The mosaic of high performance domain Decomposition Methods for Structural Mechanics: Formulation, interrelation and numerical efficiency of primal and dual methods

摘要

A multitude of domain decomposition methods (DDM) for structural mechanics is available in the literature today. A unified framework for formulating primal and dual DDM is thus presented in this paper, aiming at providing a mathematical platform for a uniform treatment of high performance DDM in structural mechanics. A novel approach for developing new DDM from existing methods is also proposed and is applied to dual and primal methods. In the field of the FETI methods, this approach leads to a new category of methods derived from existing FETI variants. Furthermore, two alternative formulations of the balancing domain decomposition method are described, while interrelations between the introduced and existing methods are established. Finally, comparative numerical tests demonstrate the differences in the computational performance of the methods in question.