Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing

Vaněk, Petr, and Brezina, Marian. "Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing." Applications of Mathematics 58.4 (2013): 369-388. <http://eudml.org/doc/260638>.

@article{Vaněk2013,
abstract = {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).},
author = {Vaněk, Petr, Brezina, Marian},
journal = {Applications of Mathematics},
keywords = {multigrid; aggressive coarsening; optimal convergence result; multigrid; aggressive coarsening; optimal convergence result; polynomial smoothing; algorithm; Richardson iteration},
language = {eng},
number = {4},
pages = {369-388},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing},
url = {http://eudml.org/doc/260638},
volume = {58},
year = {2013},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 369
EP - 388
AB - 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).
LA - eng
KW - multigrid; aggressive coarsening; optimal convergence result; multigrid; aggressive coarsening; optimal convergence result; polynomial smoothing; algorithm; Richardson iteration
UR - http://eudml.org/doc/260638
ER -