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

Chein-Shan Liu1,2,3, Wen Chen1, Ji Lin1

Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China
Department of Civil Engineering, National Taiwan University, Taipei 106-17, Taiwan
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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Cite This Article

Liu, C., Chen, W., Lin, J. (2016). A Homogenized Function to Recover Wave Source by Solving a Small Scale Linear System of Differencing Equations. CMES-Computer Modeling in Engineering & Sciences, 111(5), 421–435.



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