Numerical Solution of Direct and Inverse Problems in Diagnostics and Non-Destructive Testing of Engineering Structures and Biological Media

The presentation will address the solution of direct problems, including a mathematical model describing the propagation of ultrasonic pulses in heterogeneous anisotropic media. A numerical method based on tetrahedral meshes for simulating ultrasonic testing in domains with complex geometry will be presented, along with its software implementation using Singularity containers. The report will include results of direct problem simulations related to the impact of dynamic loading on engineering composite structures, as well as on the human thorax and skull.
In addition, a series of inverse problems associated with diagnostics and non-destructive testing of engineering structures and biological media will be considered. Results will be presented for inverse problems arising in geophysics, structural testing, and medical ultrasound. For solving a subset of these problems, a combination of classical gradient-based methods and machine learning techniques is employed.
The presentation also provides a comparison between numerical simulations and experimental data for ultrasonic inspection of composites with delaminations, loading of fibers in textile composites, and medical ultrasound studies in the presence of an acoustically contrasting layer.