Geodesic
Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates
Numerical methods and programming, Tome 24 (2023) no. 3, pp. 275-290.

Voir la notice de l'article provenant de la source Math-Net.Ru

This article is devoted to the development of efficient numerical methods for solving direct problems of wave propagation in solids in vector mathematical models. Iterative methods for solving inverse problems of wave tomography use, at each iteration, the solution of the direct problem of wave propagation both in forward and backward time to calculate the gradient of the residual functional. Therefore, the solution of the direct problem of wave propagation in elastic media is an integral part of the solution of inverse problems of wave tomography. The purpose of the article is also to determine, using the methods of mathematical modeling characteristics of Lamb waves for ultrasonic diagnostics of defects in thin plates, determination of the ranges of values of the characteristic parameters of the experiment on tomographic diagnostics in thin plates on Lamb waves. The tools for mathematical modeling are the developed numerical methods and programs for solving direct problems. The ultimate goal of the research is to develop methods for solving inverse problems of tomographic non-destructive ultrasonic testing both on Lamb waves and on bulk waves.
Keywords: Mathematical modeling; ultrasound tomography; forward and inverse problems; vector wave model; non-destructive testing; Lamb waves. 
@article{VMP_2023_24_3_a2,
     author = {A. S. Belyaev and A. V. Goncharsky and S. Y. Romanov},
     title = {Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates},
     journal = {Numerical methods and programming},
     pages = {275--290},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2023_24_3_a2/}
}
TY  - JOUR
AU  - A. S. Belyaev
AU  - A. V. Goncharsky
AU  - S. Y. Romanov
TI  - Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates
JO  - Numerical methods and programming
PY  - 2023
SP  - 275
EP  - 290
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2023_24_3_a2/
LA  - ru
ID  - VMP_2023_24_3_a2
ER  - 
%0 Journal Article
%A A. S. Belyaev
%A A. V. Goncharsky
%A S. Y. Romanov
%T Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates
%J Numerical methods and programming
%D 2023
%P 275-290
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2023_24_3_a2/
%G ru
%F VMP_2023_24_3_a2
A. S. Belyaev; A. V. Goncharsky; S. Y. Romanov. Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates. Numerical methods and programming, Tome 24 (2023) no. 3, pp. 275-290. http://geodesic.mathdoc.fr/item/VMP_2023_24_3_a2/