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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 60

Dynamic Non-linear TFETI Domain Decomposition Based Solver

J. Dobiáš1, S. Pták1, Z. Dostál2 and V. Vondrák2

1Institute of Thermomechanics, Prague, Czech Republic
2Technical University of Ostrava, Czech Republic

Full Bibliographic Reference for this paper
J. Dobiáš, S. Pták, Z. Dostál, V. Vondrák, "Dynamic Non-linear TFETI Domain Decomposition Based Solver", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 60, 2007. doi:10.4203/ccp.86.60
Keywords: dynamics, domain decomposition, FETI, geometric non-linearity, material non-linearity, contact non-linearity, finite element method.

Summary
The paper is concerned with application of a new variant of the FETI (Finite Element Tearing and Interconnecting) domain decomposition method, called the Total FETI (TFETI), to the solution of dynamic problems of deformable bodies with non-linear effects. Regarding the non-linearities, we consider geometric and material non-linear effects and also the contact phenomena. The basic relationships, solution algorithm and results of numerical experiments are given.

The TFETI method, developed by Dostál et al [1], is a version of the FETI method. The difference between the FETI and TFETI is that the latter method also enforces the Dirichlet boundary conditions in terms of the Lagrange multipliers. Then the stiffness matrices of all the sub-domains are singular but the magnitudes of their defects are the same and known beforehand. This fact has a significant bearing on computation because evaluation of unknown defects is disposed to round-off errors so that results are often not correct. The TFETI technique converts the original problem to the quadratic programming one with simple bounds and equality constraints. From the practical point of view it is essential that both FETI and TFETI exhibit parallel and numerical scalabilities [2].

Numerical experiments include solutions to dynamic problems with contact, geometric and material non-linear effects. We computed the axial impact of two identical straight bars and impact of two cylinders.

References
1
Z. Dostál, D. Horák and R. Kucera, "Total FETI - an easier implementable variant of the FETI method for numerical solution of elliptic PDE", Communications in Numerical Methods in Engineering, 22, 1155-1162, 2006. doi:10.1002/cnm.881
2
Z. Dostál, "Inexact semi-monotonic augmented Lagrangians with optimal feasibility convergence for convex bound and equality constrained quadratic programming", SIAM Journal on Numerical Analysis 43, 96-115, 2005. doi:10.1137/S0036142903436393

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