It is posed in paper [1] that Zero energy-error can be used to realize the optimization of Combined hybrid finite element methods through adjusting the combined factor. In this paper, the optimization method is used t...It is posed in paper [1] that Zero energy-error can be used to realize the optimization of Combined hybrid finite element methods through adjusting the combined factor. In this paper, the optimization method is used to plane 4-node quadrilateral Combined hybrid scheme CH(0-1) which own 5 stress parameters with energy compatibility characteristic. Based on the optimization results, the analysis of components of element stiffness matrix, and the conclusions about numerical stability and convergence, this paper deduces that the optimal form of CH(0-1) element, is let the combined factor take 1, i.e., just base on Hellinger-Reissner variational principle, and take bilinear compatible displacement interpolation instead of enrich-strain Wilson's displacements interpolation for the orthgonality of 5-parameter stresses mode with the derived strain from Wilson bubble displacements and the weak force balance.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
This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is ...This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.展开更多
文摘It is posed in paper [1] that Zero energy-error can be used to realize the optimization of Combined hybrid finite element methods through adjusting the combined factor. In this paper, the optimization method is used to plane 4-node quadrilateral Combined hybrid scheme CH(0-1) which own 5 stress parameters with energy compatibility characteristic. Based on the optimization results, the analysis of components of element stiffness matrix, and the conclusions about numerical stability and convergence, this paper deduces that the optimal form of CH(0-1) element, is let the combined factor take 1, i.e., just base on Hellinger-Reissner variational principle, and take bilinear compatible displacement interpolation instead of enrich-strain Wilson's displacements interpolation for the orthgonality of 5-parameter stresses mode with the derived strain from Wilson bubble displacements and the weak force balance.
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.
基金supported by the National Science Foundation of China under Grant No.10871130the Ph.D Foundation under Grant No.20093127110005+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.S30405the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174
文摘This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.
