## Some Nonoverlapping Domain Decomposition Methods (1998)

Citations: | 35 - 6 self |

### BibTeX

@MISC{Xu98somenonoverlapping,

author = {Jinchao Xu and Jun Zou},

title = {Some Nonoverlapping Domain Decomposition Methods},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

. The purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second-order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring--type methods and the Neumann--Neumann-type methods. The basic framework used for analysis is the parallel subspace correction method or additive Schwarz method, and other technical tools include local-global and global-local techniques. The analyses for both two- and three-dimensional cases are carried out simultaneously. Some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived. Key words. nonoverlapping domain decomposition, Schur complement, local-global and globallocal techniques, jumps in coe#cients, substructuring, Neumann--Neumann, balancing methods AMS subject classifications. 65N30, 65N55, 65F10 PII. S0036144596306800 1. Introduction. T...