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A Preconditioned Domain Decomposition Algorithm for Contact Problem

A Preconditioned Domain Decomposition Algorithm for Contact Problem. HARRACHOV 2007 A. Lotfi. Abstract: The purpose of this work is to study, the quasistatic two-body contact problem for small strains without friction.

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A Preconditioned Domain Decomposition Algorithm for Contact Problem

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  1. A Preconditioned Domain Decomposition Algorithm for Contact Problem HARRACHOV 2007 A. Lotfi

  2. Abstract: • The purpose of this work is to study, the quasistatic two-body contact problem for small strains without friction. • To obtain an approximation of this problem, we use the finite element method • Non-overlapping DD method is used to solve the resulting finite element system • Preconditioner construction to solve the interface problem: • The schur complement operator is spectrally equivalent to H1/2 seminorm [3] [4] • The circulant matrix representations of H1/2 seminorm [3] [4] A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  3. References: • [1] Kikuchi, N. and Oden, J. T.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988). • [2] B. Kiss, G. Molnárka: A preconditioned Domain Decomposition Algorithm for the Solution of the Elliptic Neumann Problem. In: W. Hackbush ed., Parallel Algorithm for PDE, Proceeding of 6th GAMM Seminar, Kiel, 119-129, 1990. • [3] B. Kiss, A. Krebsz.: On the Schur Complement Preconditioners. Computers and Structures, Vol. 73, 537--544, 1999. • [4] B. Kiss, A. Krebsz, K. Szalay.: On the Separability of the H1/2 Seminorm on Convex Polyhedral Domains. HEJ (http: hej.szif.hu) vol(1) ANM-010227-B, 20. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  4. OUTLINE • Continuos problem • Variational problem • Finite element discretisation • Domain Decomposition Method and Algorithm • The interface problem • Numerical results A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  5. Continuos problem A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  6. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  7. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  8. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  9. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  10. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  11. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  12. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  13. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  14. Algorithm A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  15. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  16. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  17. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  18. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  19. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  20. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  21. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  22. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  23. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  24. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  25. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  26. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

  27. Thank you for your attention A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007

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