@inproceedings{PastohrKornadtGuerlebeck2003,
  author    = {Pastohr, Henry and Kornadt, Oliver and G{\"u}rlebeck, Klaus},
  title     = {Numerische Untersuchungen zum Thermischen Str{\"o}mungsverhalten im Aufwindkraftwerk},
  doi       = {10.25643/bauhaus-universitaet.343},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3436},
  year      = {2003},
  abstract  = {Das Aufwindkraftwerk ist eine thermo- hydrodynamische Maschine zur Elektroenergiegewinnung, bestehend aus einem Treibhaus, einem Kamin und einer oder mehreren Turbinen. In dieser Studie wurden numerische Ergebnisse zum thermischen Str{\"o}mungsverhalten in einem Aufwindkraftwerk unter der Ber{\"u}cksichtigung der Teilmodelle Erdboden, Kollektor, Atmosph{\"a}re, Umlenkung, Kamin und Turbine erhaltenden. Hierzu wurden die station{\"a}ren Grundgleichungen der Thermofluiddynamik auf strukturierten, k{\"o}rperangepassten und rotationssymmetrischen Gittern unter Beachtung aller Rand- und Kopplungsbedingungen numerisch mit dem finite Volumenverfahren gel{\"o}st. Besonderes Augenmerk wurde dabei auf die Kalibrierung des Modells im Ruhezustand, auf die numerische Simulation, auf den Einfluss der Strahlung, auf die Betrachtung der Turbine, auf das Dichtemodell sowie auf den turbulenten Str{\"o}mungszustand gelegt. Die erhaltenen Ergebnisse werden durch Approximationen 2. Ordnung, Gitterunabh{\"a}ngigkeit und durch einen sehr geringen Abbruchfehler charakterisiert. F{\"u}r 4 verschiedene Einstrahlungen wurden die Verl{\"a}ufe von Temperatur und Geschwindigkeit im Aufwindkraftwerk erhalten. Zus{\"a}tzlich sind f{\"u}r Vergleichszwecke der Massenstrom, der Temperaturhub, die Leistung an der Turbine und der Wirkungsgrad der Anlage bestimmt wurden. Aufbauend auf den Berechnungen in dieser Arbeit und den numerischen und analytischen Berechnungen in [1] k{\"o}nnen nun erweiterte Parameterstudien und instation{\"a}re Simulationen zum Aufwindkraftwerk durchgef{\"u}hrt werden.},
  subject      = {Aufwindkraftwerk},
  language  = {de}
}
@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}
}
@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}
}
@article{LegatiukGuerlebeckHommel,
  author    = {Legatiuk, Anastasiia and G{\"u}rlebeck, Klaus and Hommel, Angela},
  title     = {Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice},
  series = {Mathematical Methods in the Applied Sciences},
  volume    = {2021},
  journal   = {Mathematical Methods in the Applied Sciences},
  publisher = {Wiley},
  address   = {Chichester},
  doi       = {10.1002/mma.7747},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45829},
  pages     = {1 -- 23},
  abstract  = {This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices.},
  subject      = {diskrete Fourier-Transformation},
  language  = {en}
}
@article{LahmerBockHildebrandetal.,
  author    = {Lahmer, Tom and Bock, Sebastian and Hildebrand, J{\"o}rg and G{\"u}rlebeck, Klaus},
  title     = {Non-destructive identification of residual stresses in steel under thermal loadings},
  series = {Inverse Problems in Science and Engineering},
  journal   = {Inverse Problems in Science and Engineering},
  pages     = {1 -- 17},
  abstract  = {Non-destructive identification of residual stresses in steel under thermal loadings},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@inproceedings{KraussharConstalesGuerlebecketal.,
  author    = {Kraußhar, Rolf S{\"o}ren and Constales, Denis and G{\"u}rlebeck, Klaus and Spr{\"o}ßig, Wolfgang},
  title     = {APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2912},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29128},
  pages     = {8},
  abstract  = {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.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@article{KavrakovLegatiukGuerlebecketal.,
  author    = {Kavrakov, Igor and Legatiuk, Dmitrii and G{\"u}rlebeck, Klaus and Morgenthal, Guido},
  title     = {A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks},
  series = {Royal Society Open Science},
  journal   = {Royal Society Open Science},
  number    = {Volume 6, Issue 3},
  doi       = {/10.1098/rsos.181848},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190314-38656},
  pages     = {20},
  abstract  = {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.},
  subject      = {Br{\"u}cke},
  language  = {en}
}
@inproceedings{HommelGuerlebeck,
  author    = {Hommel, Angela and G{\"u}rlebeck, Klaus},
  title     = {THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2801},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28010},
  pages     = {6},
  abstract  = {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.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@article{GuerlebeckLegatiukWebber,
  author    = {G{\"u}rlebeck, Klaus and Legatiuk, Dmitrii and Webber, Kemmar},
  title     = {Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures},
  series = {Mathematics},
  volume    = {2022},
  journal   = {Mathematics},
  number    = {Volume 10, issue 10, article 1670},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/math10101670},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220721-46726},
  pages     = {1 -- 22},
  abstract  = {The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions.},
  subject      = {Mauerwerk},
  language  = {en}
}
@article{GuerlebeckLegatiukNilssonetal.,
  author    = {G{\"u}rlebeck, Klaus and Legatiuk, Dmitrii and Nilsson, Henrik and Smarsly, Kay},
  title     = {Conceptual modelling: Towards detecting modelling errors in engineering applications},
  series = {Mathematical Methods in Applied Sciences},
  journal   = {Mathematical Methods in Applied Sciences},
  doi       = {10.1002/mma.5934},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20200110-40614},
  pages     = {1 -- 10},
  abstract  = {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.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}