Wavelet Approximations on Closed Surfaces and their Application to Boundary-Value Problems of Potential Theory
- Wavelets on closed surfaces in Euclidean space R3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of functional values (resp. normal derivatives) on the closed surface under consideration. A scale discrete version of multiresolution is described for potential functions harmonic outside the closed surface and regular at infinity. Furthermore, an exact fully discrete wavelet approximation is developed in case of band-limited wavelets. Finally, the role of wavelets is discussed in three problems, namely (i) the representation of a function on a closed surface from discretely given data, (ii) the (discrete) solution of the exterior Dirichlet problem, and (iii) the (discrete) solution of the exterior Neumann problem.
Author: | Willi Freeden, F. Schneider |
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URN: | urn:nbn:de:hbz:386-kluedo-5753 |
Series (Serial Number): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (171) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1998 |
Year of first Publication: | 1998 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2000/04/03 |
Note: | Altdaten, kein Volltext verfügbar ; Printversion in Bereichsbibliothek Mathematik vorhanden: MAT 144/620-171 |
Source: | Math. Meth. in the Apl. Sci., 21, 129-165 (1998) |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |