A short philosophical note on the origin of smoothed aggregations

Fraňková, Pavla, et al. "A short philosophical note on the origin of smoothed aggregations." Applications of Mathematics 2013. Prague: Institute of Mathematics AS CR, 2013. 67-76. <http://eudml.org/doc/287823>.

@inProceedings{Fraňková2013,
abstract = {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.},
author = {Fraňková, Pavla, Hanuš, Milan, Kopincová, Hana, Kužel, Roman, Vaněk, Petr, Vastl, Zbyněk},
booktitle = {Applications of Mathematics 2013},
keywords = {two-level method; pre-smoothing; coarse-grid correction; post-smoothing; error propagation; non-scalar elliptic problems; system of linear algebraic equations; symmetric positive definite matrix; smoothing; algorithms; aggregation method},
location = {Prague},
pages = {67-76},
publisher = {Institute of Mathematics AS CR},
title = {A short philosophical note on the origin of smoothed aggregations},
url = {http://eudml.org/doc/287823},
year = {2013},
}

TY - CLSWK
AU - Fraňková, Pavla
AU - Hanuš, Milan
AU - Kopincová, Hana
AU - Kužel, Roman
AU - Vaněk, Petr
AU - Vastl, Zbyněk
TI - A short philosophical note on the origin of smoothed aggregations
T2 - Applications of Mathematics 2013
PY - 2013
CY - Prague
PB - Institute of Mathematics AS CR
SP - 67
EP - 76
AB - 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.
KW - two-level method; pre-smoothing; coarse-grid correction; post-smoothing; error propagation; non-scalar elliptic problems; system of linear algebraic equations; symmetric positive definite matrix; smoothing; algorithms; aggregation method
UR - http://eudml.org/doc/287823
ER -