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An energy stable linear diffusive Crank-Nicolson scheme for the Cahn-Hilliard gradient flow 期刊论文
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 卷号: 377, 页码: 26
Authors:  Wang, Lin;  Yu, Haijun
Favorite  |  View/Download:1/0  |  Submit date:2020/06/30
Cahn-Hilliard gradient flow  Unconditionally stable  Stabilized semi-implicit scheme  Diffusive Crank-Nicolson scheme  Error analysis  Adaptive time stepping  
Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units 期刊论文
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2020, 卷号: 27, 期号: 2, 页码: 379-411
Authors:  Li, Bo;  Tang, Shanshan;  Yu, Haijun
Favorite  |  View/Download:2/0  |  Submit date:2020/05/24
Deep neural network  high dimensional approximation  sparse grids  rectified linear unit  rectified power unit  rectified quadratic unit  
NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS 期刊论文
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2019, 卷号: 9, 期号: 2, 页码: 161-186
Authors:  Wan, Xiaoliang;  Yu, Haijun
Favorite  |  View/Download:6/0  |  Submit date:2020/01/10
Wiener chaos expansion  Wick product  stochastic elliptic PDE  uncertainty quantification  log-normal random coefficient  
ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION 期刊论文
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2019, 卷号: 17, 期号: 3, 页码: 609-635
Authors:  Wang, Lin;  Yu, Haijun
Favorite  |  View/Download:9/0  |  Submit date:2020/01/10
Allen-Cahn equation  energy stable  stabilized semi-implicit scheme  second order scheme  error estimate  
A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS 期刊论文
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2017, 卷号: 14, 期号: 4-5, 页码: 762-783
Authors:  Rong, Zhijian;  Shen, Jie;  Yu, Haijun
Favorite  |  View/Download:5/0  |  Submit date:2018/07/30
Sparse grid  spectral element method  high-dimensional problem  adaptive method