MEMS中一类非线性抛物型动力学方程的数值解  

Numerical Solution of a Nonlinear Parabolic Dynamics Equations in MEMS

作　　者：孙寿文 王波 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]河南大学应用数学所,河南开封475004

出　　处：《河南大学学报（自然科学版）》2017年第6期751-756,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金项目(40805020);河南省高等学校青年骨干教师资助计划项目(2014GGJS-021);河南大学新兴交叉及特色学科培育计划(0000A40450)

摘　　要：通过研究MEMS中薄膜偏转模型的数值解,观察电压大小变化对薄膜物理状态的影响.利用有限差分方法对模型中非线性抛物型动力学方程进行数值离散,建立了关于时间及空间精确度均为2阶的有限差分格式,并用能量不等式法证明了所给差分格式的收敛性及其无条件稳定性.最后数值试验表明,在本文差分格式下计算出来的电压数值解满足薄膜对应的物理状态,验证了所构造出的差分格式对于数值模拟的有效性.因此本文所建立的差分格式对于求解电压与失稳效应之间的关系问题是切实可行的.In this paper,by studying the numerical solution of the thin film deflection model in MEMS,the effect of voltage on the physical state of the film was observed.Finite difference method was used for numerical discretization of the nonlinear parabolic equations in the model,and the estimate analysis proved it is a second order accurate scheme for both time and space.We used the energy inequality method proving the convergence of the difference scheme and its unconditional stability.At least,numerical experiments show that the numerical solution of the voltage in the difference scheme can satisfy the physical state of the thin film,and the validity of the difference scheme is verified.Therefore,the difference scheme established in this paper is feasible to solve the problem of the relationship between voltage and instability.

关 键 词：MEMS 有限差分法 能量不等式 数值解 

分 类 号：O241.8[理学—计算数学]