较扫掠预处理器与块雅可比扫掠预处理器的性能。