Domain Decomposition Based Contact Solver
Author(s)
J. Dobi´aˇs, S. Pt´ak, Z.Dost´al & V. Vondr´ak
Abstract
The paper is concerned with the application of a new variant of the FETI domain
decomposition method called the Total FETI to the solution of contact problems
by the finite element method. The basic idea is that both the compatibility between
adjacent sub-domains and Dirichlet boundary conditions are enforced by the
Lagrange multipliers with physical meaning of forces, while the displacements
are eliminated. We introduce the Total FETI technique to solve the equations and
inequalities governing the equilibrium of system of bodies in contact. Moreover,
we show implementation of the method into a code which treats the material and
geometric non-linear effects. Numerical experiments were carried out with our inhouse
general purpose package PMD.
Keywords: contact, domain decomposition, non-linear, Lagrange multipliers, finite
element method.
1 Introduction
Modelling contact phenomena is still a challenging problem of non-linear computational
mechanics. The complexity of such problems arises from the fact that we
do not knowthe regions in contact until we have run the problem. Their evaluations
have to be part of the solution. In addition, the solution across the contact interface
is non-smooth. In other words, a general contact problem is strongly non-linear
and its reasonable solution in terms of a numerical technique, usually the finite
element method, needs high quality software stemming from techniques exhibiting
qualities like fast convergence rate, good parallel and numerical scalabilities,
and so on.
In 1991 Farhat and Roux [1] came up with a novel domain decomposition
method called FETI (Finite Element Tearing and Interconnecting method). This
Keywords
contact, domain decomposition, non-linear, Lagrange multipliers, finite
element method.
Related Book
Other papers in this volume
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