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Title: A short philosophical note on the origin of smoothed aggregations (English)
Author: Fraňková, Pavla
Author: Hanuš, Milan
Author: Kopincová, Hana
Author: Kužel, Roman
Author: Vaněk, Petr
Author: Vastl, Zbyněk
Language: English
Journal: Applications of Mathematics 2013
Volume: Proceedings. Prague, May 15-17, 2013
Issue: 2013
Pages: 67-76
Category: math
Summary: We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively different, and more optimal, algorithm than the standard multigrid. (English)
Keyword: two-level method
Keyword: pre-smoothing
Keyword: coarse-grid correction
Keyword: post-smoothing
Keyword: error propagation
Keyword: non-scalar elliptic problems
Keyword: system of linear algebraic equations
Keyword: symmetric positive definite matrix
Keyword: smoothing
Keyword: algorithms
Keyword: aggregation method
MSC: 35J25
MSC: 65D10
MSC: 65F10
MSC: 65N15
MSC: 65N55
idZBL: Zbl 1340.65295
idMR: MR3204431
Date available: 2017-02-14T09:14:33Z
Last updated: 2017-03-20
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