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Dual‐primal FETI methods for linear elasticity
Author(s) -
Klawonn Axel,
Widlund Olof B.
Publication year - 2006
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20156
Subject(s) - feti , domain decomposition methods , lagrange multiplier , mathematics , finite element method , linear elasticity , mathematical optimization , elasticity (physics) , mortar methods , iterative method , convergence (economics) , algebraic equation , linear system , nonlinear system , mathematical analysis , materials science , composite material , physics , quantum mechanics , economics , thermodynamics , economic growth
Dual‐primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one‐level FETI methods. These methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems. The purpose of this article is to develop strategies for selecting these constraints, which are enforced throughout the iterations, such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them. The algorithms are described in terms of a change of basis that has proven to be quite robust in practice. A theoretical analysis is provided for the case of linear elasticity, and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the Young's modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain. The strategies have already proven quite successful in large‐scale implementations of these iterative methods. © 2006 Wiley Periodicals, Inc.