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带局部Kelvin-Voigt型阻尼一维波动问题能量模控制函数

高兴明1, 卢朓2, 姜海燕1, 张琼1   

  1. 1. 北京理工大学数学与统计学院, 北京 100081;
    2. 北京大学数学科学学院, 北京 100871
  • 收稿日期:2021-03-10 发布日期:2022-09-09

高兴明, 卢朓, 姜海燕, 张琼. 带局部Kelvin-Voigt型阻尼一维波动问题能量模控制函数[J]. 数值计算与计算机应用, 2022, 43(3): 259-269.

Gao Xingming, Lu Tiao, Jiang Haiyan, Zhang Qiong. ENERGY NORM CONTROL FUNCTION FOR ONE-DIMENTIONSIONAL WAVE EQUATION WITH LOCAL KELVIN-VOIGT DAMPING[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(3): 259-269.

ENERGY NORM CONTROL FUNCTION FOR ONE-DIMENTIONSIONAL WAVE EQUATION WITH LOCAL KELVIN-VOIGT DAMPING

Gao Xingming1, Lu Tiao2, Jiang Haiyan1, Zhang Qiong1   

  1. 1. School of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, China;
    2. CAPT, HEDPS, LMAM, IFSA Collaborative Innovation Center of MoE, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2021-03-10 Published:2022-09-09
带有局部Kelvin-Voigt型阻尼波动方程能量衰减规律是控制论中一个热点研究课题,能量衰减规律的控制函数具有重要理论价值和实际意义.本文对带局部Kelvin-Voigt型阻尼的一维波动方程设计了经典三层七点隐式差分格式,数值验证了差分格式计算波函数、能量函数的二阶收敛性,研究了阻尼参数对能量模衰减规律的影响,并采用支持向量机方法拟合了能量衰减控制函数与阻尼参数的关系.
The study of the energy decaying of the wave equation with local Kelvin-Voigt damping is a very important topic in control theory. An implicit seven-points scheme is designed to solve the one dimension wave equation numerically, and it is verified the numerical solutions of the wave function and energy function converge in second order. The effect of the damping parameter to the energy decaying is studied and the relation of the energy decaying function with the damping parameter is investigated through the support vector machine(SVM).

MR(2010)主题分类: 

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