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

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Presentation on theme: "A Preconditioned Domain Decomposition Algorithm for Contact Problem HARRACHOV 2007 A. Lotfi."— Presentation transcript:

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

2 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 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: 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]

3 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. 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 H 1/2 Seminorm on Convex Polyhedral Domains. HEJ (http: hej.szif.hu) vol(1) ANM-010227-B, 20.

4 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. 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

5 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 5 Continuos problem

6 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 6

7 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 7

8 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 8

9 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 9

10 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 10

11 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 11

12 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 12

13 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 13

14 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 14 Algorithm

15 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 15

16 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 16

17 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 17

18 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 18

19 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 19

20 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 20

21 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 21

22 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 22

23 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 23

24 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 24

25 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 25

26 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 26

27 Széchenyi István University Department of Mathmatics and Computational Sciences 2016. 03. 09. A Preconditioned DD Algorithm for Contact Problem / HARRACHOV 2007 27 Thank you for your attention


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