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Applications of Bergman kernel functions

  • In this paper we revisit the so-called Bergman kernel method (BKM) for solving conformal mapping problems. This method is based on the reproducing property of the Bergman kernel function. The main drawback of this well known technique is that it involves an orthonormalization process and thus is numerically unstable. This difficulty can be, in some cases, overcome by using the Maple system, which makes no use of numeric quadrature. We illustrate this implementation by presenting a numerical example. The construction of reproducing kernel functions is not restricted to real dimension 2. Results concerning the construction of Bergman kernel functions in closed form for special domains in the framework of hypercomplex function theory suggest that BKM can also be extended to mapping problems in higher dimensions, particularly 3-dimensional cases. We describe such a generalized BKM-approach and present numerical examples obtained by the use of specially developed software packages for quaternions.

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Metadaten
Document Type:Conference Proceeding
Author: Klaus GürlebeckGND, Sebastian Bock, M. Irene Falcao
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.299Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20111215-2994Cite-Link
Language:English
Date of Publication (online):2005/01/03
Year of first Publication:2003
Release Date:2005/01/03
Institutes:Fakultät Bauingenieurwesen / Professur Informatik im Bauwesen
GND Keyword:Konforme Abbildung; Kernel <Informatik>
Source:Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen , IKM , 16 , 2003 , Weimar , Bauhaus-Universität
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften / 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 16. 2003
Licence (German):License Logo In Copyright