NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.

Projection-based High-dimensional Sign Test

This article is concerned with the high-dimensional location testing problem.For highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels.Several modifications have been proposed to address this challenging issue and shown to perform well.However,most of modified sign-based tests abandon all the correlation information,and this results in power loss in certain cases.We propose a projection weighted sign test to utilize the correlation information.Under mild conditions,we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under alternatives.Benefiting from using the sample-splitting idea for estimating the optimal direction,the proposed test is able to retain type-I error rates pretty well with asymptotic distributions,while it can be also highly competitive in terms of robustness.Its advantage relative to existing methods is demonstrated in numerical simulations and a real data example.

MINIMUM PERIOD CONTROL PROBLEM FOR INFINITE DIMENSIONAL SYSTEM

In order to solve the so-called minimum period control problem for a class of abstract evolutionary systems, the authors study an infinite dimensional time optimal control problem with mixed type target set. To the latter problem complete results are established, which then are applied to the former to derive the desirable answer.

Galerkin Spectral Method Applied to the Chemical Master Equation

Stochastic well-stirred chemically reacting systems can be accurately modeled by a continuous-time Markov-chain.The corresponding master equation evolves the system’s probability density function in time but can only rarely be explicitly solved.We investigate a numerical solution strategy in the form of a spectral method with an inherent natural adaptivity and a very favorable choice of basis functions.Theoretical results related to convergence have been developed previously and are briefly summarized while implementation issues,including how to adapt the basis functions to follow the solution they represent,are covered in more detail here.The method is first applied to a model problem where the convergence can easily be studied.Then we take on two more realistic systems from molecular biology where stochastic descriptions are often necessary to explain experimental data.The conclusion is that,for sufficient accuracy demands and not too high dimensionality,the method indeed provides an alternative to other methods.

Integral Transform Methods for Inverse Problem of Heat Conduction with Known Boundary of a Thin Rectangular Object and its Stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D： -a〈xSa; -b〈_y〈b; 0〈z〈h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.