35 citations · 82 across the 11 of their papers we have counts for
12 papers
Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients
Zetao Ma, Jingrun Chen, Rui Du +1
In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable sc…
Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations
Mengjia Bai, Jingrun Chen, Rui Du +1
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including…
Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii-Moriya interaction
Panchi Li, Shuting Gu, Jin Lan +3
Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii-Moriya interact…
A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation
Panchi Li, Lei Yang, Jin Lan +2
Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot…
Advantages of a semi-implicit scheme over a fully implicit scheme for Landau-Lifshitz-Gilbert equation
Yifei Sun, Jingrun Chen, Rui Du +1
Magnetization dynamics in magnetic materials is modeled by the Landau-Lifshitz-Gilbert (LLG) equation. In the LLG equation, the length of magnetization is conserved and the system…
Roughness Index for Loss Landscapes of Neural Network Models of Partial Differential Equations
Keke Wu, Xiangru Jian, Rui Du +2
Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are g…
A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
Panchi Li, Zetao Ma, Rui Du +1
Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which is solved numerically in general. In micromagnetic simulations, the computation…
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…
Numerical methods for antiferromagnetics
Panchi Li, Jingrun Chen, Rui Du +1
Compared with ferromagnetic counterparts, antiferromagnetic materials are considered as the future of spintronic applications since these materials are robust against the magnetic…
Quasi-Monte Carlo sampling for machine-learning partial differential equations
Jingrun Chen, Rui Du, Panchi Li +1
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined…
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…