TY - CHAP A1 - Bock, Sebastian A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions N2 - The contribution focuses on the development of a basic computational scheme that provides a suitable calculation environment for the coupling of analytical near-field solutions with numerical standard procedures in the far-field of the singularity. The proposed calculation scheme uses classical methods of complex function theory, which can be generalized to 3-dimensional problems by using the framework of hypercomplex analysis. The adapted approach is mainly based on the factorization of the Laplace operator EMBED Equation.3 by the Cauchy-Riemann operator EMBED Equation.3 , where exact solutions of the respective differential equation are constructed by using an orthonormal basis of holomorphic and anti-holomorphic functions. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29281 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html 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 -