Determination of a space-dependent force function in the one-dimensional wave equation

S. O. Hussein, D. Lesnic

Abstract


The determination of an unknown spacewice dependent force function acting on a vibrating string from over-specied Cauchy boundary data is investigated numerically using the boundary element method (BEM) combined with a regularized method of separating variables. This linear inverse problem is ill-posed since small errors in the input data cause large errors in the output force solution. Consequently, when the input data is contaminated with noise we use the Tikhonov regularization method in order to obtain a stable solution. The choice of the regularization parameter is based on the L-curve method. Numerical results show that the solution is accurate for exact data and stable for noisy data.


Keywords


Inverse force problem; Regularization; L-curve; Boundary element method; Wave equation.

Full Text:

PDF


DOI: https://doi.org/10.14713/ejbe.v12i1.1838



Creative Commons License
Electronic Journal of Boundary Elements by https://ejbe.libraries.rutgers.edu is licensed under a Creative Commons Attribution-Noncommercial 4.0 United States License