Geodesic
Applicability of stratified models for solving problems of three-dimensional ultrasonic tomography
Numerical methods and programming, Tome 14 (2013) no. 4, pp. 533-542.

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The paper is devoted to carrying out mathematical modeling in very large scale problems of propagation of ultrasonic waves in the diagnosis of three-dimensional physical environments on supercomputers. The results allow one to use the ultrasonic studies in the diagnosis of breast cancer. The standard approach in 3D tomography offers to explore objects by their two-dimensional cross sections. This approach is ideal for X-ray tomography. In ultrasonic tomography, the consideration of thin layers is not always justified, since the rays can be bent due to the refraction and can leave the layer. In this paper, this problem is illustrated by computing the scattering on a sphere, since this problem has an analytic solution in the form of special function series. This solution is used as input data for the reconstruction of the layered sphere. The simulation results indicate the potential use of stratified schemes in ultrasonic tomography. However, one should consider the degradation of resolution in the orthogonal direction to the layers. The study and optimization of the program code are performed using a variety of means for profiling and track analysis performed. A high-performance software for supercomputers of high degree of scalability was developed. Model calculations were carried out on the MSU supercomputers “Chebyshev” and “Lomonosov”.
Keywords: coefficient inverse problems; wave equation; supercomputer modeling; ultrasonic 3D tomography; parallel computing. 
@article{VMP_2013_14_4_a11,
     author = {G. M. Agayan and Vad. V. Voevodin and S. Yu. Romanov},
     title = {Applicability of stratified models for solving problems of three-dimensional ultrasonic tomography},
     journal = {Numerical methods and programming},
     pages = {533--542},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a11/}
}
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G. M. Agayan; Vad. V. Voevodin; S. Yu. Romanov. Applicability of stratified models for solving problems of three-dimensional ultrasonic tomography. Numerical methods and programming, Tome 14 (2013) no. 4, pp. 533-542. http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a11/