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   -> Volume 2, Issue 14


Preprints available
 
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Author Message
Andreas Rieder, Computational Mathematics Laboratory, Rice University.
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PostPosted: Fri Nov 29, 2002 3:36 pm    
Subject: Preprints available
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Preprints available

The following preprints are available:

1) A WAVELET MULTILEVEL METHOD
FOR DIRICHLET BOUNDARY VALUE PROBLEMS
IN GENERAL DOMAINS

R. Glowinski, A. Rieder, R.O. Wells, X. Zhou

Abstract:
We present a multilevel method for the efficient solution
of the linear system arising from a Wavelet-Galerkin
discretization of a Dirichlet boundary value problem via
a penalty/fictitious domain formulation. The presence of
the penalty term requires a modified coarse grid correction
process in order to guarantee a convergence rate which is
independent of the discretization step size.
Numerical experiments described in the paper confirm the
theoretical results.

Key words: wavelets, multilevel methods, penalty/fictitious
domain formulation, Galerkin methods
Subject classification: AMS(MOS) 65F10, 65N30

Technical Report of the Computational Mathematics Laboratory,
No. CML TR93-06, Rice University, Houston, 1993

2) A WAVELET APPROACH TO ROBUST MULTILEVEL SOLVERS
FOR ANISOTROPIC ELLIPTIC PROBLEMS

A. Rieder, R.O. Wells, X. Zhou

Abstract:
A wavelet variation of the "Frequency decomposition multigrid
method, Part I" (FDMGM) of Hackbusch [Numer. Math. 56, pp.229-245,
1989] is presented.
Our modification allows a deeper analysis of this method. Indeed,
the orthogonality and the multiresolution structure of wavelets
yield the robustness of the additive as well as of the multiplicative
version of the FDMGM relative to any intermediate level. Aspects of
robustness of the multilevel scheme are discussed. Numerical
experiments confirm the theoretical results.
The wavelet version of the FDMGM presented here involves wavelet
packets which have been used before this primarily in signal
processing. As a by-product of our analysis we yield strong Cauchy
inequalities for the wavelet packet spaces with respect to
H^1-inner products.

Key words: wavelets, wavelet packets, robust multilevel methods,
anisotropic problems, Galerkin methods
Subject classification: AMS(MOS) 65F10, 65N30

Technical Report of the Computational Mathematics Laboratory,
No. CML TR93-07, Rice University, Houston, 1993

Compressed postscript copies of these reports are available from
the ftp site cml.rice.edu (128.42.62.23). The files are pub/reports/9306.ps.Z
(first report) or pub/reports/9307.ps.Z (second report).
(login: anonymous, password: your email-address)

Andreas Rieder, Computational Mathematics Laboratory, Rice University,
Houston, Texas 77251, USA
email: rieder@cml.rice.edu
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