Implementation and performance of wave tomography algorithms on SIMD CPU and GPU computing platforms




wave tomography, inverse problem, SIMD, GPU, ARM, benchmark


This paper is concerned with implementation of wave tomography algorithms on modern SIMD CPU and GPU computing platforms. The field of wave tomography, which is currently under development, requires powerful computing resources. Main applications of wave tomography are medical imaging, nondestructive testing, seismic studies. Practical applications depend on computing hardware. Tomographic image reconstruction via wave tomography technique involves solving coefficient inverse problems for the wave equation. Such problems can be solved using iterative gradient-based methods, which rely on repeated numerical simulation of wave propagation process. In this study, finite-difference time-domain (FDTD) method is employed for wave simulation. This paper discusses software implementation of the algorithms and compares the performance of various computing devices: multi-core Intel and ARM-based CPUs, NVidia graphics processors.

Author Biographies

Alexander V. Goncharsky

Sergey Y. Romanov

Sergey Y. Seryozhnikov


  1. M. V. Klibanov and A. A. Timonov, Carleman Estimates for CoefficientInverse Problems and Numerical Applications} (De Gruyter, Berlin, 2004), doi{10.1515/9783110915549.
  2. M. Birk, R. Dapp, N. V. Ruiter, and J. Becker, “GPU-based Iterative Transmission Reconstruction in 3D Ultrasound Computer Tomography,” J. Parallel Distrib. Comput. 74 (1), 1730-1743 (2014). doi{10.1016/j.jpdc.2013.09.007}.
  3. J. Wiskin, D. Borup, M. Andre, et al., “Three-Dimensional Nonlinear Inverse Scattering: Quantitative Transmission Algorithms, Refraction Corrected Reflection, Scanner Design, and Clinical Results,” J. Acoust. Soc. Am. 133 (2013). doi{10.1121/1.4805138}.
  4. V. A. Burov, D. I. Zotov, and O. D. Rumyantseva, “Reconstruction of Spatial Distributions of Sound Velocity and Absorption in Soft Biological Tissues Using Model Ultrasonic Tomographic Data,” Acoust. Phys. 60 (4), 479-491 (2014). doi{10.1134/S1063771014040022}.
  5. S. Romanov, “Simulations in Problems of Ultrasonic TomographicTesting of Flat Objects on a Supercomputer,” inCommunications in Computer and Information Science}(Springer, Cham, 2020), Vol. 1331, pp. 320-331. doi{10.1007/978-3-030-64616-5_28.
  6. A. V. Goncharsky and S. Y. Seryozhnikov, “Supercomputer Technology for Ultrasound Tomographic Image Reconstruction: Mathematical Methods and Experimental Results,” in Communications in Computer and Information Science}(Springer, Cham, 2019), Vol. 965, pp. 401-413. doi{10.1007/978-3-030-05807-4_34.
  7. A. V. Goncharsky and S. Y. Seryozhnikov, “Three-Dimensional Ultrasound Tomography: Mathematical Methods and Experimental Results,” in Communications in Computer and Information Science}(Springer, Cham, 2019), Vol. 1129, pp. 463-474.doi{10.1007/978-3-030-36592-9_38.
  8. A. V. Goncharsky, V. A. Kubyshkin, S. Y. Romanov, and S. Y. Seryozhnikov, “Inverse Problems of Experimental Data Interpretation in3D Ultrasound Tomography,” Vychisl. Metody Programm. 20 (3), 254-269 (2019).doi{10.26089/NumMet.v20r323}.
  9. A. Bakushinsky and A. Goncharsky, Ill-Posed Problems: Theory and Applications (Kluwer Academic Publishers, Dordrecht, 1994).
  10. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer Academic Publishers, Dordrecht, 1995).
  11. A. V. Goncharsky and S. Y. Romanov, “Iterative Methods for Solving Coefficient Inverse Problems of Wave Tomography in Models with Attenuation,” Inverse Probl. 33(2), (2017). doi{10.1088/1361-6420/33/2/025003}.
  12. F. Natterer, “Sonic Imaging,” in Handbook of Mathematical Methods in Imaging}(Springer, New York, 2014), pp. 1253-1278.doi{10.1007/978-1-4939-0790-8_37.
  13. A. Bakushinsky and A. Goncharsky, Iterative Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1989) [in Russian].
  14. R. K. Saha and S. K. Sharma, “Validity of a Modified Born Approximation for a Pulsed Plane Wave in Acoustic Scattering Problems,” Phys. Med. Biol. 50 (12) (2005).doi{10.1088/0031-9155/50/12/007}.
  15. D. Yokoyama, B. Schulze, F. Borges, and G. Mc Evoy, “The survey on ARM processors for HPC,” J. Supercomput. 75, 7003-7036 (2019).doi{10.1007/s11227-019-02911-9}.
  16. V. V. Voevodin, A. S. Antonov, D. A Nikitenko, et al., “SupercomputerLomonosov-2: Large Scale, Deep Monitoring and Fine Analytics for the User Community,” Supercomput. Front. Innov. 6 (2), 4-11 (2019).doi{10.14529/jsfi190201}.
  17. B. Engquist and A. Majda, “Absorbing Boundary Conditions for the Numerical Simulation of Waves,” Math. Comput. 31, 629-651 (1977).doi{10.1090/S0025-5718-1977-0436612-4}.
  18. B. Hamilton and S. Bilbao, “Fourth-Order and Optimised Finite Difference Schemes for the 2-D Wave Equation,” in Proc. 16th Int. Conf. on Digital Audio Effects, Maynooth, Ireland, September 2-6, 2013 ,
  19. WaveTomography software. . Cited December 10, 2021.




How to Cite

Goncharsky Alexander V., Romanov Sergey Y., Seryozhnikov Sergey Y. Implementation and Performance of Wave Tomography Algorithms on SIMD CPU and GPU Computing Platforms // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2021. 22. 322–332. doi 10.26089/NumMet.v22r421



Methods and algorithms of computational mathematics and their applications