The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of appropriate transmission conditions. In this work, we will develop an efficient solver for Helmholtz equations based on perfectly matched layers (PMLs) as transmission conditions at the interfaces within an optimised restricted additive Schwarz (ORAS) domain decomposition preconditioner, in both two and three dimensional domains. We perform a series of numerical simulations on a model problem and will assess the convergence rate and accuracy of our solutions compared to the situation where impedance boundary conditions are used.

翻译：区域分解方法（DDMs）的收敛速度强烈依赖于子域间界面处的传输条件。因此，提高此类求解器效率的关键在于精心设计合适的传输条件。本文基于优化限制型加性施瓦茨（ORAS）区域分解预条件子，在二维和三维区域中采用完美匹配层（PML）作为界面传输条件，开发了一种高效的亥姆霍兹方程求解器。我们针对模型问题开展了一系列数值模拟，并将收敛速度和计算精度与使用阻抗边界条件的情形进行了对比评估。