Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity
文献类型：期刊论文
| 作者 | Zhang, Lei5,6; Park, Chanwook4; Lu, Ye3; Li, Hengyang4; Mojumder, Satyajit2; Saha, Sourav2; Guo, Jiachen2; Li, Yangfan4; Abbott, Trevor4; Wagner, Gregory J.4 |
| 刊名 | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
 |
| 出版日期 | 2023-12-15 |
| 卷号 | 417页码:46 |
| ISSN号 | 0045-7825 |
| 关键词 | 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 |
| 通讯作者 | Liu, Wing Kam(w-liu@northwestern.edu) |
| 英文摘要 | 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. |
| WOS关键词 | ELEMENT-METHOD ; VOLUME PARAMETERIZATION ; NURBS |
| WOS研究方向 | Engineering ; Mathematics ; Mechanics |
| 语种 | 英语 |
| WOS记录号 | WOS:001114199100001 |
| 源URL | [http://dspace.imech.ac.cn/handle/311007/93631]  |
| 专题 | 力学研究所_非线性力学国家重点实验室 |
| 通讯作者 | Liu, Wing Kam |
| 作者单位 | 1.Peking Univ, Coll Engn, HEDPS & LTCS, Beijing 100871, Peoples R China 2.Northwestern Univ, Theoret & Appl Mech Program, Evanston, IL USA 3.Univ Maryland Baltimore Cty, Dept Mech Engn, Baltimore, MD 21250 USA 4.Northwestern Univ, Dept Mech Engn, Evanston, IL 60208 USA 5.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China 6.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhang, Lei,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 | Zhang, Lei.,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 | Zhang, Lei,et al."Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 417(2023):46. |
入库方式： OAI收割
来源：力学研究所
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