Dual-primal FETI methods for linear elasticity

• Published in: Communications on pure and applied mathematics Vol. 59; no. 11; pp. 1523 - 1572
• Main Authors: Klawonn, Axel, Widlund, Olof B.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.11.2006; Wiley; John Wiley and Sons, Limited
• Subjects: Algebra; Algorithms; Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Elasticity; Elasticity, plasticity: general mathematical aspects; Exact sciences and technology; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Physics; Sciences and techniques of general use; Constraint; Materials; Large system; Iterative method; Partial differential equation; Young modulus; Finite element method; Lagrange multiplier; Elliptic equation; Algebraic system; Linear elasticity; Primal dual method; Condition number; Domain decomposition
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.20156

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.