The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem

Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL ²,H ¹ andL , provided that certain relationships hold between the frequency, mesh size and outer radius.     

An algorithmic approach to Hermite-Birkhoff-interpolation

Summary This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete ebyev-systems and naturally associated differential operators [7]. A numerical example is given.     

Convergence of a penalty-finite element approximation for an obstacle problem

Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is where is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.     

La méthode de Kikuchi appliquée aux équations de von Karman

Resumé Le but de cet article est l'étude de l'approximation numérique des solutions non-triviales des équations de Von Karman pour le flambage d'une plaque mince encastrée. S'inspirant de la méthode de Kikuchi pour des problèmes quasi-linéaires du second ordre, on propose une méthode itérative d'éléments finis qui donne des approximations des solutions de norme «petite» qui bifurquent de la solution triviale au voisinage d'une valeur propre simple du problème linéarisé. On démontre la convergence et on obtient des estimations de l'erreur.

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Application of Kikuchi's method to the von Karman equations

Summary The aim of this article is to study the numerical approximation of non-trivial solutions of the Von Karman equations for the buckling of a thin elastic clamped plate. Following Kikuchi's method for second order quasilinear problems, we propose an iterative finite element method which produces approximations of non-trivial solutions of small norm which bifurcate from the trivial solution near simple eigenvalues of the linearised problem. The convergence is proved and error estimates are obtained.

     

Convergence of multistep methods for Volterra functional differential equations

Summary This paper deals with the convergence of nonstationary quasilinear multistep methods with varying step, used for the numerical integration of Volterra functional differential equations. A Perron type condition (appearing in the differential equations theory) is imposed on the increment function. This gives a generalization of some results of Tavernini ([19–21]).     

Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations

Summary GeneralizedA()-stable Runge-Kutta methods of order four with stepsize control are studied. The equations of condition for this class of semiimplicit methods are solved taking the truncation error into consideration. For application anA-stable and anA(89.3°)-stable method with small truncation error are proposed and test results for 25 stiff initial value problems for different tolerances are discussed.     

The dependence of critical parameter bounds on the monotonicity of a Newton sequence

Summary A new method is proposed for the inclusion of the critical parameter ^* of some convex operator equationu=Tu (appearing e.g. in thermal explosion theory). It is based on the fact that for a fixed Newton's method starting with a suitable subsolution is not monotonically if and only if >^*. Several numerical examples arising from nonlinear boundary value problems illustrate the efficiency of the method.     

Carrier transport and related phenomena in MOS devices

Silicon-based devices are currently the most attractive group because they are functioning at room temperature and can be easily integrated into conventional silicon microelectronics. There are many models and simulation programs available to compute CV curves with quantum correction [Choi C-H, Wu Y, Goo JS, Yu Z, Dutton RW. IEEE Trans on Electron Devi 2000; 47(10): 1843; Croci S, Plossu C, Burignat S. J Mater Sci Mater Electron 2003; 14: 311; Soliman L, Duval E, Benzohra M, Lheurette E, Ketata K, Ketata M. Mater Sci Semicond Process 2001; 4: 163]. This work deals with the simulation of electron transfer through SiO₂ barrier of metal–oxide–semiconductor structure (MOS). The carrier density is given by a self consistent resolution of Schrödinger and Poisson equations and then the MOS capacitance is deduced and compared with results available in literature. As it is well known, the MOS capacitance–voltage profiling provides a simple determination of structure parameters. The extracted tunnel oxide thickness and substrate doping are compared with those used in the simulation. For the purpose to investigate the electron tunnelling through the barrier, we have used the transfer matrix approach. Using I–V simulations, we have shown that the traps in SiO₂ matrix have a drastic influence on electron tunnelling through the barrier. The trap-assisted contribution to the tunnelling current is included in many models [Maserjian J, Zamani N. J Appl Phys 1982; 53(1): 559; Houssa M, Stesmans A, Heyns MM. Semicond Sci Technol 2001; 16: 427; Aziz A, Kassmi K, Kassmi Ka, Olivie F. Semicond Sci Technol 2004; 19: 877; Wu You-Lin, Lin Shi-Tin. IEEE Trans Dev Mater Reliab 2006; 6(1): 75; Larcher L. IEEE Trans Electron Dev 2003; 50(5): 1246]; this is the basis for the interpretation of stress induced leakage current (SILC) and breakdown events. Memory effect becomes typical for this structure. We have studied the I–V dependence with trap parameters.     

钟控神经MOS管的改进及其在多值电路中的应用

首先对钟控神经MOS管进行研究,提出了相应的改进方法.然后采用此改进的钟控神经MOS管设计了一种新型多值触发器.与传统的触发器相比较,此多值触发器具有结构简单、速度快、功耗低等特点;而且无需改变电路结构就可实现不同基的多值触发器.PSPICE模拟证明了所设计的电路具有正确的逻辑功能.     

Quantum dot resonant tunneling FET on graphene

At this paper a field effect transistor based on graphene nanoribbon (GNR) is modeled. Like in most GNR-FETs the GNR is chosen to be semiconductor with a gap, through which the current passes at on state of the device. The regions at the two ends of GNR are highly n-type doped and play the role of metallic reservoirs so called source and drain contacts. Two dielectric layers are placed on top and bottom of the GNR and a metallic gate is located on its top above the channel region. At this paper it is assumed that the gate length is less than the channel length so that the two ends of the channel region are un-gated. As a result of this geometry, the two un-gated regions of channel act as quantum barriers between channel and the contacts. By applying gate voltage, discrete energy levels are generated in channel and resonant tunneling transport occurs via these levels. By solving the NEGF and 3D Poisson equations self consistently, we have obtained electron density, potential profile and current. The current variations with the gate voltage give rise to negative transconductance.