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Supercomputer Simulation Study of the Convergence of Iterative Methods for Solving Inverse Problems of 3D Acoustic Tomography with the Data on a Cylindrical Surface

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Supercomputing (RuSCDays 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 965))

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Abstract

This paper is dedicated to developing effective methods of 3D acoustic tomography. The inverse problem of acoustic tomography is formulated as a coefficient inverse problem for a hyperbolic equation where the speed of sound and the absorption factor in three-dimensional space are unknown. Substantial difficulties in solving this inverse problem are due to its nonlinear nature. A method which uses short sounding pulses of two different central frequencies is proposed. The method employs an iterative parallel gradient-based minimization algorithm at the higher frequency with the initial approximation of unknown coefficients obtained by solving the inverse problem at the lower frequency. The efficiency of the proposed method is illustrated via a model problem. In the model problem an easy to implement 3D tomographic scheme is used with the data specified at a cylindrical surface. The developed algorithms can be efficiently parallelized using GPU clusters. Computer simulations show that a GPU cluster capable of performing 3D image reconstruction within reasonable time.

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Acknowledgement

This work was supported by Russian Science Foundation [grant number 17-11-01065]. The research is carried out at Lomonosov Moscow State University. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Sergey Romanov

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  1. Sergey Romanov
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Correspondence to Sergey Romanov .

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Editors and Affiliations

  1. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Vladimir Voevodin

  2. RCC, Moscow State University, Moscow, Russia

    Sergey Sobolev

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Romanov, S. (2019). Supercomputer Simulation Study of the Convergence of Iterative Methods for Solving Inverse Problems of 3D Acoustic Tomography with the Data on a Cylindrical Surface. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2018. Communications in Computer and Information Science, vol 965. Springer, Cham. https://doi.org/10.1007/978-3-030-05807-4_33

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  • DOI: https://doi.org/10.1007/978-3-030-05807-4_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05806-7

  • Online ISBN: 978-3-030-05807-4

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