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Deep Domain Decomposition Methods: Helmholtz Equation 期刊论文
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2023, 卷号: 15, 期号: 1, 页码: 118-138
作者:  Li, Wuyang;  Wang, Ziming;  Cui, Tao;  Xu, Yingxiang;  Xiang, Xueshuang
收藏  |  浏览/下载：108/0  |  提交时间：2023/02/07
Helmholtz equation  deep learning  domain decomposition method  plane wave method  
INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 470, 页码: 18
作者:  Wu, Sidi;  Lu, Benzhuo
收藏  |  浏览/下载：77/0  |  提交时间：2023/02/07
Interface problems  Multiple-gradient descent  Neural network  PDEs  
Dual-variable-horizon peridynamics and continuum mechanics coupling modeling and adaptive fracture simulation in porous materials 期刊论文
ENGINEERING WITH COMPUTERS, 2022, 页码: 21
作者:  Shen Shangkun;  Yang Zihao;  Cui Junzhi;  Zhang Jieqiong
收藏  |  浏览/下载：43/0  |  提交时间：2023/02/07
Porous materials  Peridynamics  Surface correction  Hybrid model  Adaptive algorithm  Fracture simulation  
Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data 期刊论文
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 卷号: 222, 页码: 14
作者:  Liu, Yechi
收藏  |  浏览/下载：96/0  |  提交时间：2023/02/07
Viscous conservation law  Asymptotic behavior  Time decay rate  Viscous shock wave  Discontinuous initial data  
An inverse problem for the transmission wave equation with Kelvin-Voigt damping 期刊论文
APPLICABLE ANALYSIS, 2022, 页码: 23
作者:  Zhao, Zhongliu;  Zhang, Wensheng
收藏  |  浏览/下载：60/0  |  提交时间：2023/02/07
Wave equation with Kelvin-Voigt damping  discontinuous coefficients  global Carleman estimate  inverse problem  single measurement  
Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 451, 页码: 20
作者:  Hong, Jialin;  Hou, Baohui;  Sun, Liying
收藏  |  浏览/下载：166/0  |  提交时间：2022/04/29
Compact finite difference method  Interior penalty discontinuous Galerkin finite element method  Pade approximation  Averaged energy evolution law  Stochastic wave equation  Multiplicative noise  
A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations 期刊论文
JOURNAL OF SCIENTIFIC COMPUTING, 2022, 卷号: 90, 期号: 2, 页码: 30
作者:  Zhang, Xiaodi;  Wang, Xiaorong
收藏  |  浏览/下载：116/0  |  提交时间：2022/04/02
Mixed finite element method  Divergence-free  Inductionless MHD equations  Conservation of charge and mass  
IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION 期刊论文
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 卷号: 44, 期号: 4, 页码: A2464-A2505
作者:  Gong, Wei;  Li, Jiajie;  Zhu, Shengfeng
收藏  |  浏览/下载：87/0  |  提交时间：2023/02/07
shape optimization  shape gradient  boundary formulation  boundary correction  gradient recovery  finite element method  
Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning 期刊论文
PHYSICA D-NONLINEAR PHENOMENA, 2021, 卷号: 428, 页码: 15
作者:  Wang, Li;  Yan, Zhenya
收藏  |  浏览/下载：127/0  |  提交时间：2022/04/02
Nonlinear dispersive equation  Initial-boundary value conditions  Physics-informed neural networks  Deep learning  Data-driven peakon and periodic peakon  solutions Data-driven parameter discovery  
Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions 期刊论文
JOURNAL OF SCIENTIFIC COMPUTING, 2021, 卷号: 89, 期号: 2, 页码: 42
作者:  Lyu, Maohui;  Bokil, Vrushali A.;  Cheng, Yingda;  Li, Fengyan
收藏  |  浏览/下载：136/0  |  提交时间：2022/04/02
Maxwell's equations  Kerr and Raman nonlinear effects  Linear Lorentz  Nodal discontinuous Galerkin methods  Energy stable  High dimensions