| 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 |
| Year:
|
|
| 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 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702932 |
| . |
