Hybrid coupling with operator inference and the overlapping Schwarz alternating method

TL;DR

This paper introduces a hybrid coupling method combining Operator Inference ROMs with high-fidelity models using the overlapping Schwarz method, significantly improving efficiency in complex 3D simulations.

Contribution

The paper presents a novel hybrid coupling approach that integrates non-intrusive ROMs with FOMs via O-SAM, enabling flexible, efficient multiscale modeling.

Findings

Achieved up to 106x speedup in 3D solid dynamics simulations.

Demonstrated seamless integration of different models and meshes.

Enhanced computational efficiency without sacrificing accuracy.

Abstract

This paper presents a novel hybrid approach for coupling subdomain-local non-intrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local high-fidelity full order models (FOMs) with using the overlapping Schwarz alternating method (O-SAM). The proposed methodology addresses significant challenges in multiscale modeling and simulation, particularly the long runtime and complex mesh generation requirements associated with traditional high-fidelity simulations. By leveraging the flexibility of O-SAM, we enable the seamless integration of disparate models, meshes, and time integration schemes, enhancing computational efficiency while maintaining high accuracy. Our approach is demonstrated through a series of numerical experiments on complex three-dimensional (3D) solid dynamics problems, showcasing speedups of up to 106x compared to conventional FOM-FOM couplings. This work paves the way for more efficient simulation workflows in engineering applications, with potential extensions to a wide range of partial differential equations.