Development of numerical algorithms for solving the direct problem of propagation of ultrasonic waves in thin plates

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.