论文标题
helmholtz方程的域分解方法中PML传输条件的数值评估
Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
论文作者
论文摘要
域分解方法（DDM）的收敛速率在很大程度上取决于子域之间界面的传输条件。因此，提高此类求解器效率的一个重要方面是仔细设计适当的传输条件。在这项工作中，我们将开发一个基于完美匹配的层（PML）作为在两个二维域中的优化受限限制的添加剂schwarz（ORAS）域分解预处理器中的界面的传输条件的有效求解器。我们在模型问题上执行一系列数值模拟，并将与使用阻抗边界条件的情况相比，将评估解决方案的收敛速率和准确性。
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.
