A5014226512- Advanced Numerical Methods in Computational Mathematics
- Numerical methods in engineering
- Advanced Mathematical Modeling in Engineering
- Electromagnetic Simulation and Numerical Methods
- Numerical methods for differential equations
- Differential Equations and Numerical Methods
- Matrix Theory and Algorithms
- Electromagnetic Scattering and Analysis
- Textile materials and evaluations
- Advanced Numerical Analysis Techniques
- Computational Fluid Dynamics and Aerodynamics
- Numerical methods in inverse problems
- Iterative Methods for Nonlinear Equations
- Mechanical and Optical Resonators
- Advanced MEMS and NEMS Technologies
- Traffic Prediction and Management Techniques
- Advanced Optimization Algorithms Research
- Mathematical functions and polynomials
- Transportation Planning and Optimization
- Photonic and Optical Devices
- Fractional Differential Equations Solutions
- Lattice Boltzmann Simulation Studies
- Composite Material Mechanics
- Rheology and Fluid Dynamics Studies
- Autonomous Vehicle Technology and Safety
Zhejiang Chinese Medical University
2025
Beijing Normal University
2020-2024
Ming Chi University of Technology
2024
Beijing Normal University - Hong Kong Baptist University United International College
2020-2024
Weifang University
2024
Southwest Forestry University
2020-2024
Soochow University
2024
Beijing Information Science & Technology University
2023
Ministry of Education
2023
Fuyang Normal University
2017-2022
A rapid solidification strategy was developed for simultaneously avoiding the Marangoni effect and suppressing molecular aggregation. The resultant 15.64 cm 2 large-area OSC module exhibited a record power conversion efficiency of 16.03%.
In this paper, we study the stability and convergence of Crank–Nicolson/Adams–Bashforth scheme for two‐dimensional nonstationary Navier–Stokes equations. A finite element method is applied spatial approximation velocity pressure. The time discretization based on Crank–Nicolson linear term explicit Adams–Bashforth nonlinear term. Moreover, present optimal error estimates prove that almost unconditionally stable convergent, i.e., convergent when step less than or equal to a constant.
We present a micromechanical device designed to be used as non-volatile mechanical memory. The structure is composed of suspended slender nanowire (width: 100 nm, thickness: 430 length: 8 30 µm) clamped at both ends. Electrodes are placed on each side the (1) actuate during data writing and erasing mode (2) determine its position by measuring capacitive bridge in reading mode. patterned electron beam lithography pre-stressed thermally grown silicon dioxide layer. When later released plasma...
In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with linearized semi-implicit Euler scheme for equations incompressible miscible flow in porous media. We prove that optimal $L^2$ hold without any time-step (convergence) conditions, while all previous works require certain restrictions. Our theoretical results provide new understanding on commonly used schemes. The proof is based splitting into two parts: from time discretization PDEs finite...
This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank--Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in $d$-dimensional space, $d=2,3$. In our analysis, we split function into two parts, one from spatial discretization temporal discretization, by introducing a corresponding time-discrete (elliptic) system. We present rigorous regularity solution system estimates time discretization. With these proved...
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class L1-Galerkin finite element methods.The analysis L1 methods for limited mainly due to the lack fundamental Gronwall type inequality.In this paper, we establish such inequality approximation Caputo fractional derivative.In terms inequality, provide optimal error estimates several fully discrete linearized Galerkin problems.The theoretical results are illustrated applying our proposed...
A fast algorithm is presented for solving electromagnetic scattering from a rectangular open cavity embedded in an infinite ground plane. The medium inside the assumed to be (vertically) layered. By introducing transparent (artificial) boundary condition, problem reduced bounded domain problem. simple finite difference method then applied solve model Helmholtz equation. designed resulting discrete system terms of Fourier transform horizontal direction, Gaussian elimination vertical and...
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs Galerkin finite element approximations. In particular, we study time-dependent Joule heating equations. We present optimal error estimates Euler scheme in both $L^2$ norm and $H^1$ without any restriction. Theoretical analysis based on a new splitting precise corresponding time-discrete system. The method used this can be applied to more general systems many...
The method of characteristics type is especially effective for convection-dominated diffusion problems. Due to the nature characteristic temporal discretization, allows one use a large time step in many practical computations, while all previous theoretical analyses always required certain restrictions on stepsize. Here, we present new analysis establish unconditionally optimal error estimates modified with mixed finite element approximation miscible displacement problem $\mathbb{R}^d\...
Abstract Despite abundant accessible traffic data, researches on flow estimation and optimization still face the dilemma of detailedness integrity in measurement. A dataset city-scale vehicular continuous trajectories featuring finest resolution integrity, as known holographic would be a breakthrough, for it could reproduce every detail evolution reveal personal mobility pattern within city. Due to high coverage Automatic Vehicle Identification (AVI) devices Xuancheng city, we constructed...
In this paper, the Legendre--Petrov--Galerkin method for Korteweg--de Vries equation with nonperiodic boundary conditions is analyzed. The nonlinear term computed Legendre spectral and some pseudospectral methods, respectively. Optimal error estimates in L2 -norm are obtained both semidiscrete fully discrete schemes. also applicable to (2m+1)th-order differential equations.
In this paper, we study linearized Crank--Nicolson Galerkin finite element methods for time-dependent Ginzburg--Landau equations under the Lorentz gauge. We present an optimal error estimate schemes (almost) unconditionally (i.e., when spatial mesh size $h$ and temporal step $\tau$ are smaller than a given constant), while previous analyses were only some with strong restrictions on time step-size. The key to our analysis is boundedness of numerical solution in norm. prove cases $\tau\ge h$...
A Legendre--Petrov--Galerkin (LPG) method for the third-order differential equation is developed. By choosing appropriate base functions, can be implemented efficiently. Also, this new approach enables us to derive an optimal rate of convergence in L2 -norm. The applied some nonlinear problems such as Korteweg--de Vries (KdV) with Chebyshev collocation treatment term. It a and (LPG-CC) method. Numerical experiments are given confirm theoretical result.
Hermite spectral methods are investigated for linear diffusion equations and nonlinear convection-diffusion in unbounded domains. When the solution domain is unbounded, operator no longer has a compact resolvent, which makes unstable. To overcome this difficulty, time-dependent scaling factor employed expansions, yields positive bilinear form. As consequence, stability convergence can be established approach. The present method plays similar role of {similarity transformation} technique...