Parallel CPU- and GPU-Algorithms for Inverse Problems in Nondestructive Testing

Abstract

This paper is concerned with developing efficient methods for solving inverse problems of ultrasonic nondestructive imaging in the framework of a scalar wave model, which describes the propagation, diffraction and refraction of longitudinal ultrasonic waves. The problem of recovering the velocity of a longitudinal wave in a solid is formulated as a coefficient inverse problem, which in this formulation is nonlinear. The proposed scalable numerical algorithms can be efficiently parallelized both on CPU- and GPU-equipped supercomputers. The efficiency of the algorithms is illustrated by applying them to model problems. The computations were performed on the “Lomonosov” supercomputer at Lomonosov Moscow State University.