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Deep Domain Decomposition Methods: Helmholtz Equation

文献类型：期刊论文

作者Li, Wuyang2,4; Wang, Ziming1,3; Cui, Tao1,3; Xu, Yingxiang4; Xiang, Xueshuang2
刊名ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
出版日期2023-02-01
卷号15期号:1页码:118-138
关键词Helmholtz equation deep learning domain decomposition method plane wave method
ISSN号2070-0733
DOI10.4208/aamm.OA-2021-0305
英文摘要This paper proposes a deep-learning-based Robin-Robin domain decom-position method (DeepDDM) for Helmholtz equations. We first present the plane wave activation-based neural network (PWNN), which is more efficient for solving Helmholtz equations with constant coefficients and wavenumber k than finite differ-ence methods (FDM). On this basis, we use PWNN to discretize the subproblems di-vided by domain decomposition methods (DDM), which is the main idea of Deep-DDM. This paper will investigate the number of iterations of using DeepDDM for continuous and discontinuous Helmholtz equations. The results demonstrate that: DeepDDM exhibits behaviors consistent with conventional robust FDM-based domain decomposition method (FDM-DDM) under the same Robin parameters, i.e., the num-ber of iterations by DeepDDM is almost the same as that of FDM-DDM. By choosing suitable Robin parameters on different subdomains, the convergence rate is almost constant with the rise of wavenumber in both continuous and discontinuous cases. The performance of DeepDDM on Helmholtz equations may provide new insights for improving the PDE solver by deep learning.
资助项目National Key R&D Program of China[2019YFA0709600] ; National Key R&D Program of China[2019YFA0709602] ; China NSF[11831016] ; China NSF[12171468] ; China NSF[11771440] ; China NSF[12071069] ; Fundamental Research Funds for the Central Universities[JGPY202101] ; Innovation Foundation of Qian Xuesen Laboratory of Space Technology
WOS研究方向Mathematics ; Mechanics
语种英语
WOS记录号WOS:000880390000004
出版者GLOBAL SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60661]  
专题中国科学院数学与系统科学研究院
通讯作者Xiang, Xueshuang
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC, Beijing 100190, Peoples R China
2.China Acad Space Technol, Qian Xuesen Lab Space Technol, Beijing 100094, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Northeast Normal Univ, Jilin Natl Appl Math Ctr NENU, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
推荐引用方式
GB/T 7714		 Li, Wuyang,Wang, Ziming,Cui, Tao,et al. Deep Domain Decomposition Methods: Helmholtz Equation[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS,2023,15(1):118-138.
APA Li, Wuyang,Wang, Ziming,Cui, Tao,Xu, Yingxiang,&Xiang, Xueshuang.(2023).Deep Domain Decomposition Methods: Helmholtz Equation.ADVANCES IN APPLIED MATHEMATICS AND MECHANICS,15(1),118-138.
MLA Li, Wuyang,et al."Deep Domain Decomposition Methods: Helmholtz Equation".ADVANCES IN APPLIED MATHEMATICS AND MECHANICS 15.1(2023):118-138.

入库方式： OAI收割

来源：数学与系统科学研究院

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