Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-2792 Konferenzveröffentlichung Al-Yasiri, Zainab; Gürlebeck, Klaus Gürlebeck, Klaus; Lahmer, Tom ON BOUNDARY VALUE PROBLEMS FOR P-LAPLACE AND P-DIRAC EQUATIONS The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem. 8 Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar urn:nbn:de:gbv:wim2-20170314-27928 10.25643/bauhaus-universitaet.2792 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2928 Konferenzveröffentlichung Bock, Sebastian; Gürlebeck, Klaus Gürlebeck, Klaus; Könke, Carsten A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions 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. 14 urn:nbn:de:gbv:wim2-20170327-29281 10.25643/bauhaus-universitaet.2928 Institut für Mathematik-Bauphysik
OPUS4-299 Konferenzveröffentlichung Gürlebeck, Klaus; Bock, Sebastian; Falcao, M. Irene Applications of Bergman kernel functions 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. 2003 urn:nbn:de:gbv:wim2-20111215-2994 10.25643/bauhaus-universitaet.299 Professur Informatik im Bauwesen
OPUS4-4061 Wissenschaftlicher Artikel Gürlebeck, Klaus; Legatiuk, Dmitrii; Nilsson, Henrik; Smarsly, Kay Conceptual modelling: Towards detecting modelling errors in engineering applications Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer "simple" objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems. 9 Mathematical Methods in Applied Sciences 1 10 urn:nbn:de:gbv:wim2-20200110-40614 10.1002/mma.5934 Professur Angewandte Mathematik
OPUS4-2801 Konferenzveröffentlichung Hommel, Angela; Gürlebeck, Klaus Gürlebeck, Klaus; Lahmer, Tom THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics. 6 Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar urn:nbn:de:gbv:wim2-20170314-28010 10.25643/bauhaus-universitaet.2801 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-3865 Wissenschaftlicher Artikel Kavrakov, Igor; Legatiuk, Dmitrii; Gürlebeck, Klaus; Morgenthal, Guido A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications. 20 Royal Society Open Science Volume 6, Issue 3 urn:nbn:de:gbv:wim2-20190314-38656 /10.1098/rsos.181848 Professur Modellierung und Simulation - Konstruktion
OPUS4-2912 Konferenzveröffentlichung Kraußhar, Rolf Sören; Constales, Denis; Gürlebeck, Klaus; Sprößig, Wolfgang Gürlebeck, Klaus; Könke, Carsten APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction. 8 urn:nbn:de:gbv:wim2-20170327-29128 10.25643/bauhaus-universitaet.2912 Professur Angewandte Mathematik
OPUS4-3569 Wissenschaftlicher Artikel Lahmer, Tom; Bock, Sebastian; Hildebrand, Jörg; Gürlebeck, Klaus Non-destructive identification of residual stresses in steel under thermal loadings Non-destructive identification of residual stresses in steel under thermal loadings 16 Inverse Problems in Science and Engineering 1 17 Institut für Strukturmechanik
OPUS4-2773 Konferenzveröffentlichung Legatiuk, Dmitrii; Bock, Sebastian; Gürlebeck, Klaus Gürlebeck, Klaus; Lahmer, Tom; Werner, Frank THE PROBLEM OF COUPLING BETWEEN ANALYTICAL SOLUTION AND FINITE ELEMENT METHOD 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. 11 Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar urn:nbn:de:gbv:wim2-20170314-27730 10.25643/bauhaus-universitaet.2773 Graduiertenkolleg 1462
OPUS4-2783 Konferenzveröffentlichung Nguyen, Manh Hung; Gürlebeck, Klaus Gürlebeck, Klaus; Lahmer, Tom; Werner, Frank ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES 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. 7 Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar urn:nbn:de:gbv:wim2-20170314-27833 10.25643/bauhaus-universitaet.2783 Institut für Mathematik-Bauphysik