A MIXED FINITE ELEMENT METHOD FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device is described by a system of three quasilinear partial differential equations. One is elliptic in form for the electric potential and the other two are parabolic in form for the conservation of electron and hole concentrations. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by a Galerkin method that applies a variant of the method of characteristics to the transport terms. Optimal order convergence analysis in L2 is given for the proposed method.     

UPWIND FINITE VOLUME SCHEMES FOR SEMICONDUCTOR DEVICE

The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations. One equation in elliptic form is for the electrostatic potential; two equations of convection-dominated diffusion type are for the electron and hole concentrations. Finite volume element procedure are put forward for the electrostatic potential, while upwind     

FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.     

半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

SURFACE FINITE ELEMENTS FOR

In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.     

The high-order SPDEs driven by multi-parameter fractional noises

The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.     

FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS

A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.     

ON A NEW 3D MODEL FOR INCOMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS

In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented.     

A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE IMMISCIBLE PROBLEMS

Two-phase,incompressible,immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations.The pressure equation is elliptic, whereas the concentration equation is parabolic,and both are treated by the collocation scheme.Existence and uniqueness of solutions of the algorithm are proved.A optimal convergence analysis is given for the method.     

Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential

We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain Ω R3. The viscosity, heat conduc- tion coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solu- tions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyper- bolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set.     

半导体设备热传输中的隐式-显式多步有限元法

考虑热引导半导体设备中的传输行为，用一个有限元法离散电子位势所满足的Rpoisson方程；用隐式－显式多步有限元法处理电子密度和空洞密度满足的两个对流－扩散方程，热传导方程用隐式多步有限元法离散，推导了优化的L^2范误差估计。     

三维热传导型半导体问题的特征混合元方法和分析

本文研究三维热传导型半导体态问题的特征混合元方法及其理论分析,其数学模型是一类非线性偏微分方程的初边值问题,对电子位势方程提出混合元逼近,对电子,空穴浓度方程笔挺表限元逼近;对热传导方程采用对时间向后差分的Ｇａｌｅｒｋｉｎ逼近,应用微分方程先验估计理论和技巧得到了最优阶Ｌ＾２误差估计。     

半导体器件瞬态模拟的对称正定混合元方法

提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题。提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定失窃工格式求解电场位势和电场强度方程;提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程,浓度函数和流函数被同时求解;采用标准的有限元方法求解热传导方程。建立了误差分析理论。     

热传导型半导体瞬态问题的迎风有限体积元方法

半导体瞬态问题的数学模型是由四个方程组成的非线性偏微分方程组的初边值问题所决定．其中电子浓度和空穴浓度方程往往是对流占优扩散问题,普通的方法已不适用,为此本文用迎风格式处理对流项部分,提出一种全离散迎风有限体积元方法,并进行收敛性分析,在最一般的情况下得到了一阶精度L2模误差估计结果．     

热传导型半导体问题的配置方法及误差分析

热传导型半导体瞬态问题的数学模型是一类非线性偏微分方程的初边值问题．电子位势方程是椭圆型的，电子、空穴浓度方程及热传导方程是抛物型的．该文给出求解的配置方法，得到次优犔２模误差估计，并将配置法和Ｇａｌｅｒｋｉｎ有限元方法进行数值结果比较．     

三维热传导型半导体问题的交替方向特征有限元方法

提出交替方向特征有限元方法,对电场位势方程采用混合元格式,对电子,空穴浓度方程采用交替方向特征有限元格式,对温度方程提出交替方向格式.应用向量积计算及先验估计理论和技巧,得到最佳的L2误差估计.     

半导体瞬态问题的混合迎风有限体积格式

半导体器件的瞬时状态由包含3个拟线性偏微分方程所组成的方程组的初边值问题来描述.在三角剖分的基础上,对椭圆型的电子位势方程采用混合有限体积元法来逼近,对对流扩散型的电子浓度和空穴浓度方程采用迎风有限体积元方法来逼近,并进行了详细的理论分析,得到了最优阶的误差估计结果.最后,针对混合有限体积元法和迎风有限体积元法分别单独使用以及两种方法结合使用的情形给出了不同的数值算例.     

半导体器件数值模拟的混合元逼近

半导体器件瞬时状态的模型由三个非线性偏微分方程组所决定.一个是关于电子位势的方程外型是椭圆的,另两个是关于电子和空穴浓度方程外型是抛物的,电子位势通过其电场强度在浓度方程中出现,以及相应的边界和初始条件.我们讨论平面区域Ω上的问题: