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   -> Volume 6, Issue 1

Preprint: Solving Hyperbolic PDEs Using Interpolating Wavelets
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Mats Holmstr|m (

PostPosted: Mon Jan 13, 1997 2:28 pm    
Subject: Preprint: Solving Hyperbolic PDEs Using Interpolating Wavelets
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#4 Preprint: Solving Hyperbolic PDEs Using Interpolating Wavelets

Title : Solving Hyperbolic PDEs Using Interpolating Wavelets

Author: Mats Holmstr=F6m

Abstract. A method is presented for adaptively solving hyperbolic
PDEs. The method is based on an interpolating wavelet transform using
polynomial interpolation on dyadic grids. The adaptability is
performed automatically by thresholding the wavelet coefficients.
Operations such as differentiation and multiplication are fast and
simple due to the one-to-one correspondence between point values and
wavelet coefficients in the interpolating basis. Treatment of
boundary conditions is simplified in this sparse point representation.
Numerical examples are presented for one- and two-dimensional
problems. It is found that the underlying finite difference method's
order of convergence is preserved, and that the proposed method
outperforms a finite difference method for certain problems in terms
of flops.

The full report is available at =


Mats Holmstr=F6m =

Uppsala University
tsh =

Dept. of Scientific Computing Ph.: +46 18 18 29 80 =

Box 120, S-751 04 Uppsala, Sweden. Fax: +46 18 52 30 49 =
All times are GMT + 1 Hour
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