An Algorithm for Recovering the Characteristics of the Initial State of Supernova

Кабанихин, С. И.; Kulikov, Igor; Shishlenin, Maxim A.

doi:10.1134/s0965542520060135

Cited by 9 publications

(2 citation statements)

References 30 publications

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“…Its advantage relies on its close connection to the physics of wave propagation, since the equations can be derived straight from the conservation laws. We mention several papers [9][10][11][12][13][14], where authors investigated inverse problems for a system of hyperbolic partial differential equations. One can also mention the following papers [15,16], where authors considered the direct problems for linear hyperbolic systems and studied their well-posedness.…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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.

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Section: Introductionmentioning

confidence: 99%

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

2021

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“…This field was studied intensively lately [4][5][6][7][8][9][10]. On the mathematical level, such problems are usually formulated in terms of an inverse problem, where some parameters of the medium are to be determined by using additional information [11][12][13][14][15]. Thus, an important issue is the construction of effective algorithms for solving the inverse problem, and, therefore, direct problem due to their tightly connected efficiency.…”

Section: Introductionmentioning

confidence: 99%

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

2020

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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.

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CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach

Klyuchinskiy

Novikov

Shishlenin

2021

Journal of Computational Physics

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An Algorithm for Recovering the Characteristics of the Initial State of Supernova

Cited by 9 publications

References 30 publications

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

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

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach

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