scholarly journals 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 ◽  
Vol 9 (2) ◽  
pp. 199
Author(s):  
Dmitriy Klyuchinskiy ◽  
Nikita Novikov ◽  
Maxim Shishlenin

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.

2020 ◽  
Vol 28 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Sergey I. Kabanikhin ◽  
Dmitriy V. Klyuchinskiy ◽  
Nikita S. Novikov ◽  
Maxim A. Shishlenin

AbstractWe 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.


Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 73
Author(s):  
Dmitriy Klyuchinskiy ◽  
Nikita Novikov ◽  
Maxim Shishlenin

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.


2021 ◽  
Vol 2099 (1) ◽  
pp. 012044
Author(s):  
N S Novikov ◽  
D V Klyuchinskiy ◽  
M A Shishlenin ◽  
S I Kabanikhin

Abstract In this paper we consider the inverse problem of detecting the inclusions inside the human tissue by using the acoustic sounding wave. The problem is considered in the form of coefficient inverse problem for first-order system of PDE and we use the gradient descent approach to recover the coefficients of that system. The important part of the sceme is the solution of the direct and adjoint problem on each iteration of the descent. We consider two finite-volume methods of solving the direct problem and study their Influence on the performance of recovering the coefficients.


2020 ◽  
Vol 56 (12) ◽  
pp. 1634-1643
Author(s):  
D. K. Durdiev ◽  
Kh. Kh. Turdiev

2021 ◽  
Vol 2092 (1) ◽  
pp. 012020
Author(s):  
D.V. Klyuchinskiy ◽  
N.S. Novikov ◽  
M.A. Shishlenin

Abstract In this paper we study properties of the model, that describes the plane acoustic waves propagation. The model is based on the hyperboliv system of PDE, which is solved numerically by using the finite-volume method, based on Godunov scheme. After studying the direct problem we turn to the inverse one, where our goal is to recover the parameters of the system of PDE by using the initial data, measured in the receivers. We obtain the formula for the gradient of the misfits functional, which allows us to apply gradient-based optimization for recovering the density of the medium. We present the results of numerical experiments for different number of receivers, thus, studying the influence of the quantity of the data of inverse problem on the accuracy of the solution.


2021 ◽  
Vol 2099 (1) ◽  
pp. 012046
Author(s):  
M A Shishlenin ◽  
N S Novikov ◽  
D V Klyuchinskiy

Abstract The inverse problem of recovering the acoustic attenuation in the inclusions inside the human tissue is considered. The coefficient inverse problem is formulated for the first-order system of PDE. We reduce the inverse problem to the optimization of the cost functional by gradient method. The gradient of the functional is determined by solving a direct and conjugate problem. Numerical results are presented.


Author(s):  
Volodymyr Fedorov ◽  
Vasyl’ Yanovsky ◽  
Dmytro Kovalshuk

Ecological requirements for cars grow from year to year, both in the world as a whole, and in Ukraine in particular. This is especially true of noise pollution. Additionally, noise reduction becomes relevant, taking into account the conduct of military operations during the last 5 years on the territory of Ukraine. The war has caused a special need for military vehicles for which masking properties are vital. Noise is a serious disincentive factor. Therefore, its reduction for a military vehicle, apart from the environmental aspect, is of a purely military nature, that is, it is extremely important. The car has many sources of noise there are many ways to deal with them. One of the most powerful source of noise is the sleeping bag. This kind of noise is reduced by means of silencers of noise. The vast majority of silencer data in the basis of its design has a reactive (or resonant) muffler. To calculate the jet silencer you must know the speed of sound in the sleeping bags. In order to increase the acoustic efficiency of reactive and resonant mufflers of exhaust gases noise of the ICE of cars, an experimental method was proposed for determining the speed of sound in the sleighs. Implementation of the method is carried out by measuring the attenuation of acoustic waves. The noise level of the bedrooms is measured without silencer and silencer. Based on the data obtained, the noise reduction performance of the residual is established. From the well-known formula, based on the calculation of the efficiency of the silencing of a jet muffler, a formula is obtained for calculating the speed of sound in the sleeping quays. In this formula, all parameters are known: the level of silencer efficiency, the noise level of the sleeping, the ratio of areas of cross sections of the muffler and the inlet pipe and the length of the muffler. The sound speed thus established can continue to be used not only for engines of the type for which measurements and calculations were made, but also with a certain approximation for some other types of engines. This method provides high accuracy for determining the required parameter. In the given work on the example of the armored car KrAZ “Fiona” the calculation of efficiency increase of the reactive silencer is made due to the above-mentioned method. Also, the projected decrease in the external noise level of the KrAZ Armored Vehicle “Fiona” is considered by determining the speed of sound in the recesses on the trunk cycle on the road with acceleration up to speed of 50 km/h (75 km/h) and the movement with this speed, as well as when driving at a speed of 45 km/h. Keywords: transport, armored car, internal combustion engine, exhaust, exhaust gases, noise, source, acoustic efficiency, acoustic efficiency, speed of sound, jet muffler.


2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.


Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.


2011 ◽  
Vol 354 (4) ◽  
pp. 1431-1464
Author(s):  
Katsiaryna Krupchyk ◽  
Matti Lassas

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