| Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond | |
| Lu, Ye; Li, Hengyang; Zhang L(张磊); Park, Chanwook; Mojumder, Satyajit; Knapik, Stefan; Sang, Zhongsheng; Tang, Shaoqiang; Apley, DanielW; Wagner, GregoryJ; Liu, WingKam | |
| Source Publication | COMPUTATIONAL MECHANICS
 |
| 2023-05 | |
| ISSN | 0178-7675 |
| Abstract | This paper presents a general Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN) computational frame-work for solving partial differential equations. This is the first paper of a series of papers devoted to C-HiDeNN. We focus on the theoretical foundation and formulation of the method. The C-HiDeNN framework provides a flexible way to construct high-order C(n )approximation with arbitrary convergence rates and automatic mesh adaptivity. By constraining the C-HiDeNN to build certain functions, it can be degenerated to a specification, the so-called convolution finite element method (C-FEM). The C-FEM will be presented in detail and used to study the numerical performance of the convolution approximation. The C-FEM combines the standard C-0 FE shape function and the meshfree-type radial basis interpolation. It has been demon-strated that the C-FEM can achieve arbitrary orders of smoothness and convergence rates by adjusting the different controlling parameters, such as the patch function dilation parameter and polynomial order, without increasing the degrees of freedom of the discretized systems, compared to FEM. We will also present the convolution tensor decomposition method under the reduced-order modeling setup. The proposed methods are expected to provide highly efficient solutions for extra-large scale problems while maintaining superior accuracy. The applications to transient heat transfer problems in additive manufacturing, topology optimization, GPU-based parallelization, and convolution isogeometric analysis have been discussed. |
| Keyword | Convolution FEM and HiDeNN Tensor decomposition Reduced order modeling Additive manufacturing High-order smoothness Isogeometric analysis (IGA) |
| DOI | 10.1007/s00466-023-02336-5 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:000988723200001 |
| Funding Organization | National Natural Science Foundation of China (NSFC) [11832001, 11988102, 12202451] |
| Classification | 一类 |
| Ranking | 3+ |
| Contributor | Lu, Y ; Liu, WK |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/92234 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 1.(Lu Ye, Li Hengyang, Park Chanwook, Knapik Stefan, Sang Zhongsheng, Wagner Gregory J., Liu Wing Kam) Northwestern Univ Dept Mech Engn Evanston IL 60208 USA 2.(Zhang Lei) Chinese Acad Sci Inst Mech State Key Lab Nonlinear Mech Beijing Peoples R China 3.(Zhang Lei) Univ Chinese Acad Sci Sch Engn Sci Beijing Peoples R China 4.(Mojumder Satyajit) Northwestern Univ Theoret & Appl Mech Program Evanston IL USA 5.(Tang Shaoqiang) Peking Univ Coll Engn HEDPS & LTCS Beijing Peoples R China 6.(Apley Daniel W.) Northwestern Univ Dept Ind Engn & Management Sci Evanston IL USA 7.(Lu Ye) Univ Maryland Baltimore Cty Dept Mech Engn 1000 Hilltop Cir Baltimore MD 21250 USA |
| Recommended Citation GB/T 7714 | Lu, Ye,Li, Hengyang,Zhang L,et al. Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond[J]. COMPUTATIONAL MECHANICS,2023.Rp_Au:Lu, Y, Liu, WK |
| APA | Lu, Ye.,Li, Hengyang.,张磊.,Park, Chanwook.,Mojumder, Satyajit.,...&Liu, WingKam.(2023).Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond.COMPUTATIONAL MECHANICS. |
| MLA | Lu, Ye,et al."Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond".COMPUTATIONAL MECHANICS (2023). |
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| Jp2023A056.pdf（5358KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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