The Dual Schur Complement Method with Well-Posed Local Neumann Problems: Regularization with a Perturbed Lagrangian Formulation

The dual Schur complement (DSC) domain decomposition (DD) method introduced by Farhat and Roux is an efficient and practical algorithm for the parallel solution of self-adjoint elliptic partial differential equations. A given spatial domain is partitioned into disconnected subdomains where an incomplete solution for the primary field is first evaluated using a direct method. Next, intersubdomain field continuity is enforced via a combination of discrete, polynomial, and/or piece-wise polynomial Lagrange multipliers, applied at the subdomain interfaces. This leads to a smaller size symmetric dual problem where the unknowns are the “gluing” Lagrange multipliers, and which is best solved with a preconditioned conjugate gradient (PCG) algorithm. However, for time-independent elasticity problems, every floating subdomain is associated with a singular stiffness matrix, so that the dual interface operator is in general indefinite. Previously, we have dealt with this issue by filtering out at each iteration of th...