论文标题
Helmholtz方程的双扫方式的统一框架
A Unified Framework for Double Sweep Methods for the Helmholtz Equation
论文作者
论文摘要
我们认为在带有或没有重叠的条带域分解的情况下，扫描域分解预处理以求解Helmholtz方程。我们通过将它们表示为雅各比，高斯 - 塞德尔和对称的高斯 - 西德尔方法来统一它们的衍生和收敛研究，以实现不同的未知数。提出的框架可以在[Nataf and Nier（1997），Vion和Geuzaine（2018）中的双重扫描方法与[Stolk（2013，2017），Vion和Geuzaine（2014）]中进行理论比较。此外，它有助于引入一种新的清扫算法。我们提供数值测试案例以评估理论研究的有效性。
We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their derivation and convergence studies by expressing them as Jacobi, Gauss-Seidel, and Symmetric Gauss-Seidel methods for different numbering of the unknowns. The proposed framework enables theoretical comparisons between the double sweep methods in [Nataf and Nier (1997), Vion and Geuzaine (2018)] and those in [Stolk (2013, 2017), Vion and Geuzaine (2014)]. Additionally, it facilitates the introduction of a new sweeping algorithm. We provide numerical test cases to assess the validity of the theoretical studies.
