Numerics of acoustical 2D tomography based on the conservation laws

Sergey I. Kabanikhin; Dmitriy V. Klyuchinskiy; Nikita S. Novikov; Maxim A. Shishlenin

doi:10.1515/jiip-2019-0061

Numerics of acoustical 2D tomography based on the conservation laws

Sergey I. Kabanikhin, Dmitriy V. Klyuchinskiy, Nikita S. Novikov, Maxim A. Shishlenin

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented.

Original language	English
Pages (from-to)	287-297
Number of pages	11
Journal	Journal of Inverse and Ill-Posed Problems
Volume	28
Issue number	2
Early online date	20 Feb 2020
DOIs	https://doi.org/10.1515/jiip-2019-0061
Publication status	Published - Apr 2020

Keywords

Acoustics
coefficient inverse problem
conservation laws
Godunov scheme
optimization method
INVERSE PROBLEM
RECONSTRUCTION
MODEL
SIMULATION
SPATIAL DISTRIBUTIONS
WAVES
ABSORPTION
SOUND-VELOCITY
ULTRASOUND TOMOGRAPHY

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10.1515/jiip-2019-0061

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title = "Numerics of acoustical 2D tomography based on the conservation laws",

abstract = "We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented.",

keywords = "Acoustics, coefficient inverse problem, conservation laws, Godunov scheme, optimization method, INVERSE PROBLEM, RECONSTRUCTION, MODEL, SIMULATION, SPATIAL DISTRIBUTIONS, WAVES, ABSORPTION, SOUND-VELOCITY, ULTRASOUND TOMOGRAPHY",

author = "Kabanikhin, {Sergey I.} and Klyuchinskiy, {Dmitriy V.} and Novikov, {Nikita S.} and Shishlenin, {Maxim A.}",

year = "2020",

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doi = "10.1515/jiip-2019-0061",

language = "English",

volume = "28",

pages = "287--297",

journal = "Journal of Inverse and Ill-Posed Problems",

issn = "0928-0219",

publisher = "Walter de Gruyter GmbH",

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T1 - Numerics of acoustical 2D tomography based on the conservation laws

AU - Kabanikhin, Sergey I.

AU - Klyuchinskiy, Dmitriy V.

AU - Novikov, Nikita S.

AU - Shishlenin, Maxim A.

PY - 2020/4

Y1 - 2020/4

N2 - We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented.

AB - We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented.

KW - Acoustics

KW - coefficient inverse problem

KW - conservation laws

KW - Godunov scheme

KW - optimization method

KW - INVERSE PROBLEM

KW - RECONSTRUCTION

KW - MODEL

KW - SIMULATION

KW - SPATIAL DISTRIBUTIONS

KW - WAVES

KW - ABSORPTION

KW - SOUND-VELOCITY

KW - ULTRASOUND TOMOGRAPHY

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U2 - 10.1515/jiip-2019-0061

DO - 10.1515/jiip-2019-0061

M3 - Article

AN - SCOPUS:85082703889

VL - 28

SP - 287

EP - 297

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 2

ER -

Numerics of acoustical 2D tomography based on the conservation laws

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Keywords

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