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.

EUDML-ID : urn:eudml:doc:287823
Mots clés:
Mots clés:

@article{702932,
     title = {A short philosophical note on the origin of smoothed aggregations},
     booktitle = {Applications of Mathematics 2013},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {67-76},
     mrnumber = {MR3204431},
     zbl = {1340.65295},
     url = {http://dml.mathdoc.fr/item/702932}
}

Fraňková, Pavla; Hanuš, Milan; Kopincová, Hana; Kužel, Roman; Vaněk, Petr; Vastl, Zbyněk. A short philosophical note on the origin of smoothed aggregations, dans Applications of Mathematics 2013, GDML_Books,  (2013), pp. 67-76. http://gdmltest.u-ga.fr/item/702932/