Song, Songhe

1. Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions
   2022/06/25 by Ziyuan Liu, Haifeng Wang, Liu, Ziyuan +9 · 6 citations
   Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
2. High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation
   2021/02/28 by Chaolong Jiang, Cui Jin, Jiang, Chaolong +5 · 4 citations
   Mathematics · Physics and Astronomy · #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics
3. SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions
   2023/12/12 by Ziyuan Liu, Yuhang Wu, Liu, Ziyuan +9 · 3 citations
   Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
4. Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation
   2020/06/15 by Jingye Yan, Qian Xu, Yan, Jingye +5 · 1 citation
   Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods for differential equations
5. An exponential-free Runge--Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn--Hilliard equation
   2024/11/25 by Wang, Haifeng, Sun, Jingwei, Zhang, Hong +2 · 1 citation
   #35Q92 #65M12 #65M15 #65M70 #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)