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CivilComp Proceedings
ISSN 17593433 CCP: 96
PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping and Y. Tsompanakis
Paper 117
Scalable TFETI based Dynamic Contact Algorithm J. Dobiáš^{1}, S. Pták^{1}, Z. Dostál^{2}, A. Markopoulos^{2}, T. Kozubek^{2} and T. Brzobohatý^{2}
^{1}Institute of Thermomechanics, Prague, Czech Republic
J. DobiáÂš, S. Pták, Z. Dostál, A. Markopoulos, T. Kozubek, T. Brzobohatý, "Scalable TFETI based Dynamic Contact Algorithm", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 117, 2011. doi:10.4203/ccp.96.117
Keywords: scalability, dynamics, Newmark method, impact problem, geometric nonlinearity, material nonlinearity.
Summary
This paper is concerned with application of our TFETI based algorithm
suggested in [1] to the impact problems accompanied by geometric
and material nonlinear effects.
The TFETI method belongs to the class of nonoverlapping spatial decompositions.
Its key concept is based on the idea that the compatibility between subdomains is ensured by Lagrange
multipliers. The primal variables, which are displacements, are eliminated so that we solve
the problem for the dual variables or Lagrange multipliers.
The difference between the wellknown FETI and TFETI is that the latter method,
unlike the former one, also enforces
the Dirichlet boundary conditions in terms of the Lagrange multipliers, which has
a significant bearing on some segments of computations because of lesser sensitivity to roundoff errors.
The TFETI technique converts the original problem to the quadratic programming one and
if applied to the contact problems, this approach transforms the general
nonpenetration constraints to the simple bound constraints.
After eliminating the primal variables, the original problem is reduced to a small and relatively
well conditioned one.
Our approach stems from an optimal algorithm to the solution of strictly convex bound constrained
quadratic programming problems with preconditioning by the conjugate projector to the subspace
defined by the trace of the rigid body modes on the fictitious interfaces between subdomains.
Application of this algorithm to transient problems shows that if the time steps and
the ratio of the decomposition and discretisation parameters are kept uniformly bounded,
then the cost of time step computations is proved to be proportional to the number of nodal variables.
The time integration requires a special treatment to guarantee stability and removal of the undesired
nonphysical oscillations of solution along the contact interfaces. We applied the contact stabilised
Newmark scheme introduced in [2] that reduces
the solution to a sequence of quadratic programming problems. We show that our
transient algorithm can be applied to the solution of problems exhibiting geometric and material
nonlinearities. Results of numerical experiments document that the proposed algorithm is highly accurate
and exhibits both parallel and numerical scalabilities which is quite essential for its application
to high performance computers.
References
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