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 and a three-dimensional footing problem. 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用于耦合问题的整体时空多重率方案。其创新之处在于多重率方法的整体化公式化，这需要精心设计函数框架、相应的离散化方案及实现过程。我们选择的求解方法是张量积伽辽金时空离散化方法。研究针对两类典型耦合问题展开，即界面耦合问题（如耦合波动-热传导问题）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）。后者被应用于著名的Mandel基准问题及三维地基问题。详细的数值计算研究与收敛性分析表明，我们所提出的整体多重率框架具有良好的性能表现。