In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form（i.e., by use of numerical quadrature ...In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form（i.e., by use of numerical quadrature in the procedure of computing the left load）, we obtain the optimal estimate O（h）, which is as same as in the traditionalfinite element analysis when the load f ∈ H1 （Ω）η Co（Ω） which is weaker than the previousstudies. The results obtained in this paper are also valid to the conforming triangular elementand nonconforming Carey＇s element.展开更多
This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) ...This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.展开更多
Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper s...Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.展开更多
We consider the drift-diffusion （DD） model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Po...We consider the drift-diffusion （DD） model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin （LDG） schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit （IMEX） time discretization with the LDG spatial diseretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.展开更多
基金Supported by NNSF of China(10371113)Supported by Foundation of Overseas Scholar of Chin&((2001)119)Supported by the project of Creative Engineering of Henan Province of China
文摘In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form（i.e., by use of numerical quadrature in the procedure of computing the left load）, we obtain the optimal estimate O（h）, which is as same as in the traditionalfinite element analysis when the load f ∈ H1 （Ω）η Co（Ω） which is weaker than the previousstudies. The results obtained in this paper are also valid to the conforming triangular elementand nonconforming Carey＇s element.
基金Project (Nos. 60174009 and 70071017) supported by the NationalNatural Science Foundation of China
文摘This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.
文摘Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
基金supported by National Natural Science Foundation of China(Grant No.11471194)Department of Energy of USA(Grant No.DE-FG02-08ER25863)National Science Foundation of USA(Grant No.DMS-1418750)
文摘We consider the drift-diffusion （DD） model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin （LDG） schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit （IMEX） time discretization with the LDG spatial diseretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.
