论文标题
单层耦合多物理问题的强大预处理
Robust preconditioning of monolithically coupled multiphysics problems
论文作者
论文摘要
在许多应用程序中，一个人希望对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，这些域在一个共同的接口上耦合。那么一个至关重要的挑战是，两个不同域的解决方案通常急切地取决于界面上的相互作用，因此问题不能轻易地将其解耦到其子问题中。在这里，我们提出了一个框架，可以通过利用代表界面上代表分数和加权拉普拉斯人的操作员来寻找相当一般的此类问题类别的框架。此外，我们显示了两个常见多物理问题的框架的可行性。即达西 - 斯托克斯问题和流体结构的相互作用问题。包括证明该方法有效性的数值实验。
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.
