袁龙

2025

Discontinuous hybrid neural networks for the one-dimensional partial differential equations

arXiv.org

DOI

2025

A Space-Time Trefftz DG Method for the Second Order Time-Dependent Maxwell System in Anisotropic Media

Journal of Computational Mathematics

DOI

2025

A combined method based on PWDG and local spectral element methods for the nonhomogeneous Helmholtz equation and Maxwell equations in anisotropic media

Applicable Analysis

DOI

2025

A framework of discontinuous Galerkin neural networks for iteratively approximating residuals

arXiv.org

DOI

2025

An unconditionally convergent discontinuous Galerkin neural network method activated by plane waves for Helmholtz equation and Maxwell's equations

2024

A global space-time Trefftz DG scheme for the time-dependent isotropic elastic wave equations

Journal of Computational and Applied Mathematics

DOI

2023

A discontinuous plane wave neural network method for Helmholtz equation and time-harmonic Maxwell’s equations

Advances in Computational Mathematics

DOI

2023

Global space-time Trefftz DG schemes for the time-dependent linear wave equation

Computers and Mathematics with Applications

DOI

2023

A space-time Trefftz DG scheme for the time-dependent Maxwell equations in anisotropic media

Mathematics and Computers in Simulation

DOI

2023

A PWDG method for the Maxwell system in anisotropic media with piecewise constant coefficient matrix

ESAIM: Mathematical Modelling and Numerical Analysis

DOI

2022

A generalized plane wave discontinuous Galerkin method for three-dimensional anisotropic Helmholtz equations with variable wave numbers

Applied Mathematics Letters

DOI

2021

Plane wave discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in anisotropic media

Computers and Mathematics with Applications

DOI

2020

A plane wave least squares method for the Maxwell equations in anisotropic media

Numerical Algorithms

DOI

2020

A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation

DOI

2019

A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems

Computational and Applied Mathematics

DOI

2019

Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell’s Equations in Anisotropic Media

Communications in Computational Physics

DOI

2019

Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers

International Journal of Computational Mathematics

DOI

2018

Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers

Journal of Computational and Applied Mathematics

DOI

2018

The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

Numerical Mathematics Theory Methods and Applications

DOI

2017

A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations

Advances in Computational Mathematics

DOI

2015

复波数Helmholtz方程和时谐Maxwell方程组的平面波间断Petrov-Galerkin方法

《数值计算与计算机应用》

2014

A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations

International Journal of Numerical Analysis and Modeling

DOI

2014

A Plane-Wave Least-Squares Method for Time-Harmonic Maxwell's Equations in Absorbing Media

SIAM Journal on Scientific Computing

DOI

2013

A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions

DOI