20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
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  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Abstract Rob Stevenson, Thu, 16.00-16.30 Previous Contents Next  
  Composite wavelets with extended stability and cancellation properties
Rob Stevenson (University Utrecht)

The solution of boundary integral equations using wavelets requires wavelets that generate a Riesz basis for the relevant Sobolev space and that have sufficiently many vanishing moments, or more precisely, cancellation properties. A general construction principle for wavelets on a manifold that is given as a disjoint union of smooth patches is to lift scaling functions or wavelets defined on a reference domain to the manifold by a parametric mapping, after which along the interfaces a kind of stitching procedure is applied. We discuss such a procedure that yield continuous wavelets that have the same range of stability in the Sobolev scale and the same cancellation properties with respect to the canonical L2-scalar product as the wavelets on the reference domain. We illustrate our construction by a numerical example.

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30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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