A Wavelet Approach to Time-Harmonic Maxwells Equations

  • By means of the limit and jump relations of classical potential theory with respect to the vectorial Helmholtz equation a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging scalar, vectorial and tensorial potential kernels act as scaling functions. Corresponding wavelets are defined via a canonical refinement equation. A tree algorithm for fast decomposition of a complex-valued vector field given on a regular surface is developed based on numerical integration rules. By virtue of this tree algorithm, an effcient numerical method for the solution of vectorial Fredholm integral equations on regular surfaces is discussed in more detail. The resulting multiscale formulation is used to solve boundary-value problems for the time harmonic Maxwell's equations corresponding to regular surfaces.

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Author:Willi Freeden, Carsten Mayer
URN (permanent link):urn:nbn:de:hbz:386-kluedo-14080
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (22)
Document Type:Preprint
Language of publication:English
Year of Completion:2005
Year of Publication:2005
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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