TY - JOUR
A1 - Lahmer, Tom
A1 - Bock, Sebastian
A1 - Hildebrand, Jörg
A1 - Gürlebeck, Klaus
T1 - Non-destructive identification of residual stresses in steel under thermal loadings
JF - Inverse Problems in Science and Engineering
N2 - Non-destructive identification of residual stresses in steel under thermal loadings
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2016
SP - 1
EP - 17
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 -
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 - Gürlebeck, Klaus
A1 - Bock, Sebastian
A1 - Falcao, M. Irene
T1 - Applications of Bergman kernel functions
N2 - 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.
KW - Konforme Abbildung
KW - Kernel
Y1 - 2003
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2994
ER -