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Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations. / Klyuchinskiy, Dmitriy; Novikov, Nikita; Shishlenin, Maxim.

In: Mathematics, Vol. 9, No. 2, 199, 02.01.2021, p. 1-13.

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

Harvard

Klyuchinskiy, D, Novikov, N & Shishlenin, M 2021, 'Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations', Mathematics, vol. 9, no. 2, 199, pp. 1-13. https://doi.org/10.3390/math9020199

APA

Klyuchinskiy, D., Novikov, N., & Shishlenin, M. (2021). Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations. Mathematics, 9(2), 1-13. [199]. https://doi.org/10.3390/math9020199

Vancouver

Klyuchinskiy D, Novikov N, Shishlenin M. Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations. Mathematics. 2021 Jan 2;9(2):1-13. 199. doi: 10.3390/math9020199

Author

Klyuchinskiy, Dmitriy ; Novikov, Nikita ; Shishlenin, Maxim. / Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations. In: Mathematics. 2021 ; Vol. 9, No. 2. pp. 1-13.

BibTeX

@article{24c2ad5df9bc4a68a66e74e80647cb89,
title = "Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations",
abstract = "We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.",
keywords = "Acoustics, Density reconstruction, First-order hyperbolic system, Godunov method, Gradient descent method, Inverse problem, Speed of sound reconstruction, Tomography",
author = "Dmitriy Klyuchinskiy and Nikita Novikov and Maxim Shishlenin",
note = "Funding Information: Funding: The work has been supported by the RSCF under grant 19-11-00154 “Developing of new mathematical models of acoustic tomography in medicine. Numerical methods, HPC and software”. Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jan,
day = "2",
doi = "10.3390/math9020199",
language = "English",
volume = "9",
pages = "1--13",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "2",

}

RIS

TY - JOUR

T1 - Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations

AU - Klyuchinskiy, Dmitriy

AU - Novikov, Nikita

AU - Shishlenin, Maxim

N1 - Funding Information: Funding: The work has been supported by the RSCF under grant 19-11-00154 “Developing of new mathematical models of acoustic tomography in medicine. Numerical methods, HPC and software”. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/2

Y1 - 2021/1/2

N2 - We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

AB - We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

KW - Acoustics

KW - Density reconstruction

KW - First-order hyperbolic system

KW - Godunov method

KW - Gradient descent method

KW - Inverse problem

KW - Speed of sound reconstruction

KW - Tomography

UR - http://www.scopus.com/inward/record.url?scp=85099859140&partnerID=8YFLogxK

U2 - 10.3390/math9020199

DO - 10.3390/math9020199

M3 - Article

AN - SCOPUS:85099859140

VL - 9

SP - 1

EP - 13

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 2

M1 - 199

ER -

ID: 27607547