标题： 广义界面条件下的Stokes-Darcy问题的优化Schwarz方法 显示英文标题

标题： Optimized Schwarz method for the Stokes-Darcy problem with generalized interface conditions

摘要： 由于Stokes-Darcy问题及其不同界面条件集在环境设置以及工业和医学应用中的广泛出现，在数学建模和计算科学领域的研究者们对此展开了积极的研究。 在实际应用中，对于这类耦合问题的数值模拟，需要稳健且高效的计算算法。 在这项工作中，我们考虑了最近利用均匀化和边界层理论发展起来的一种Beavers-Joseph界面条件的推广形式。 这一扩展不仅适用于与流体-多孔介质界面平行的流动（如同其前辈），还适用于任意流动方向。 为了高效求解带有这些广义界面条件的Stokes-Darcy问题，我们开发并分析了一种基于Fourier分析来确定Robin界面条件最优权重的Robin-Robin区域分解方法。 我们研究了所提出方法的效率和稳健性，并提供了数值模拟结果，这些结果验证了所得出的理论结果。 显示英文摘要

摘要： Due to their wide appearance in environmental settings as well as industrial and medical applications, the Stokes-Darcy problems with different sets of interface conditions establish an active research area in the community of mathematical modelers and computational scientists. For numerical simulation of such coupled problems in applications, robust and efficient computational algorithms are needed. In this work, we consider a generalization of the Beavers-Joseph interface condition recently developed using homogenization and boundary layer theory. This extension is applicable not only for the parallel flows to the fluid-porous interface as its predecessor, but also for arbitrary flow directions. To solve the Stokes-Darcy problem with these generalized interface conditions efficiently, we develop and analyze a Robin-Robin domain decomposition method using Fourier analysis to identify optimal weights in the Robin interface conditions. We study efficiency and robustness of the proposed method and provide numerical simulations which confirm the obtained theoretical results.