Premium
FETI‐DP, BDDC, and block Cholesky methods
Author(s) -
Li Jing,
Widlund Olof B.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1553
Subject(s) - cholesky decomposition , domain decomposition methods , feti , mathematics , positive definite matrix , block (permutation group theory) , constraint algorithm , lagrange multiplier , mathematical optimization , eigenvalues and eigenvectors , algorithm , finite element method , combinatorics , physics , quantum mechanics , thermodynamics
The FETI‐DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI‐DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two‐dimensional Laplace's equation also confirm this result. Copyright © 2005 John Wiley & Sons, Ltd.