TY - CHAP
A1 - Nguyen, Manh Hung
A1 - Gürlebeck, Klaus
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
ED - Werner, Frank
T1 - ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - 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 Möbius transformations only and that the Möbius 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.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27833
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -
TY - CHAP
A1 - Legatiuk, Dmitrii
A1 - Bock, Sebastian
A1 - Gürlebeck, Klaus
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
ED - Werner, Frank
T1 - THE PROBLEM OF COUPLING BETWEEN ANALYTICAL SOLUTION AND FINITE ELEMENT METHOD
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - 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.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27730
UR - http://euklid.bauing.uni-weimar.de/ikm2012
SN - 1611-4086
ER -