In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The FROSch-deal.II interface works for both Lagrange-based and N\'ed\'elec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell's equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.

翻译：本工作中，采用来自Trilinos软件包FROSch（快速鲁棒重叠施瓦茨）的限制性加性施瓦茨（RAS）与优化限制性加性施瓦茨（ORAS）预处理器，求解基于deal.II（微分方程分析库）实现的模型问题。为此，我们实现了一个基于Tpetra的接口用于耦合deal.II与FROSch。虽然RAS预处理器此前已可用，但ORAS预处理器是新近加入FROSch的功能。该FROSch-deal.II接口同时适用于基于拉格朗日与Nédélec的有限元。本文以非定常非线性变分单一体流固耦合问题及不定时间调和麦克斯韦方程组作为模型问题。在二维与三维空间中的若干数值实验验证了预处理器的性能以及FROSch-deal.II接口的有效性。综上所述，该软件接口整体设计直观易用，同时能为具有挑战性的偏微分方程系统提供令人满意的求解器性能。