Chein-Shan Liu1
CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 1-20, 2010, DOI:10.3970/cmc.2010.018.001
Abstract We are concerned with the reconstruction of an unknown space-dependent rigidity coefficient in a wave equation. This problem is known as one of the inverse scattering problems. Based on a two-point Lie-group equation we develop a Lie-group adaptive method (LGAM) to solve this inverse scattering problem through iterations, which possesses a special character that by using onlytwo boundary conditions and two initial conditions, as those used in the direct problem, we can effectively reconstruct the unknown rigidity function by aself-adaption between the local in time differential governing equation and the global in time algebraic Lie-group equation. The accuracy and efficiency… More >
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