The purpose of this work is to improve the estimates for the $\Delta$-GenEO method from the paper "Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems" by N. Bootland, V. Dolean, I. G Graham, C. Ma, R. Scheichl (https://doi.org/10.1093/imanum/drac036) when applied to the indefinite Helmholtz equation. We derive k-dependent estimates of quantities of interest ensuring the robustness of the method.

翻译：本文旨在改进N. Bootland、V. Dolean、I. G Graham、C. Ma、R. Scheichl 在论文《Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems》（https://doi.org/10.1093/imanum/drac036）中提出的针对不定亥姆霍兹方程的$\Delta$-GenEO方法的估计。我们推导了相关量的依赖于波数$k$的估计，确保了该方法的鲁棒性。