@techreport{Griebel.Kiefer:2001,
author = {M. Griebel and F. Kiefer},
title = {Generalized Hierarchical Basis Multigrid Methods for
Convection-Diffusion Problems},
institution = {Sonderforschungsbereich 256, Institut f\"ur Angewandte
Mathematik, Universit\"at Bonn},
year = {2001},
type = {{SFB} {P}reprint 720},
abstract = {We consider the efficient solution of discrete
convection-diffusion problems with dominating convection.
It is well known that the standard hierarchical basis
multigrid method (HBMG) leads neither to optimal (w.r.t.
mesh size) nor to robust solvers for discrete operators
arising from singularly perturbed convection-diffusion
problems. Its performance is strongly dependent on the
coefficients in the differential equation (e.g. strength of
convection) {\em and}\, the mesh size. (Pre-)Wavelet
splittings of the underlying function spaces allow for
efficient algorithms which can be viewed as generalized
HBMG methods. They can be interpreted as ordinary multigrid
methods which employ a special kind of multiscale smoother
and show an optimal convergence behavior for the respective
non-perturbed equations similar to classical multigrid.
Here, we present a general Petrov--Galerkin multiscale
approach which makes use of problem-dependent coarsening
strategies known from robust multigrid techniques
(matrix-dependent prolongations, algebraic coarsening)
together with certain (pre-)wavelet-like and hierarchical
multiscale decompositions of the trial and test spaces on
the finest grid. The presented numerical results show that
by this choice generalized HBMG methods can be constructed
which result in robust yet efficient solvers.},
ps = {http://wissrech.ins.uni-bonn.de/research/pub/kiefer/numlaa.ps.gz 1},
annote = {report,multigrid}
}