Many multiphysics simulations involve processes evolving on disparate time scales, posing a challenge for efficient coupling. A naive approach that synchronizes all processes using the smallest time scale wastes computational resources on slower processes and typically achieves only linear convergence in time. Waveform iteration is a promising numerical technique that enables higher-order, multi-rate coupling while treating coupled components as black boxes. However, applying this approach to PDE-based coupled simulations is nontrivial. In this paper, we integrate waveform iteration into the black-box coupling library preCICE with minimal modifications to its API. We detail how this extension interacts with key preCICE features, including data mapping for non-matching meshes, quasi-Newton acceleration for strongly coupled problems, and parallel peer-to-peer communication. We then showcase that waveform iteration significantly reduces numerical errors -- often by orders of magnitude. This advancement greatly enhances preCICE, benefiting its extensive user community.

翻译：许多多物理场仿真涉及在差异显著的时间尺度上演化的过程，这对高效耦合提出了挑战。采用最小时间尺度同步所有过程的朴素方法会浪费计算资源于较慢过程，且通常仅能实现时间上的线性收敛。波形迭代是一种有前景的数值技术，可在将耦合组件视为黑盒的同时实现高阶、多速率耦合。然而，将这种方法应用于基于偏微分方程的耦合仿真并非易事。本文以最小化API修改的方式，将波形迭代集成至黑盒耦合库preCICE中。我们详细阐述了该扩展如何与preCICE的关键特性交互，包括非匹配网格的数据映射、强耦合问题的拟牛顿加速以及并行点对点通信。随后我们展示波形迭代能显著降低数值误差——通常达数量级幅度。这一进展极大增强了preCICE的功能，惠及其广泛的用户群体。