@Article{cmes.2016.111.421,
AUTHOR = {Chein-Shan  Liu, Wen  Chen, Ji  Lin},
TITLE = {A Homogenized Function to Recover Wave Source by Solving a Small Scale Linear System of Differencing Equations},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {111},
YEAR = {2016},
NUMBER = {5},
PAGES = {421--435},
URL = {http://www.techscience.com/CMES/v111n5/27329},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2016.111.421}
}