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Russian Supercomputing Days

RuSCDays 2017: Supercomputing pp 67–79Cite as

Optimization of Numerical Algorithms for Solving Inverse Problems of Ultrasonic Tomography on a Supercomputer

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 793))

Abstract

The paper is dedicated to optimizing numerical algorithms to solve wave tomography problems by using supercomputers. The problem is formulated as a non-linear coefficient inverse problem for the wave equation. Due to the huge amount of computations required, solving such problems is impossible without the use of high-performance supercomputers. Gradient iterative methods are employed to solve the problem. The gradient of the residual functional is calculated from the solutions of the direct and the “conjugate” wave-propagation problems with transparent boundary conditions. Two formulations of the transparency condition are compared. We show that fourth-order finite-difference schemes allow us to reduce the size of the grid by a factor of 1.5–2 in each coordinate compared to second-order schemes. This makes it possible to significantly reduce the amount of computations and memory required, which is especially important for 3D problems of wave tomography. The primary application of the method is medical ultrasonic tomography.

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Acknowledgements

This research was supported by Russian Science Foundation (project No. 17–11–01065). The study was carried out at the 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. Moscow State University, Moscow, Russia

    Sergey Sobolev

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Romanov, S. (2017). Optimization of Numerical Algorithms for Solving Inverse Problems of Ultrasonic Tomography on a Supercomputer. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2017. Communications in Computer and Information Science, vol 793. Springer, Cham. https://doi.org/10.1007/978-3-319-71255-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-71255-0_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71254-3

  • Online ISBN: 978-3-319-71255-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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