A waveform iteration implementation for black-box multi-rate higher-order coupling

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.