@inproceedings{NguyenGuerlebeck, author = {Nguyen, Manh Hung and G{\"u}rlebeck, Klaus}, title = {ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2783}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27833}, pages = {7}, abstract = {Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of M{\"o}bius transformations only and that the M{\"o}bius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane.}, subject = {Angewandte Informatik}, language = {en} } @inproceedings{LegatiukBockGuerlebeck, author = {Legatiuk, Dmitrii and Bock, Sebastian and G{\"u}rlebeck, Klaus}, title = {THE PROBLEM OF COUPLING BETWEEN ANALYTICAL SOLUTION AND FINITE ELEMENT METHOD}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2773}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27730}, pages = {11}, abstract = {This paper is focused on the first numerical tests for coupling between analytical solution and finite element method on the example of one problem of fracture mechanics. The calculations were done according to ideas proposed in [1]. The analytical solutions are constructed by using an orthogonal basis of holomorphic and anti-holomorphic functions. For coupling with finite element method the special elements are constructed by using the trigonometric interpolation theorem.}, subject = {Angewandte Informatik}, language = {en} } @inproceedings{PastohrKornadtGuerlebeck2003, author = {Pastohr, Henry and Kornadt, Oliver and G{\"u}rlebeck, Klaus}, title = {Numerische Untersuchungen zum Thermischen Str{\"o}mungsverhalten im Aufwindkraftwerk}, doi = {10.25643/bauhaus-universitaet.343}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3436}, year = {2003}, abstract = {Das Aufwindkraftwerk ist eine thermo- hydrodynamische Maschine zur Elektroenergiegewinnung, bestehend aus einem Treibhaus, einem Kamin und einer oder mehreren Turbinen. In dieser Studie wurden numerische Ergebnisse zum thermischen Str{\"o}mungsverhalten in einem Aufwindkraftwerk unter der Ber{\"u}cksichtigung der Teilmodelle Erdboden, Kollektor, Atmosph{\"a}re, Umlenkung, Kamin und Turbine erhaltenden. Hierzu wurden die station{\"a}ren Grundgleichungen der Thermofluiddynamik auf strukturierten, k{\"o}rperangepassten und rotationssymmetrischen Gittern unter Beachtung aller Rand- und Kopplungsbedingungen numerisch mit dem finite Volumenverfahren gel{\"o}st. Besonderes Augenmerk wurde dabei auf die Kalibrierung des Modells im Ruhezustand, auf die numerische Simulation, auf den Einfluss der Strahlung, auf die Betrachtung der Turbine, auf das Dichtemodell sowie auf den turbulenten Str{\"o}mungszustand gelegt. Die erhaltenen Ergebnisse werden durch Approximationen 2. Ordnung, Gitterunabh{\"a}ngigkeit und durch einen sehr geringen Abbruchfehler charakterisiert. F{\"u}r 4 verschiedene Einstrahlungen wurden die Verl{\"a}ufe von Temperatur und Geschwindigkeit im Aufwindkraftwerk erhalten. Zus{\"a}tzlich sind f{\"u}r Vergleichszwecke der Massenstrom, der Temperaturhub, die Leistung an der Turbine und der Wirkungsgrad der Anlage bestimmt wurden. Aufbauend auf den Berechnungen in dieser Arbeit und den numerischen und analytischen Berechnungen in [1] k{\"o}nnen nun erweiterte Parameterstudien und instation{\"a}re Simulationen zum Aufwindkraftwerk durchgef{\"u}hrt werden.}, subject = {Aufwindkraftwerk}, language = {de} } @inproceedings{GuerlebeckBockFalcao2003, author = {G{\"u}rlebeck, Klaus and Bock, Sebastian and Falcao, M. Irene}, title = {Applications of Bergman kernel functions}, doi = {10.25643/bauhaus-universitaet.299}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2994}, year = {2003}, abstract = {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.}, subject = {Konforme Abbildung}, language = {en} }