4 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…