论文标题
具有分数接口扰动的操作员的域分解求解器
Domain decomposition solvers for operators with fractional interface perturbations
论文作者
论文摘要
具有分数扰动的运算符是对接口耦合多物理系统进行鲁棒预处理的关键组件。但是，如果扰动很强，标准方法可能无法提供逆的可扩展近似，从而损害了整个多物理求解器的效率。在这项工作中，我们基于非重叠域分解方法为接口扰动操作员开发了有效的参数式算法。作为最终的Schur补体问题的预处理，我们使用的（对倒置）界面拉普拉斯的分数力量的加权总和。讨论了从理性近似方面实现预处理。我们通过数值示例（包括应用于达西 - 斯托克斯问题的应用）来证明求解器的性能。
Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation of the inverse, thus compromising efficiency of the entire multiphysics solver. In this work, we develop efficient and parameter-robust algorithms for interface-perturbed operators based on the non-overlapping domain decomposition method. As preconditioners for the resulting Schur complement problems we utilize (inverses of) weighted sums of fractional powers of the interfacial Laplacian. Realization of the preconditioner in terms of rational approximation is discussed. We demonstrate performance of the solvers by numerical examples including application to coupled Darcy-Stokes problem.
