论文标题
DTN和Geneo粗空间是否足以适应异质Helmholtz问题？
Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?
论文作者
论文摘要
异质Helmholtz问题的数值解决方案提出了各种计算挑战，描述性理论对于许多流行的方法仍无法触及。鲁棒性和可伸缩性对于大规模应用中的实用和可靠求解器是关键，尤其是对于大波浪数问题。在这项工作中，我们探讨了使用基因型粗空间来构建适用于高度不确定的Helmholtz问题的两级添加剂Schwarz方法。通过对2D模型问题的一系列数值测试，该测试由无污染网格的有限元素离散，我们观察到可靠的收敛性，迭代计数不会随波浪数的增加而增加，并且我们的方法可扩展性良好。我们进一步提供结果，显示了与DTN粗空间的有利比较。我们的数值研究表明，我们的求解器方法可以有效地挑战异质应用。
Numerical solution of heterogeneous Helmholtz problems presents various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications.
