A5101926587- Advanced Numerical Methods in Computational Mathematics
- Computational Fluid Dynamics and Aerodynamics
- Numerical methods for differential equations
- Electromagnetic Simulation and Numerical Methods
- Gas Dynamics and Kinetic Theory
- Model Reduction and Neural Networks
- Fluid Dynamics and Turbulent Flows
- Lattice Boltzmann Simulation Studies
- Numerical methods in engineering
- Differential Equations and Numerical Methods
- Numerical methods in inverse problems
- Meteorological Phenomena and Simulations
- Advanced Mathematical Physics Problems
- Magneto-Optical Properties and Applications
- Advanced Mathematical Modeling in Engineering
- Navier-Stokes equation solutions
- Nuclear reactor physics and engineering
- Drilling and Well Engineering
- Spectroscopy and Quantum Chemical Studies
- Radiation Dose and Imaging
- Nanoplatforms for cancer theranostics
- Spectroscopy and Laser Applications
- Electron Spin Resonance Studies
- Photoacoustic and Ultrasonic Imaging
- Optical Imaging and Spectroscopy Techniques
Rensselaer Polytechnic Institute
2015-2024
Linyi University
2022
Shengli Oilfield Central Hospital
2021
Hangzhou Normal University
2019-2020
Nankai University
2008
University of South Carolina
2006
Brown University
2003-2005
Peking University
2003
Wuhan Institute of Physics and Mathematics
2000
Chinese Academy of Sciences
2000
Discontinuous Galerkin methods are developed for solving the Vlasov--Maxwell system, that designed to be systematically as accurate one wants with provable conservation of mass and possibly total energy. Such properties in general hard achieve within other numerical method frameworks simulating system. The proposed scheme employs discontinuous discretizations both Vlasov Maxwell equations, resulting a consistent description distribution function electromagnetic fields. It is proven, up some...
A new numerical method for computing the divergence-free part of solution time-harmonic Maxwell equations is studied in this paper. It based on a discretization that uses locally Crouzeix-Raviart nonconforming $P_1$ vector fields and includes consistency term involving jumps across element boundaries. Optimal convergence rates (up to an arbitrary positive $\epsilon$) both energy norm $L_2$ are established graded meshes. The theoretical results confirmed by experiments.
An interior penalty method for certain two-dimensional curl-curl problems is investigated in this paper. This computes the divergence-free part of solution using locally discontinuous $P_1$ vector fields on graded meshes. It has optimal order convergence (up to an arbitrarily small $\epsilon$) source problem and eigenproblem. Results numerical experiments that corroborate theoretical results are also presented.
In [F. Li, C.-W. Shu, Y.-T. Zhang, H. Zhao, J. Comput. Phys., 227 (2008) pp. 8191–8208], we developed a fast sweeping method based on hybrid local solver which is combination of discontinuous Galerkin (DG) finite element and first order difference for Eikonal equations. The has second accuracy in the $L^1$ norm very convergence speed, but only $L^\infty$ general cases. This an obstacle to design higher DG methods. this paper, overcome problem by developing uniformly accurate methods solving...
In this paper, some theoretical aspects will be addressed for the asymptotic preserving discontinuous Galerkin implicit-explicit (DG-IMEX) schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu, and T. Xiong, High order DG-IMEX discrete-velocity kinetic equations a diffusive scaling, http://arxiv.org/abs/1306.0227, 2013, submitted] transport under scaling. We focus on methods that are based (DG) spatial discretizations with $P^k$ polynomial space first (IMEX) temporal discretization, apply...
Simulating wave propagation is one of the fundamental problems in scientific computing. In this paper, we consider one-dimensional two-way equations, and investigate a family $L^2$ stable high order discontinuous Galerkin methods defined through general form numerical fluxes. For these methods, systematically establish stability (hence energy conservation), error estimates (in both negative-order norms), dispersion analysis. One novelty work to identify sub-family fluxes, termed $\alpha...