半导体器件数值模拟的块中心差分法

此处(1.1)～(1.3)分别是电位势方程,电子浓度(e)和空穴浓度(p)方程,其中α是由介电常数和电子电荷决定的正常数,N(x)表示掺杂分布,r,r_p是正常数,μ(x),μ_p(x)表示迁移率,R(e,p)=(ep—1)/(e+p+2)表示电子和空穴的产生复合率,△是拉普拉斯算子,是梯度算子,v是区域Ω边界Ω的外法线方向,p_0(x),e_0(x)是已知的初始浓度函数。     

Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of difference operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l ² norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.     

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.