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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Balancing domain decomposition for problems with large jumps in coefficients


Authors: Jan Mandel and Marian Brezina
Journal: Math. Comp. 65 (1996), 1387-1401
MSC (1991): Primary 65N55, 65F10
MathSciNet review: 1351204
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Abstract: The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size $h$. Computational experiments for two- and three-dimensional problems confirm the theory.


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Additional Information

Jan Mandel
Affiliation: Center for Computational Mathematics, University of Colorado at Denver, Denver, Colorado 80217-3364
Email: jmandel@colorado.edu

Marian Brezina
Affiliation: Center for Computational Mathematics, University of Colorado at Denver, Denver, Colorado 80217-3364
Email: mbrezina@carbon.denver.colorado.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00757-0
PII: S 0025-5718(96)00757-0
Keywords: Domain decomposition, second-order elliptic boundary value problems, two-level iterative methods, discontinuous coefficients
Received by editor(s): March 18, 1993
Received by editor(s) in revised form: December 2, 1993, and September 21, 1994
Additional Notes: Submitted March 1993; revised September 1994.
Article copyright: © Copyright 1996 American Mathematical Society