Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain
A.B. Bakushinsky1, A.S. Leonov2
1Institute for Systems Analysis, Moscow, Russia
2National Nuclear Research University В«MEPHI», Moscow, Russia
Keywords: трехмерное волновое уравнение, обратная коэффициентная задача, регуляризующий алгоритм, быстрое преобразование Фурье, three-dimensional wave equation, wave field, inverse coefficient problem, regularizing algorithm, fast Fourier transform
Abstract
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 512x512x512 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.
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