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Wavelet Methods for Elliptic Partial Differential Equations$
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Karsten Urban

Print publication date: 2008

Print ISBN-13: 9780198526056

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780198526056.001.0001

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Wavelet-Galerkin Methods

Wavelet-Galerkin Methods

(p.170) 6 Wavelet-Galerkin Methods
Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Oxford University Press

Using wavelets as basis for the test and trial spaces of a Galerkin method allows an optimal preconditioning of the stiffness matrix. It is proven that a diagonal scaling provides such a preconditioning. In order to avoid to compute and store the non-sparse wavelet stiffness matrix one uses the Fast Wavelet Transform. Several numerical comparisons are provided.

Keywords:   Wavelet preconditioning, Fast Wavelet Transform, Diagonal preconditioning

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