一类非线性动力学MEMS方程的数值解

发布时间：2018-06-28 15:16

本文选题：MEMS + 有限差分法　；参考：《河南大学》2017年硕士论文

【摘要】：本文通过研究MEMS中薄膜偏转模型的数值解,观察电压变化对薄膜物理状态的影响,从而确定击穿电压临界值的大小.利用有限差分方法,对非线性抛物型MEMS方程建立了时间空间精确度分别为(1, 2), (2, 2)的两种差分格式,并采用能量法证明了两种差分格式的收敛性及无条件稳定性.数值试验表明,两种格式对抛物型MEMS方程数值模拟是有效的;对一维非线性双曲型MEMS方程建立了时间空间精确度分别为(2, 2),(2, 4)的两种差分格式,用能量法证明出了两种差分格式的收敛性及无条件稳定性.相应的数值试验表明,两种格式对双曲型MEMS方程数值模拟是有效的;对二维非线性双曲型MEMS方程,建立了时间空间精确度为(2, 2)的交替方向隐格式,用能量法证明出了格式的收敛性及无条件稳定性.数值试验表明,格式对二维非线性双曲型MEMS方程数值模拟是有效的.采用上述差分格式均能有效的模拟出相应电压临界值的大小.
[Abstract]:By studying the numerical solution of the film deflection model in MEMS, the influence of voltage variation on the physical state of the film is observed, and the critical value of breakdown voltage is determined. Using finite difference method, two kinds of difference schemes with accuracy of (1,2), (2,2) are established for nonlinear parabolic MEMS equations. The convergence and unconditional stability of the two schemes are proved by energy method. Numerical experiments show that the two schemes are effective for the numerical simulation of parabolic), (equations, and two difference schemes with the accuracy of (2,2), (2,4) for one-dimensional nonlinear hyperbolic MEMS equations are established. The convergence and unconditional stability of two difference schemes are proved by energy method. The corresponding numerical experiments show that the two schemes are effective for the numerical simulation of hyperbolic MEMS equations, and for two-dimensional nonlinear hyperbolic MEMS equations, an alternating direction implicit scheme with the accuracy of (2,2) is established. The convergence and unconditional stability of the scheme are proved by the energy method. Numerical experiments show that the scheme is effective for the numerical simulation of two dimensional nonlinear hyperbolic MEMS equations. By using the above difference scheme, the corresponding voltage critical value can be effectively simulated.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8

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