most citedA comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions

35 citations · 49 across the 3 of their papers we have counts for

collaborators

5 papers

math.NA202010 cited

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…

math.NA202035 cited

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…

math.NA2019

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…

physics.comp-ph2019

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…

math.AP20194 cited

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…