6 papers
BTF-PINN: Enforcing Dirichlet Boundary Conditions Without Boundary Training
Wenyu Dong, Shuo Zhang
The homogeneous Dirichlet boundary value problem captures the core difficulty of solving Dirichlet problems with non-interpolatory methods. We propose BTF-PINN (Boundary-Training-F…
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…
Primal finite element scheme of the Hodge-Laplace problem
Wenyu Dong, Shuo Zhang
In this paper, we construct nonconforming finite element spaces for the approximation of on si…
A Natural Decomposition Method for Essential Boundary Conditions in Noninterpolatory Meshfree Spaces
Jingkai Zhang, Tiexiang Li, Shuo Zhang
This paper develops a natural decomposition method (NDM)for imposing essential boundary conditions in noninterpolatory meshfree Galerkin spaces without boundary parameter tuning or…
A Natural Deep Ritz Method for Essential Boundary Value Problems
Haijun Yu, Shuo Zhang
Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential bo…
Lowest-degree robust finite element schemes for inhomogeneous bi-Laplace problems
Bin Dai, Huilan Zeng, Chensong Zhang +1
In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respe…