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：本工作的目的是改进N. Bootland、V. Dolean、I. G Graham、C. Ma、R. Scheichl（https://doi.org/10.1093/imanum/drac036）在论文《用于非定常与非自伴问题的含GenEO粗空间的重叠Schwarz方法》中提出的$\Delta$-GenEO方法应用于非定常Helmholtz方程时的估计。我们推导了与波数k相关的关键量估计，从而确保该方法的鲁棒性。