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math.NA2025
A Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning
Yan Shen, Jingrun Chen, Keke Wu
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining t…
math.NA2025
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…
math.NA2025
Finite volume element method for Landau-Lifshitz equation
Yunjie Gong, Jingrun Chen, Rui Du +1
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved…