Inverse space-dependent force problems for the wave equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:306

Article

Lesnic, D.¹  Hussein, S. O.¹  Johansson, B. T.² 

[1] Univ Leeds, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England

[2] Aston Univ, Sch Math, Birmingham B4 7ET, W Midlands, England

关键词: Inverse force problem;    Finite difference method;    Landweber method;    Conjugate gradient method;    Wave equation;   

DOI  :  10.1016/j.cam.2016.03.034

来源: Elsevier

【 摘 要 】

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free