Domain decomposition based contact solver (original) (raw)
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FETI domain decomposition method to solution of contact problems with large displacements
2005
The solution to contact problems between solid bodies poses difficulties to solvers because in general neither the distributions of the contact tractions throughout the areas currently in contact nor the configurations of these areas are known a priori. This implies that the contact problems are inherently strongly nonlinear. Probably the most popular solution method is based on direct iterations with the non-penetration conditions imposed by the penalty method ([Z93] or [W02]). The method enables easily enhance other non-linearity such as in the case of large displacements. In this paper we are concerned with application of a variant of the FETI domain decomposition method that enforces feasibility of Lagrange multipliers by the penalty [DH04b]. The dual penalty method, which has been shown to be optimal for small displacements is used in inner loop of the algorithm that treats large displacements. We give results of numerical experiments that demonstrate high efficiency of the FET...
A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation
Mathematical Modelling of Natural Phenomena, 2009
The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.
On the Efficient Reconstruction of Displacements in FETI Methods for Contact Problems
Advances in Electrical and Electronic Engineering, 2017
The final step in the solution of contact problems of elasticity by FETI-based domain decomposition methods is the reconstruction of displacements corresponding to the Lagrange multipliers for "gluing" of subdomains and non-penetration conditions. The rigid body component of the displacements is usually obtained by means of a well known but quite complex formula, the application of which requires reassembling and factorization of some large matrices. Here we propose a simple formula which is applicable to many variants of the FETI based algorithms for contact problems. The method takes a negligible time and avoids reassembling or factorization of any matrices.
Domain Decomposition Algorithm for Solving Contact of Elastic Bodies
Lecture Notes in Computer Science, 2002
A non-overlapping domain decomposition is applied to a multibody unilateral contact problem with given friction (Tresca's model). Approximations are proposed on the basis of the primary variational formulation (in terms of displacements) and linear finite elements. For the discretized problem we employ the concept of local Schur complements, grouping every two subdomains which share a contact area. The proposed algorithm of successive approximations can be recommended for "short" contacts only, since the contact areas are not divided by interfaces.
A numerically scalable domain decomposition method for the solution of frictionless contact problems
International Journal for Numerical Methods in Engineering, 2001
We present a domain decomposition method with Lagrange multipliers for solving iteratively frictionless contact problems. This method, which is based on the FETI method and therefore is named here the FETI-C method, incorporates a coarse contact system that guides the iterative prediction of the active zone of contact. We demonstrate numerically that this method is numerically scalable with respect to both the problem size and the number of subdomains.
Use of Matlab for Domain Decomposition Method for Contact Problem in Elasticity
2005
In the present paper we will deal with numerical solution of a generalized semicoercive contact problem in linear elasticity, for the case that several bodies of arbitrary shapes are in mutual contacts and are loaded by external forces, by using the non-overlapping domain decomposition and finite elements method. The numerical example will be presented.
Scalable FETI Algorithms for Frictionless Contact Problems
Lecture Notes in Computational Science and Engineering, 2008
We review our FETI based domain decomposition algorithms for the solution of 2D and 3D frictionless contact problems of elasticity and related theoretical results. We consider both cases of restrained and unrestrained bodies. The scalability of the presented algorithms is demonstrated on the solution of 2D and3D benchmarks.
Two domain decomposition methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These methods are based on the FETI and FETI-DP substructuring algorithms. In the case of linear constraints, they do not perform any New-ton-like iteration. Instead, they solve a constrained problem by an active set strategy and a generalized conjugate gradient based descent method equipped with controls to guarantee convergence monotonic-ity. Both methods possess the desirable feature of minimizing numerical oscillations during the iterative solution process. Performance results and comparisons are reported for several numerical simulations that suggest that both methods are numerically scalable with respect to both the problem size and the number of subdomains. Their parallel scalability is also illustrated on a Linux cluster for a complex 1.4 million degree of freedom multibody problem with frictionless contact and nonconforming discrete interfaces.