Abstract
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.
Highlights
The FETI methods proposed by Farhat and Roux [1] turned out to be an efficient tool for the solution of large problems arising from the discretization of elliptic partial differential equations
Using FETI, the domain is partitioned into non-overlapping subdomains, an elliptic problem with Neumann boundary conditions is defined for each subdomain, and the inter-subdomain field continuity is enforced via Lagrange multipliers
As a model of 3D linear elasticity contact problem, we considered an elastic cube in contact with a rigid obstacle decomposed into 4096, 32768 and 110592 subdomains
Summary
The FETI methods proposed by Farhat and Roux [1] turned out to be an efficient tool for the solution of large problems arising from the discretization of elliptic partial differential equations. Using FETI, the domain is partitioned into non-overlapping subdomains, an elliptic problem with Neumann boundary conditions is defined for each subdomain, and the inter-subdomain field continuity is enforced via Lagrange multipliers. Let us briefly describe a structure of the discretized contact problem without friction. Such a problem arises from the application of a variant of FETI under the assumption that the kernels of the subdomains are known a priori, as is always the case if the TFETI method [2] is applied. 1 uT Ku − f T u 2 s.t. where K† denotes a left generalized inverse of K so that KK†K = K, we can formulate the dual problem in Lagrange multipliers where α = −(GGT )−1GBK†(f − BT λ), G = RT BT ,.
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