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

TL;DR

This paper introduces a waveform iteration method integrated into the preCICE coupling library, enabling higher-order, multi-rate coupling for PDE-based simulations, significantly reducing numerical errors and improving efficiency.

Contribution

It presents a novel integration of waveform iteration into preCICE, allowing black-box, multi-rate, higher-order coupling with minimal API modifications.

Findings

Waveform iteration reduces numerical errors by orders of magnitude.

The method enhances the efficiency of multiphysics simulations with disparate time scales.

Integration with preCICE improves coupling accuracy and computational performance.

Abstract

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.