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

Computation

Dmitriy Klyuchinskiy¹  Maxim Shishlenin¹  Nikita Novikov¹ 

[1] Novosibirsk State University, Novosibirsk 630090, Russia;

关键词: acoustics;    tomography;    first-order hyperbolic system;    inverse problem;    Godunov method;    gradient descent method;   

DOI  :  10.3390/computation8030073

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown