Premium
General theory of domain decomposition: Beyond Schwarz methods
Author(s) -
Herrera Ismael,
Yates Robert
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1024
Subject(s) - schwarz alternating method , domain decomposition methods , additive schwarz method , mathematics , domain (mathematical analysis) , decomposition method (queueing theory) , decomposition , general theory , calculus (dental) , algebra over a field , mathematical economics , pure mathematics , discrete mathematics , finite element method , mathematical analysis , medicine , ecology , physics , dentistry , biology , thermodynamics
Recently, Herrera presented a general theory of domain decomposition methods (DDM). This article is part of a line of research devoted to its further development and applications. According to it, DDM are classified into direct and indirect, which in turn can be subdivided into overlapping and nonoverlapping. Some articles dealing with general aspects of the theory and with indirect (Trefftz–Herrera) methods have been published. In the present article, a very general direct‐overlapping method, which subsumes Schwarz methods, is introduced. Also, this direct‐overlapping method is quite suitable for parallel implementation. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 495–517, 2001