Supercomputer Methods of Ultrasound Tomographic Imaging in NDT Based on Lamb Waves

Alexander S. Belyaev; Alexander V. Goncharsky; Sergey Y. Romanov; Vadim V. Voevodin

doi:10.14529/jsfi250403

Authors

Alexander S. Belyaev Lomonosov Moscow State University, Moscow, Russian Federation https://orcid.org/0000-0001-9762-1505
Alexander V. Goncharsky Lomonosov Moscow State University, Moscow, Russian Federation https://orcid.org/0000-0001-9953-611X
Sergey Y. Romanov Lomonosov Moscow State University, Moscow, Russian Federation https://orcid.org/0000-0001-7882-2061
Vadim V. Voevodin Lomonosov Moscow State University, Moscow, Russian Federation https://orcid.org/0000-0003-1897-1828

DOI:

https://doi.org/10.14529/jsfi250403

Keywords:

supercomputer, mathematical modeling, guided wave tomography, inverse problems, Lamb waves

Abstract

This article concerns the developing of supercomputer methods for solving inverse problems of ultrasonic tomography in application to nondestructive testing of thin plates using Lamb waves. Such problems are computationally expensive, as longitudinal, shear, and other waves propagate in solids, requiring the use of vector elastic models of wave propagation. Iterative methods for solving the inverse problem have been developed. The methods are based on gradient descent methods of minimizing the residual functional. Efficiency of the proposed algorithms is illustrated on model problems. The field of wave tomography, which is currently under development, requires powerful computing resources. Parallel computations in this study have been performed on generalpurpose processors of the Lomonosov supercomputer complex. Solving the Helmholtz equation is the core element of the developed algorithms for solving inverse problems of wave tomography. The most demanding computations involve solving linear equations with large-scale sparse matrices using LU-decomposition method. The algorithms were implemented using linear algebra libraries with serial and parallel code. Effectiveness, scalability and performance of the method has been evaluated on CPU computing platforms.

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