用重叠施瓦茨法融合低阶模型与高保真模型，提升三维固体力学仿真效率。
Hybrid coupling with operator inference and the overlapping Schwarz alternating method
- 采用重叠施瓦茨交替法耦合局部非侵入式算子推断模型与高保真模型。
- 在三维固体力学问题上实现最高106倍的计算加速。
- 适合需高效多尺度仿真的工程领域，尤其擅长处理异构模型与网格。
本文提出一种新型混合方法，利用重叠施瓦茨交替法（O-SAM）将子域局部的非侵入式算子推断（OpInf）降阶模型（ROM）与高保真全阶模型（FOM）相互耦合。该方法有效应对传统高保真模拟中运行时间长、网格生成复杂等挑战。通过O-SAM的灵活性，实现了不同模型、网格和时间积分方案的无缝集成，在保持高精度的同时显著提升计算效率。在一系列复杂的三维固体力学问题上进行了数值验证，相较于传统的FOM-FOM耦合，计算速度最高提升了106倍。本工作为工程应用中的高效仿真流程开辟了新路径，并可推广至多种偏微分方程系统。
原文摘要 · Abstract (English)
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.
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