Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain

A three-dimensional coefficient inverse problem for the wave equation (with losses) in a cylindrical domain is under consideration. The data for its solution are special time integrals of the wave field measured in a cylindrical layer. We present and substantiate an efficient algorithm for solving such a three-dimensional problem based on the fast Fourier transform. The algorithm proposed makes possible to obtain a solution on grids of $512\times 512\times 512$ size in a time of about $1.4$ hours on a typical PC without parallelizing the calculations. The results of the numerical experiments for solving the corresponding model inverse problems are presented.