Geodesic
Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
Applications of Mathematics, Tome 58 (2013) no. 4, pp. 369-388.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level $k$, at least $C h_{k+1}/h_k$, we prove a convergence result independent of $h_{k+1}/h_k$. The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis of our smoother is completely algebraic and independent of geometry of the problem and prolongators (the geometry of coarse spaces).
DOI : 10.1007/s10492-013-0018-2
Classification : 65F10, 65M55, 65N30, 65N55
Keywords: multigrid; aggressive coarsening; optimal convergence result 
@article{10_1007_s10492_013_0018_2,
     author = {Van\v{e}k, Petr and Brezina, Marian},
     title = {Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing},
     journal = {Applications of Mathematics},
     pages = {369--388},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {2013},
     doi = {10.1007/s10492-013-0018-2},
     mrnumber = {3083519},
     zbl = {06221236},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0018-2/}
}
TY  - JOUR
AU  - Vaněk, Petr
AU  - Brezina, Marian
TI  - Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
JO  - Applications of Mathematics
PY  - 2013
SP  - 369
EP  - 388
VL  - 58
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0018-2/
DO  - 10.1007/s10492-013-0018-2
LA  - en
ID  - 10_1007_s10492_013_0018_2
ER  - 
%0 Journal Article
%A Vaněk, Petr
%A Brezina, Marian
%T Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
%J Applications of Mathematics
%D 2013
%P 369-388
%V 58
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0018-2/
%R 10.1007/s10492-013-0018-2
%G en
%F 10_1007_s10492_013_0018_2
Vaněk, Petr; Brezina, Marian. Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing. Applications of Mathematics, Tome 58 (2013) no. 4, pp. 369-388. doi : 10.1007/s10492-013-0018-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0018-2/

Cité par Sources :