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Open AccessArticle

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

by Dmitriy Klyuchinskiy 1,2,†, Nikita Novikov 1,2,*,† and Maxim Shishlenin 1,2,3,†
1
Department of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk 630090, Russia
2
Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk 630090, Russia
3
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Computation 2020, 8(3), 73; https://doi.org/10.3390/computation8030073
Received: 22 June 2020 / Revised: 3 August 2020 / Accepted: 11 August 2020 / Published: 20 August 2020
(This article belongs to the Section Computational Engineering)
We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent. View Full-Text
Keywords: acoustics; tomography; first-order hyperbolic system; inverse problem; Godunov method; gradient descent method acoustics; tomography; first-order hyperbolic system; inverse problem; Godunov method; gradient descent method
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Klyuchinskiy, D.; Novikov, N.; Shishlenin, M. A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations. Computation 2020, 8, 73.

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