Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network
<|reference_start|>Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network: A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN (in short, C-IGA) [2]. C-IGA achieves higher order approximations without increasing the degree of freedom. Due to the Kronecker delta property of C-IGA shape functions, one can refine the mesh in the physical domain like standard finite element method (FEM) while maintaining the exact geometrical mapping of IGA. In this article, C-IGA theory is generalized for multi-CAD-patch systems with a mathematical investigation of the compatibility conditions at patch interfaces and convergence of error estimates. Two compatibility conditions (nodal compatibility and G^0 (i.e., global C^0) compatibility) are presented and validated through numerical examples.<|reference_end|>
@article{zhang2024multi-patch,
    title={Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural
  Network},
    author={Lei Zhang, Chanwook Park, T.J.R. Hughes, Wing Kam Liu},
    journal={arXiv preprint arXiv:2406.03307},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03307},
    primaryClass={math.NA cs.CE cs.NA}
}