论文标题
在高频制度中的赫尔姆霍尔兹问题的粗空间的比较
A comparison of coarse spaces for Helmholtz problems in the high frequency regime
论文作者
论文摘要
解决频域和异质媒体中的时谐波传播问题带来了许多数学和计算挑战，尤其是在高频制度中。我们将重点关注计算挑战，并尝试确定一些在应用中出现的一些众所周知的基准案例的最佳算法和数值策略。目的是通过数值实验和考虑最佳实施策略来涵盖近年来Helmholtz方程开发的主要两级域分解方法。这些方法的理论要么与标准数学工具无法触及，要么不能涵盖所有实际兴趣的情况。更确切地说，我们将重点放在三个产生两级方法的粗空间的比较上：网格粗糙空间，DTN粗空间和Geneo粗糙空间。我们将证明它们显示出不同的利弊，并取决于问题和特定的数值设置。
Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational challenges and try to identify the best algorithm and numerical strategy for a few well-known benchmark cases arising in applications. The aim is to cover, through numerical experimentation and consideration of the best implementation strategies, the main two-level domain decomposition methods developed in recent years for the Helmholtz equation. The theory for these methods is either out of reach with standard mathematical tools or does not cover all cases of practical interest. More precisely, we will focus on the comparison of three coarse spaces that yield two-level methods: the grid coarse space, DtN coarse space, and GenEO coarse space. We will show that they display different pros and cons, and properties depending on the problem and particular numerical setting.
