| Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity | |
| Zhang L(张磊); Park, Chanwook; Lu, Ye; Li, Hengyang; Mojumder, Satyajit; Saha, Sourav; Guo, Jiachen; Li, Yangfan; Abbott, Trevor; Wagner, Gregory J.; Tang, Shaoqiang; Liu, Wing Kam | |
| Corresponding Author | Liu, Wing Kam(w-liu@northwestern.edu) |
| Source Publication | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
 |
| 2023-12-15 | |
| Volume | 417Pages:46 |
| ISSN | 0045-7825 |
| Abstract | We are witnessing a rapid transition from Software 1.0 to 2.0. Software 1.0 focuses on manually designed algorithms, while Software 2.0 leverages data and machine learning algorithms (or artificial intelligence) for optimized, fast, and accurate solutions. For the past few years, we have been developing Convolution Hierarchical Deep-learning Neural Network Artificial Intelligence (C-HiDeNN-AI), which enables the realization of Engineering Software 2.0 by opening the next-generation neural network-based computational tools that can simultaneously train data and solve mechanistic equations. This paper focuses on solving partial differential equations with C-HiDeNN. Still, the same neural network can be used for training and calibration with experimental data, which will be discussed in a separate paper. This paper presents a computational framework combining the C-HiDeNN theory with isogeometric analysis (IGA), called Convolution IGA (C-IGA). C-IGA has five key features that advance IGA: (1) arbitrarily high-order smoothness and convergence rates without increasing degrees of freedom; (2) a Kronecker delta property that enables direct imposition of Dirichlet boundary conditions; (3) automatic and flexible global/local mesh-adaptivity with built-in length scale control and adjustable radial basis functions; (4) ability to handle irregular meshes and triangular/tetrahedral elements; and (5) GPU implementation that speeds up the program as fast as finite element method (FEM). Mathematically, we prove that both IGA and C-IGA mappings are equivalent, and by taking a special design and modified anchors as nodes, C-IGA degenerates to IGA. We demonstrate the accuracy, convergence rates, mesh-adaptivity, and performance of C-IGA with several 1D, 2D, and 3D numerical examples. The future applications of C-IGA from topology optimization to product manufacturing with multi-GPU programming are discussed.(c) 2023 Elsevier B.V. All rights reserved. |
| Keyword | Convolution isogeometric analysis (C-IGA) Convolution hierarchical deep-learning neural network (C-hiDeNN) Software 2.0 r-h-p-s-a adaptive finite element method (FEM) High-order smoothness and convergence |
| DOI | 10.1016/j.cma.2023.116356 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:001114199100001 |
| WOS Keyword | ELEMENT-METHOD ; VOLUME PARAMETERIZATION ; NURBS |
| WOS Research Area | Engineering ; Mathematics ; Mechanics |
| WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics |
| Classification | 一类 |
| Ranking | 1 |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/93632 |
| Collection | 非线性力学国家重点实验室 |
| Recommended Citation GB/T 7714 | Zhang L,Park, Chanwook,Lu, Ye,et al. Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2023,417:46. |
| APA | 张磊.,Park, Chanwook.,Lu, Ye.,Li, Hengyang.,Mojumder, Satyajit.,...&Liu, Wing Kam.(2023).Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,417,46. |
| MLA | 张磊,et al."Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 417(2023):46. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| Jp2023A124.pdf（9021KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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