8 papers · 1 filter
Penalty-Free Natural Deep Ritz Method Based on de Rham Complex for High-Dimensional Dirichlet Boundary Value Problems
Jiarong Chen, Xia Ji, Haijun Yu +1
Deep neural networks show great promise for high-dimensional PDEs, yet enforcing essential boundary conditions remains challenging, especially as penalty parameters require problem…
Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
Beining Xu, Bocheng Zhang, Haijun Yu +2
Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space--time do…
Fast Jacobi Spectral Methods and Closure Approximations for the Homogeneous FENE Model of Complex Fluids
Runkai Feng, Jie Shen, Haijun Yu
The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is com…
Scaling Optimized Spectral Approximations on Unbounded Domains: The Generalized Hermite and Laguerre Methods
Hao Hu, Haijun Yu
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shan…
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
Scaling Optimized Hermite Approximation Methods
Hao Hu, Haijun Yu
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather t…