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Wavelets on Regular Surfaces Generated by Stokes Potentials
Author(s) -
Mayer Carsten
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610267
Subject(s) - discretization , mathematics , wavelet , mathematical analysis , scaling , surface (topology) , fredholm integral equation , ansatz , limit (mathematics) , boundary value problem , kernel (algebra) , jump , function (biology) , representation (politics) , integral equation , pure mathematics , geometry , physics , mathematical physics , quantum mechanics , computer science , artificial intelligence , evolutionary biology , politics , political science , biology , law
By means of the limit and jump relations of potential theory with respect to the Stokes equations the framework of a tensorial wavelet approach on a regular (Lyapunov‐) surface is established. The setup of a multiresolution analysis is defined by interpreting the kernel functions of the limit and jump integral operators as scaling functions on the regular surfaces. The distance of the parallel surface to the surface under consideration thereby represents the scale level in the scaling function. Tensorial scaling functions and wavelets show space localizing properties. Thus, they can be used to represent vector fields locally on a regular surface. Furthermore, these functions can be used as ansatz functions for the discretization of Fredholm integral equations of the second kind which result from the Stokes boundary‐value problems with respect to a regular surface. By this, scaling functions and wavelets enable us to give a multiscale representation of the solution of the Stokes problem. This representation will be demonstrated in a concrete example. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)