INVERSE SOLUTION TO THE WAVE EQUATION USING THE LAGUERRE TRANSFORM
A.F. Mastryukov, B.G. Mikhailenko
Institute of Computing Mathematics and Mathematical Geophysics, Siberian Branch of the RAS, 6 prosp. Akad. Lavrentieva, Novosibirsk, 630090, Russia
Keywords: Inverse problem; wave equation; Maxwell's equations; electromagnetic waves; conductivity; permittivity; finitedifference method; Laguerre transform; accuracy
Pages: 575580
Abstract
An inverse solution to the 1D wave equation is obtained using the spectral Laguerre transform to find the distribution of wave velocities at some point of the medium. The problem is solved as optimization in which the function of Laguerre harmonics is minimized by the conjugate gradient or Newton's algorithms. Reported are velocities of a wave defined by a stepwise constant function. The accuracy of the inverse solution for the Laguerre harmonics is investigated against the approximation accuracy in the boundary problem. The accuracy and efficiency of the Laguerre method are compared to those in the Fourier method.
