A5038179929- Numerical methods in engineering
- Electromagnetic Simulation and Numerical Methods
- Advanced Numerical Methods in Computational Mathematics
- Model Reduction and Neural Networks
- Composite Material Mechanics
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Electromagnetic Scattering and Analysis
- Advanced Mathematical Physics Problems
- Fractional Differential Equations Solutions
- Numerical methods for differential equations
- Gas Dynamics and Kinetic Theory
- Differential Equations and Numerical Methods
- Lattice Boltzmann Simulation Studies
- Rock Mechanics and Modeling
- Navier-Stokes equation solutions
- Fluid Dynamics and Turbulent Flows
- Nonlinear Photonic Systems
- Advanced Numerical Analysis Techniques
- Thermal properties of materials
- Nonlinear Waves and Solitons
- Theoretical and Computational Physics
- Stability and Controllability of Differential Equations
- High-pressure geophysics and materials
- Quantum and electron transport phenomena
Peking University
2015-2024
State Key Laboratory of Turbulence and Complex Systems
2022
Institute of Mechanics
2022
Chinese Academy of Sciences
2022
University of Chinese Academy of Sciences
2022
Tsinghua University
2008-2021
Shanghai Jiao Tong University
2016-2018
Chengdu University of Technology
2017
Guilin University of Electronic Technology
2013
California Institute of Technology
2005
Abstract In this paper, we present a mathematical framework of the bridging scale method (BSM), recently proposed by Liu et al . Under certain conditions, it had been designed for accurately and efficiently simulating complex dynamics with different spatial scales. From clear consistent derivation, identify two error sources in method. First, use linear finite element interpolation, derive coarse grid equations directly from Newton's second law. Numerical length exists mainly due to...
Abstract Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with constant limiting speed when time becomes sufficiently large. Both the wave fronts are determined system itself independent of values. Comparing other studies, numerical scheme used in this paper satisfactory regard to its accuracy...
In this work, the self-consistent clustering analysis (SCA) framework is extended to include homogenization and full field of 3D anisotropic woven composite Representative Unit Cell (RUC). The developed has two new features, namely, (i), reconstruct local variables, a strain refinement stage presented by solving Lippmann–Schwinger equations within RUC following online predictive in SCA, (ii), discrete Green's operator based on finite difference adopted improve accuracy refined point-wise...
We design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection. These are based on discrete BGK models where both characteristic velocities and the source-term depend singularly relaxation parameter. General stability conditions derived, convergence is proved to entropy solutions scalar equations.
SUMMARY We design a class of accurate and efficient absorbing boundary conditions for molecular dynamics simulations crystalline solids. In one space dimension, the proposed matching take form linear constraint displacement velocity at atoms near boundary, where coefficients are determined by dispersion relation with minimal number involved. Bearing nice features compactness, locality, high efficiency, then extended to treat out‐of‐plane wave problems in square lattice. construct...
In recent years, neural networks have become an increasingly powerful tool in scientific computing. The universal approximation theorem asserts that a network may be constructed to approximate any given continuous function at desired accuracy. backpropagation algorithm further allows efficient optimization of the parameters training network. Powered by GPU's, effective computations for and engineering problems are thereby enabled. addition, we show finite element shape functions also...