A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations
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 init...
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| Format: | Article |
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MDPI AG
2020-08-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/8/3/73 |
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| author | Dmitriy Klyuchinskiy Nikita Novikov Maxim Shishlenin |
| author_facet | Dmitriy Klyuchinskiy Nikita Novikov Maxim Shishlenin |
| author_sort | Dmitriy Klyuchinskiy |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T17:07:17Z |
| format | Article |
| id | doaj.art-d08eee5f2b8d439c9254504efeaa8dab |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T17:07:17Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-d08eee5f2b8d439c9254504efeaa8dab2023-11-20T10:47:26ZengMDPI AGComputation2079-31972020-08-01837310.3390/computation8030073A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics EquationsDmitriy Klyuchinskiy0Nikita Novikov1Maxim Shishlenin2Department of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk 630090, RussiaDepartment of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk 630090, RussiaDepartment of Mathematics and Mechanics, Novosibirsk State University, Novosibirsk 630090, RussiaWe 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.https://www.mdpi.com/2079-3197/8/3/73acousticstomographyfirst-order hyperbolic systeminverse problemGodunov methodgradient descent method |
| spellingShingle | Dmitriy Klyuchinskiy Nikita Novikov Maxim Shishlenin A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations Computation acoustics tomography first-order hyperbolic system inverse problem Godunov method gradient descent method |
| title | A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations |
| title_full | A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations |
| title_fullStr | A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations |
| title_full_unstemmed | A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations |
| title_short | A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations |
| title_sort | modification of gradient descent method for solving coefficient inverse problem for acoustics equations |
| topic | acoustics tomography first-order hyperbolic system inverse problem Godunov method gradient descent method |
| url | https://www.mdpi.com/2079-3197/8/3/73 |
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