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FETI and Neumann‐Neumann iterative substructuring methods: Connections and new results
Author(s) -
Klawonn Axel,
Widlund Olof
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/1097-0312(200101)54:1<57::aid-cpa3>3.0.co;2-d
Subject(s) - feti , mathematics , domain decomposition methods , neumann boundary condition , von neumann architecture , convergence (economics) , neumann series , domain (mathematical analysis) , iterative method , partial differential equation , von neumann algebra , boundary (topology) , finite element method , mathematical analysis , mathematical optimization , pure mathematics , physics , economics , thermodynamics , economic growth
The FETI and Neumann‐Neumann families of algorithms are among the best known and most severely tested domain decomposition methods for elliptic partial differential equations. They are iterative substructuring methods and have many algorithmic components in common, but there are also differences. The purpose of this paper is to further unify the theory for these two families of methods and to introduce a new family of FETI algorithms. Bounds on the rate of convergence, which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients, are established for these new algorithms. The theory for a variant of the Neumann‐Neumann algorithm is also redeveloped stressing similarities to that for the FETI methods. © 2001 John Wiley & Sons, Inc.