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Domain Decomposition Methods in Science and Engineering XX pp 647–654Cite as

Penalty Robin-Robin Domain Decomposition Schemes for Contact Problems of Nonlinear Elasticity

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

Many domain decomposition techniques for contact problems have been proposed on discrete level, particularly substructuring and FETI methods [1, 4].

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Bibliography

  1. P. Avery and C. Farhat. The FETI family of domain decomposition methods for inequality-constrained quadratic programming: Application to contact problems with conforming and nonconforming interfaces. Comput. Methods Appl. Mech. Engrg., 198:1673–1683, 2009.

    Article  MathSciNet  Google Scholar 

  2. G. Bayada, J. Sabil, and T. Sassi. A Neumann–Neumann domain decomposition algorithm for the Signorini problem. Appl. Math. Lett., 17(10):1153–1159, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Céa. Optimisation. Théorie et algorithmes. Dunod, Paris, 1971. [In French].

    Google Scholar 

  4. Z. Dostál, D. Horák, and D. Stefanica. A scalable FETI–DP algorithm with non-penetration mortar conditions on contact interface. Journal of Computational and Applied Mathematics, 231:577–591, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  5. I.I. Dyyak and I.I. Prokopyshyn. Convergence of the Neumann parallel scheme of the domain decomposition method for problems of frictionless contact between several elastic bodies. Journal of Mathematical Sciences, 171(4):516–533, 2010a.

    Article  MathSciNet  Google Scholar 

  6. I.I. Dyyak and I.I. Prokopyshyn. Domain decomposition schemes for frictionless multibody contact problems of elasticity. In G. Kreiss et al., editor, Numerical Mathematics and Advanced Applications 2009, pages 297–305. Springer Berlin Heidelberg, 2010b.

    Google Scholar 

  7. R. Glowinski, J.L. Lions, and R. Trémolières. Analyse numérique des inéquations variationnelles. Dunod, Paris, 1976. [In French].

    MATH  Google Scholar 

  8. A.A. Ilyushin. Plasticity. Gostekhizdat, Moscow, 1948. [In Russian].

    Google Scholar 

  9. N. Kikuchi and J.T. Oden. Contact problem in elasticity: A study of variational inequalities and finite element methods. SIAM, 1988.

    Google Scholar 

  10. J. Koko. An optimization-bazed domain decomposition method for a two-body contact problem. Num. Func. Anal. Optim., 24(5–6):586–605, 2003.

    MathSciNet  Google Scholar 

  11. R. Krause and B. Wohlmuth. A Dirichlet–Neumann type algorithm for contact problems with friction. Comput. Visual. Sci., 5(3):139–148, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  12. A.S. Kravchuk. Formulation of the problem of contact between several deformable bodies as a nonlinear programming problem. Journal of Applied Mathematics and Mechanics, 42(3):489–498, 1978.

    Article  MathSciNet  Google Scholar 

  13. J.L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaire. Dunod Gauthier-Villards, Paris, 1969. [In French].

    Google Scholar 

  14. I.I. Prokopyshyn. Parallel domain decomposition schemes for frictionless contact problems of elasticity. Visnyk Lviv Univ. Ser. Appl. Math. Comp. Sci., 14:123–133, 2008. [In Ukrainian].

    MATH  Google Scholar 

  15. I.I. Prokopyshyn. Penalty method based domain decomposition schemes for contact problems of elastic solids. PhD thesis, IAPMM NASU, Lviv, 2010. URL:194.44.15.230:8080/v25/resources/thesis/Prokopyshyn.pdf. [In Ukrainian].

    Google Scholar 

  16. T. Sassi, M. Ipopa, and F.-X. Roux. Generalization of Lion’s nonoverlapping domain decomposition method for contact problems. Lect. Notes Comput. Sci. Eng., 60:623–630, 2008.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Pidstryhach IAPMM NASU, Naukova 3-b, Lviv, 79060, Ukraine

    Ihor I. Prokopyshyn & Rostyslav M. Martynyak

  2. Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine

    Ivan I. Dyyak & Ivan A. Prokopyshyn

Authors
  1. Ihor I. Prokopyshyn
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  2. Ivan I. Dyyak
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  3. Rostyslav M. Martynyak
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  4. Ivan A. Prokopyshyn
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Corresponding author

Correspondence to Ihor I. Prokopyshyn .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Prokopyshyn, I.I., Dyyak, I.I., Martynyak, R.M., Prokopyshyn, I.A. (2013). Penalty Robin-Robin Domain Decomposition Schemes for Contact Problems of Nonlinear Elasticity. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_77

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