In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two different domains often depend critically on the interaction at the interface and therefore the problem cannot be easily decoupled into its subproblems. Here, we present a framework for finding robust preconditioners for a fairly general class of such problems by exploiting operators representing fractional and weighted Laplacians at the interface. Furthermore, we show feasibility of the framework for two common multiphysics problems; namely the Darcy-Stokes problem and a fluid--structure interaction problem. Numerical experiments that demonstrate the effectiveness of the approach are included.

中文翻译：

---

单片耦合多物理场问题的稳健预处理

在许多应用程序中，人们想要对由两个不同域中的两个不同物理过程组成的物理系统进行建模，这些过程通过一个公共接口耦合。一个关键的挑战是，两个不同领域的解决方案通常严重依赖于接口处的交互，因此问题不能轻易地分解为它的子问题。在这里，我们提出了一个框架，通过利用表示接口处的分数和加权拉普拉斯算子的算子，为相当普遍的此类问题寻找稳健的预处理器。此外，我们展示了该框架对两个常见多物理场问题的可行性；即达西-斯托克斯问题和流固耦合问题。包括证明该方法有效性的数值实验。