TY  - EJOU
AU  - Liu, Chein-Shan  
AU  - Chen, Wen  
AU  - Lin, Ji  

TI  - A Homogenized Function to Recover Wave Source by Solving a Small Scale Linear System of Differencing Equations
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2016
VL  - 111
IS  - 5
SN  - 1526-1506

AB  - 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.
KW  - Wave source recovery problem
KW  -  Eigenfunctions
KW  -  Homogenized function
KW  -  Differencing equations

DO  - 10.3970/cmes.2016.111.421