The aim of this paper is to give a unified comparison of non-overlapping domain decomposition methods (DDMs) for solving magnetic field problems. The methods under investigation are the Schur complement method and the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method, and their solvers. The performance of these methods has been investigated in detail for two-dim...

We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear–quadratic optimal control problems, which arise in many science and engineering applications. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear–quadratic optimal control problem into smaller subdomain optimality co...

and Applied Analysis 3 denotes a class of continuous functions f(x, t) : R × [0, +∞) → R n satisfying (x − y) T P (f (x, t) − f (y, t) − Δ (x − y)) ≤ −η(x − y) T (x − y) (4) for some η > 0, all x, y ∈ R and all t ≥ 0. Lemma 4 (Schur complement [25]). The following linear matrix inequality (LMI)

Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality. Particular cases are Dirac-Coulomb operators where distinguished selfadjoint extensions are obtained for the optimal range of coupling constants.

We present a Schur complement domain decomposition method that can significantly accelerate simulation of ensembles of locally differing optical structures. We apply the method to design a multi-spatial-mode photonic crystal waveguide splitter that exhibits high transmission and preservation of modal content, showing design acceleration by more than a factor of 20.

A parallel version of the Algebraic Recursive Multilevel Solver (ARMS) is developed for distributed computing environments. The method adopts the general framework of distributed sparse matrices and relies on solving the resulting distributed Schur complement system. Numerical experiments are presented which compare these approaches on regularly and irregularly structured problems.

In this paper we give representations of the Drazin and MP-inverse of a 2×2 block matrix and quotient identities for the generalized Schur complement of a partitioned 3 × 3 matrix under conditions different than those used in recent papers on the subject. We present numerical examples to illustrate our results. 2000 Mathematics Subject Classification: 15A09

Domain decomposition methods used for solving linear systems are strongly related to dynamic substructuring methods commonly used to build a reduced model. In this study we investigate some theoretical relations between the methods. In particular we discuss the conceptual similarities between the Schur Complement solvers and the Craig-Bampton substructuring techniques, both for their primal and...