@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{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}
}