A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations

A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations Full article

Journal

Computation
, E-ISSN: 2079-3197

Output data

Year: 2020, Volume: 8, Number: 3, Article number : 73, Pages count : DOI: 10.3390/COMPUTATION8030073

Tags

Acoustics; First-order hyperbolic system; Godunov method; Gradient descent method; Inverse problem; Tomography

Authors

Klyuchinskiy D. ^1,2 , Novikov N. ^1,2 , Shishlenin M. ^1,2,3

Affiliations

1	Department of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk, 630090, Russian Federation
2	Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, 630090, Russian Federation
3	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation

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. © 2020 by the authors.

Klyuchinskiy D. , Novikov N. , Shishlenin M.
A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations
Computation. 2020. V.8. N3. 73 . DOI: 10.3390/COMPUTATION8030073 WOS Scopus OpenAlex

Web of science:	WOS:000578297100001
Scopus:	2-s2.0-85090595430
OpenAlex:	W3065075035

DB	Citing
Scopus	18
OpenAlex	12
Web of science	11