In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Galerkin space-time discretization. The developments are carried out for both prototype interface- and volume coupled problems such as coupled wave-heat-problems and a displacement equation coupled to Darcy flow in a poro-elastic medium. The latter is applied to the well-known Mandel's benchmark. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well.

翻译：本文提出并计算研究了适用于耦合问题的单一时空多率方案。其创新之处在于多率方法的单一公式化设计，这需要仔细构建泛函框架、相应的离散化及实现方案。我们选择的方法是基于张量积的伽辽金时空离散化。研究分别针对原型界面耦合问题（如波-热耦合问题）和体积耦合问题（如多孔弹性介质中位移方程与达西流的耦合）展开，后者应用于著名的曼德尔基准问题。详细的计算研究与收敛性分析表明，我们的单一多率框架性能良好。