Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds
<|reference_start|>Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds: The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.<|reference_end|>
@article{li2024data-free,
    title={Data-free Non-intrusive Model Reduction for Nonlinear Finite Element
  Models via Spectral Submanifolds},
    author={Mingwu Li, Thomas Thurnher, Zhenwei Xu, Shobhit Jain},
    journal={arXiv preprint arXiv:2409.10126},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10126},
    primaryClass={math.NA cs.CE cs.NA math.DS}
}