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Adaptive Solution of Multidimensional PDEs via Tensor Product Wavelet Decomposition

Summary: Adaptive Solution of Multidimensional PDEs via Tensor
Product Wavelet Decomposition
A. Averbuch1, G. Beylkin2, R. Coifman3, P. Fischer4, M. Israeli5
1School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978
2Program in Applied Mathematics, University of Colorado at Boulder, Boulder
CO 80309-0526, USA
3 Department of Mathematics, Yale University, P.O.Box 2155 Yale Station
New Haven, CT 06520, USA
4 Mathematiques Appliquees de Bordeaux, Universite de Bordeaux 1, France
5 Faculty of Computer Science, Technion- Israel Institute of Technology
Haifa 32000, Israel
In this paper we describe e cient adaptive discretization and solution of ellip-
tic PDEs which are forced by right hand side (r.h.s) with regions of smooth (non-
oscillatory) behavior and possibly localized regions with non-smooth structures. Clas-
sical discretization methods lead to dense representations for most operators. The
method described in this paper is based on the wavelet transformwhich provides sparse
representations of operator kernels. In addition, the wavelet basis allows for automatic
adaptation (using thresholding) in the sense that only a few coe cients are needed to


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University
Fischer, Patrick - Institut de Mathematiques de Bordeaux, Université Bordeaux


Collections: Computer Technologies and Information Sciences; Mathematics