Open Access

ARTICLE

A Homogenized Function to Recover Wave Source by Solving a Small Scale Linear System of Differencing Equations

Chein-Shan Liu^1,2,3, Wen Chen¹, Ji Lin¹

1 Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China
2 Department of Civil Engineering, National Taiwan University, Taipei 106-17, Taiwan
3 Corresponding author, E-mail: liucs@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2016, 111(5), 421-435. https://doi.org/10.3970/cmes.2016.111.421

Abstract

In order to recover unknown space-dependent function G(x) or unknown time-dependent function H(t) in the wave source F(x; t) = G(x)H(t), we develop a technique of homogenized function and differencing equations, which can significantly reduce the difficulty in the inverse wave source recovery problem, only needing to solve a few equations in the problem domain, since the initial condition/ boundary conditions and a supplementary final time condition are satisfied automatically. As a consequence, the eigenfunctions are used to expand the trial solutions, and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations. Because the ill-posedness of the inverse wave source problem is greatly reduced, the present method is accurate and stable against a large noise up to 50%, of which the numerical tests confirm the observation.

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Keywords

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