Geodesic
Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 381-397

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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. 
@article{SJVM_2019_22_4_a0,
     author = {A. B. Bakushinsky and A. S. Leonov},
     title = {Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {381--397},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a0/}
}
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A. B. Bakushinsky; A. S. Leonov. Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 381-397. http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a0/