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A Modified Duality Method for Solving an Elasticity Problem with a Crack Extending to the Outer Boundary

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Optimization and Applications (OPTIMA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

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Abstract

A modified dual method for solving an elasticity problem with a crack extending to the outer boundary is considered. The method is based on a modified Lagrange functional. The convergence of the method is investigated in detail under a natural assumption of \(H^1\)-regularity of the solution to the crack problem. Basic duality relation for the primal and dual problems is proposed.

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Acknowledgments

This study was supported by the Russian Foundation for Basic Research (Project 17-01-00682 A). Numerical experiments were performed on a computational cluster of the Shared Facility Center “Data Center of FEB RAS” [20].

Author information

Authors and Affiliations

  1. Computing Center of Far Eastern Branch Russian Academy of Sciences, Kim Yu Chen 65, 680021, Khabarovsk, Russia

    Robert Namm & Georgiy Tsoy

  2. School of Fundamental and Computer Sciences, Pacific National University, Tihookeanskaya 136, 680035, Khabarovsk, Russia

    Ellina Vikhtenko

Authors
  1. Robert Namm
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  2. Georgiy Tsoy
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  3. Ellina Vikhtenko
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Corresponding author

Correspondence to Robert Namm .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Namm, R., Tsoy, G., Vikhtenko, E. (2019). A Modified Duality Method for Solving an Elasticity Problem with a Crack Extending to the Outer Boundary. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_3

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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