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：领域分解方法（DDMs）的收敛速率强烈取决于子域之间的接口传输条件，因此，提高此类求解器的效率的重要方面之一是仔细设计适当的传输条件。在这项工作中，我们将在优化的受限附加施瓦茨（ORAS）领域分解预处理器中使用完美匹配层（PMLs）作为接口处的传输条件，从而开发出基于Helmholtz方程的高效求解器，包括二维和三维域。我们对一个模型问题进行一系列数值模拟，并将评估我们的解的收敛速率和精度，与使用阻抗边界条件的情况进行比较。