Supercomputer Simulations of Ultrasound Tomography Problems of Flat Objects

Abstract

This paper is concerned with investigating the capabilities of wave tomography methods via supercomputer numerical simulations on a model problem of imaging the wave velocity structure inside flat solid objects. The problem of reconstructing the velocity structure is formulated as a nonlinear coefficient inverse problem. Iterative algorithms for solving this inverse problem are based on computing the gradient of the residual functional between the experimentally measured wave field and the numerically computed wave field. A tomographic diagnostic method is proposed for imaging flat objects which are accessible only from a single side. The method employs two ultrasonic transducer arrays and takes into account reflections from the flat bottom of the object, assuming that the thickness of the object is known. The use of the reflections from the bottom is a key feature of the method, since it significantly increases the number of sounding angles and allows the transmitted waves to be registered. This study compares the results of solving inverse problems with complete and incomplete data sets. The proposed scalable numerical algorithms can be efficiently parallelized on supercomputers. The computations were performed on 50 CPU cores of the ‘‘Lomonosov-2’’ supercomputer at Lomonosov Moscow State University. Numerical simulations were carried out for various tomographic schemes using the high-performance algorithms and supercomputer software developed in this study. The acoustic and geometric parameters of the simulations correspond to a real experiment on nondestructive testing (NDT) of solids.