Dual-primal Feti Methods for Linear Elasticity

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. 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, which are independent of even large changes in the stiffnesses of the subdomains across the interface between them. A theoretical analysis is provided and condition number bounds are established which are uniform with respect to arbitrarily large jumps in the Young’s modulus of the material and otherwise only depend polylogarithmically on the number of unknowns of a single subdomain.