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

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Presentation transcript:

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

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 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: 1.The schur complement operator is spectrally equivalent to H 1/2 seminorm [3] [4] 2.The circulant matrix representations of H 1/2 seminorm [3] [4]

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 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, , [3] B. Kiss, A. Krebsz.: On the Schur Complement Preconditioners. Computers and Structures, Vol. 73, , [4] B. Kiss, A. Krebsz, K. Szalay.: On the Separability of the H 1/2 Seminorm on Convex Polyhedral Domains. HEJ (http: hej.szif.hu) vol(1) ANM B, 20.

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV OUTLINE Continuos problem Variational problem Finite element discretisation Domain Decomposition Method and Algorithm The interface problem Numerical results

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV Continuos problem

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV Algorithm

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV

Széchenyi István University Department of Mathmatics and Computational Sciences A Preconditioned DD Algorithm for Contact Problem / HARRACHOV Thank you for your attention