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.

翻译：在这项工作中,我们根据非重叠域分解法,为隔热操作员制定高效的参数-滚动算法。作为由此产生的Schur问题的补充前提,我们使用了(反的)跨面拉平板的加权分数。我们讨论了在合理近似法方面实现先决条件的问题。我们通过数字实例,包括应用与达西-斯托克问题相关的应用,展示了解决者的业绩。