35 citations · 49 across the 3 of their papers we have counts for
5 papers
Enforcing exact boundary and initial conditions in the deep mixed residual method
Liyao Lyu, Keke Wu, Rui Du +1
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in cl…
A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions
Jingrun Chen, Rui Du, Keke Wu
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical…
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
Panchi Li, Changjian Xie, Rui Du +2
In this paper, we present two improved Gauss-Seidel projection methods with unconditional stability. The first method updates the gyromagnetic term and the damping term simultaneou…
Second-order semi-implicit projection methods for micromagnetics simulations
Changjian Xie, Carlos J. García-Cervera, Cheng Wang +2
Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, nonlocal, and has a n…
Convergence Analysis of A Second-order Semi-implicit Projection Method for Landau-Lifshitz Equation
Jingrun Chen, Cheng Wang, Changjian Xie
The numerical approximation for the Landau-Lifshitz equation, the dynamics of magnetization in a ferromagnetic material, is taken into consideration. This highly nonlinear equation…