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The purpose of this text is to offer a comprehensive and self-contained pre sentation of some of the most successful and popular domain decomposition methods for partial differential equations. Strong emphasis is put on both al gorithmic and mathematical aspects. In addition, we have wished to present a number of methods that have not been treated previously in other mono graphs and surveys. We believe that this monograph will offer something new and that it will complement those of Smith, Bj0rstad, and Gropp  and Quarteroni and Valli . Our monograph is also more extensive and broader than the surveys given in Chan and Mathew , Farhat and Roux , Le Tallec , the habilitation thesis by Wohlmuth , and the well-known SIAM Review articles by Xu  and Xu and Zou . Domain decomposition generally refers to the splitting of a partial differen tial equation, or an approximation thereof, into coupled problems on smaller subdomains forming a partition of the original domain. This decomposition may enter at the continuous level, where different physical models may be used in different regions, or at the discretization level, where it may be con venient to employ different approximation methods in different regions, or in the solution of the algebraic systems arising from the approximation of the partial differential equation. These three aspects are very often interconnected in practice. This monograph is entirely devoted to the third aspect of domain decompo sition.
Content Level »Research
Keywords »Sobolev space - algorithms - domain decomposition - finite elements - linear algebra - partial differential equation - preconditioning - spectral elements - statistics