4 papers
High-Precision Phase-Shift Transferable Neural Networks for High-Frequency Function Approximation and PDE Solution
Xuyang Gao, Liang Chen, Minqiang Xu +1
Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial…
A class of positive-preserving,energy stable and high order numerical schemes for the Poission-Nernst-Planck system
Waixiang Cao, Yuzhe Qin, Minqiang Xu
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stabilit…
Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients
Minqiang Xu, Yanting yuan, Waixiang Cao +1
In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods…
A Linear Finite Element Method for a Second Order Elliptic Equation in Non-Divergence Form with Cordes Coefficients
Minqiang Xu, Runchang Lin, Qingsong Zou
In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and a Hessian recovery based linear (HRBL) FEM for second order elliptic equations in…