Solution of the inverse problem of the acoustic equation by the multilevel optimization method

The inverse problem of the acoustic equation for attenuation in the frequency region is solved by the optimization method. A spectral multilevel adaptive algorithm with expansion of the unknown quantities into a Fourier series is proposed. Comparison is made between the efficiencies of spectral adaptive variants of three iteration minimization methods: gradient method, conjugate-gradient method, and Newton method. It is shown that transition to the spectral region increases the convergence of both adaptive and nonadaptive algorithms. This transition is most profitable for the gradient and conjugate-gradient methods. A spectral multilevel adaptive algorithm requires 2-5 times less calculations than a nonadaptive one. Compared with both nonspectral adaptive and nonadaptive algorithms, a spectral algorithm provides a more precise solution to the inverse problem for the gradient and conjugate-gradient methods.