@inproceedings{WiggenbrockSmarsly,
  author    = {Wiggenbrock, Jens and Smarsly, Kay},
  title     = {A GENERIC FRAMEWORK SUPPORTING DISTRIBUTED COMPUTING IN ENGINEERING APPLICATIONS},
  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.2826},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28260},
  pages     = {9},
  abstract  = {Modern distributed engineering applications are based on complex systems consisting of various subsystems that are connected through the Internet. Communication and collaboration within an entire system requires reliable and efficient data exchange between the subsystems. Middleware developed within the web evolution during the past years provides reliable and efficient data exchange for web applications, which can be adopted for solving the data exchange problems in distributed engineering applications. This paper presents a generic approach for reliable and efficient data exchange between engineering devices using existing middleware known from web applications. Different existing middleware is examined with respect to the suitability in engineering applications. In this paper, a suitable middleware is shown and a prototype implementation simulating distributed wind farm control is presented and validated using several performance measurements.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{KoenigLang,
  author    = {K{\"o}nig, Markus and Lang, H.},
  title     = {ANWENDUNG DES CASE-BASED REASONING BEI DER ERMITTLUNG VON VARIANTEN F{\"u}R DEN OBERBAU VON VERKEHRSFL{\"A}CHEN},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2980},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29808},
  pages     = {9},
  abstract  = {F{\"u}r die Ausf{\"u}hrung des Oberbaus von Verkehrsfl{\"a}chen existiert in Abh{\"a}ngigkeit von projektspezifischen Voraussetzungen eine Vielzahl von verschiedenen Varianten. Aufgrund von Erfahrungen der Projektplaner werden bei {\"a}hnlichen Voraussetzungen h{\"a}ufig gleichartige Ausf{\"u}hrungsvarianten gew{\"a}hlt. Um eine m{\"o}gliche L{\"o}sungsvariante f{\"u}r den Straßenoberbau zu erhalten, sollten daher nicht nur die gesetzlichen Richtlinien sondern auch bereits beendete Projekte ber{\"u}cksichtigt werden. Im Rahmen eines Wissenschaftlichen Kollegs an der Bauhaus-Universit{\"a}t Weimar wurde die Anwendung des Case-Based Reasoning f{\"u}r die Auswahl von Ausf{\"u}hrungsvarianten f{\"u}r den Straßenoberbau untersucht. In diesem Beitrag werden die grundlegenden Konzepte des Case-Based Reasoning und die Bestimmung von {\"a}hnlichen Varianten anhand einfacher Beispiele aus dem Straßenoberbau dargestellt.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@inproceedings{KinzlerGrabe,
  author    = {Kinzler, Steffen and Grabe, J{\"u}rgen},
  title     = {APPLICATION OF MULTICRITERIAL NUMERICAL OPTIMISATION IN GEOTECHNICAL ENGINEERING},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2861},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28616},
  pages     = {10},
  abstract  = {Geotechnical constructions are sophisticated structures due to the non-linear soil behaviour and the complex soil-structure interaction, which entails great exigencies on the liable engineer during the design process. The process can be schematised as a difficult and, depending on the opportunities and skills of the processor more or less innovative, creative and heuristic search for one or a multiple of defined objectives under given boundary conditions. Wholistic approaches including numerical optimisation which support the constructing engineer in this task do not currently exist. Abstract problem formulation is not state of the art; commonly parameter studies are bounded by computational effort. Thereby potential regarding cost effectiveness, construction time, load capacity and/or serviceability are often used insufficiently. This paper describes systematic approaches for comprehensive optimisation of selected geotechnical constructions like combined pile raft foundations and quay wall structures. Several optimisation paradigms like the mono- and the multi-objective optimisation are demonstrated and their use for a more efficient design concerning various intentions is shown in example. The optimisation is implemented by using Evolutionary Algorithms. The applicability to geotechnical real world problems including nonlinearities, discontinuities and multi-modalities is shown. The routines are adapted to common problems and coupled with conventional analysis procedures as well as with numerical calculation software based on the finite element method. Numerical optimisation of geotechnical design using efficient algorithms is able to deliver highly effective solutions after investing more effort into the parameterization of the problem. Obtained results can be used for realizing different constructions near the stability limit, visualizing the sensitivity regarding the construction parameters or simply procuring more effective solutions.},
  subject      = {Angewandte Informatik},
  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}
}
@misc{Bock2004,
  type      = {Master Thesis},
  author    = {Bock, Sebastian},
  title     = {Approximation mit polynomialen L{\"o}sungen der Lam{\´e}schen Differentialgleichung},
  doi       = {10.25643/bauhaus-universitaet.640},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6409},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2004},
  abstract  = {Grundidee der Arbeit ist es, L{\"o}sungen von Randwertaufgaben durch Linearkombinationen exakter klassischer L{\"o}sungen der Differentialgleichung zu approximieren. Die freien Koeffizienten werden dabei durch die Bestimmung der besten Approximation der Randwerte berechnet. Als Basis der Approximation werden vollst{\"a}ndige orthogonale und nahezu orthogonale Funktionensysteme verwendet. Anhand ausgew{\"a}hlter Beispiele mit Randvorgaben unterschiedlicher Glattheit wird am Beispiel der Kugel die prinzipielle Anwendbarkeit der Methode getestet und hinsichtlich der Entwicklung des Fehlers der N{\"a}herungsl{\"o}sung, der Stabilit{\"a}t des Verfahrens und des numerischen Aufwandes untersucht. Die erhaltenen Resultate geben einen begr{\"u}ndeten Anlass, die Anwendung der Methode als Bestandteil einer hybriden analytisch-numerischen Methode, insbesondere der Verkn{\"u}pfung mit der FEM, weiterzuverfolgen.},
  subject      = {Legendre-Funktion},
  language  = {de}
}
@inproceedings{KoenigTauscher,
  author    = {K{\"o}nig, Markus and Tauscher, Eike},
  title     = {BERECHNUNG VON BAUABL{\"A}UFEN MIT VERSCHIEDENEN AUSF{\"U}HRUNGSVARIANTEN},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2981},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29816},
  pages     = {11},
  abstract  = {Prozesse im Bauingenieurwesen sind komplex und beinhalten eine große Anzahl verschiedener Aufgaben mit vielen logischen Abh{\"a}ngigkeiten. Basierend auf diesen projektspezifischen Abh{\"a}ngigkeiten wird gew{\"o}hnlich ein Bauablaufplan manuell erstellt. In der Regel existieren mehrere Varianten und somit alternative Bauabl{\"a}ufe um ein Projekt zu realisieren. Welche dieser Ausf{\"u}hrungsvarianten zur praktischen Anwendung kommt, wird durch den jeweiligen Projektmanager bestimmt. Falls {\"A};nderungen oder St{\"o}rungen w{\"a}hrend des Bauablaufs auftreten, m{\"u}ssen die davon betroffenen Aufgaben und Abl{\"a}ufe per Hand modifiziert und alternative Aufgaben sowie Abl{\"a}ufe stattdessen ausgef{\"u}hrt werden. Diese Vorgehensweise ist oft sehr aufw{\"a}ndig und teuer. Aktuelle Forschungsans{\"a}tze besch{\"a}ftigen sich mit der automatischen Generierung von Bauabl{\"a}ufen. Grundlage sind dabei Aufgaben mit ihren erforderlichen Voraussetzungen und erzeugten Ergebnissen. Im Rahmen dieses Beitrags wird eine Methodik vorgestellt, um Bauabl{\"a}ufe mit Ausf{\"u}hrungsvarianten in Form von Workflow-Netzen zu jeder Zeit berechnen zu k{\"o}nnen. Die vorgestellte Methode wird anhand eines Beispiels aus dem Straßenbau schematisch dargestellt.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@inproceedings{AlaladeKafleWuttkeetal.,
  author    = {Alalade, Muyiwa and Kafle, Binod and Wuttke, Frank and Lahmer, Tom},
  title     = {CALIBRATION OF CYCLIC CONSTITUTIVE MODELS FOR SOILS BY OSCILLATING FUNCTIONS},
  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.2793},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27932},
  pages     = {6},
  abstract  = {In order to minimize the probability of foundation failure resulting from cyclic action on structures, researchers have developed various constitutive models to simulate the foundation response and soil interaction as a result of these complex cyclic loads. The efficiency and effectiveness of these model is majorly influenced by the cyclic constitutive parameters. Although a lot of research is being carried out on these relatively new models, little or no details exist in literature about the model based identification of the cyclic constitutive parameters. This could be attributed to the difficulties and complexities of the inverse modeling of such complex phenomena. A variety of optimization strategies are available for the solution of the sum of least-squares problems as usually done in the field of model calibration. However for the back analysis (calibration) of the soil response to oscillatory load functions, this paper gives insight into the model calibration challenges and also puts forward a method for the inverse modeling of cyclic loaded foundation response such that high quality solutions are obtained with minimum computational effort. Therefore model responses are produced which adequately describes what would otherwise be experienced in the laboratory or field.},
  subject      = {Angewandte Informatik},
  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}
}
@article{LegatiukWeiszPatrault,
  author    = {Legatiuk, Dmitrii and Weisz-Patrault, Daniel},
  title     = {Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann-Hilbert Problem},
  series = {Computational Methods and Function Theory},
  volume    = {2021},
  journal   = {Computational Methods and Function Theory},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s40315-021-00403-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210805-44763},
  pages     = {1 -- 23},
  abstract  = {In this paper we present a theoretical background for a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical-numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann-Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@inproceedings{JahrSchlichDragosetal.,
  author    = {Jahr, Katrin and Schlich, Robert and Dragos, Kosmas and Smarsly, Kay},
  title     = {DECENTRALIZED AUTONOMOUS FAULT DETECTION IN WIRELESS STRUCTURAL HEALTH MONITORING SYSTEMS USING STRUCTURAL RESPONSE DATA},
  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.2803},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28031},
  pages     = {8},
  abstract  = {Sensor faults can affect the dependability and the accuracy of structural health monitoring (SHM) systems. Recent studies demonstrate that artificial neural networks can be used to detect sensor faults. In this paper, decentralized artificial neural networks (ANNs) are applied for autonomous sensor fault detection. On each sensor node of a wireless SHM system, an ANN is implemented to measure and to process structural response data. Structural response data is predicted by each sensor node based on correlations between adjacent sensor nodes and on redundancies inherent in the SHM system. Evaluating the deviations (or residuals) between measured and predicted data, sensor faults are autonomously detected by the wireless sensor nodes in a fully decentralized manner. A prototype SHM system implemented in this study, which is capable of decentralized autonomous sensor fault detection, is validated in laboratory experiments through simulated sensor faults. Several topologies and modes of operation of the embedded ANNs are investigated with respect to the dependability and the accuracy of the fault detection approach. In conclusion, the prototype SHM system is able to accurately detect sensor faults, demonstrating that neural networks, processing decentralized structural response data, facilitate autonomous fault detection, thus increasing the dependability and the accuracy of structural health monitoring systems.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{SpiekermannDonath,
  author    = {Spiekermann, Christoph and Donath, Dirk},
  title     = {DIGITAL SUPPORT OF MATERIAL- AND PRODUCT SELECTION IN THE ARCHITECTURAL DESIGN- AND PLANNING PROCESS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.3023},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-30235},
  pages     = {10},
  abstract  = {Architecture is predominantly perceived over the surfaces limiting the space. The used surface materials thereby should support the design intention and have to fulfil various technical and economical requirements. If the architect wants to select the "right" or the "best" material he has to play with very different and sometimes contradicting criteria and must weight these individually for the special purpose. This selection process is supported only insufficiently by today's digital systems. If it would be possible to illustrate all the various parameters by numerical values, the method of multidimensional scaling will offer a solution for architects to find the material which is best fitting on basis of his individual weighting of criteria. By displaying the result of the architect's multidimensional query in a spatial arrangement multidimensional scaling can support an interactive selection process with additional feedback over the applied search strategy.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@article{CerejeirasKaehlerLegatiuketal.,
  author    = {Cerejeiras, Paula and K{\"a}hler, Uwe and Legatiuk, Anastasiia and Legatiuk, Dmitrii},
  title     = {Discrete Hardy Spaces for Bounded Domains in Rn},
  series = {Complex Analysis and Operator Theory},
  volume    = {2021},
  journal   = {Complex Analysis and Operator Theory},
  number    = {Volume 15, article 4},
  publisher = {Springer},
  address   = {Heidelberg},
  doi       = {10.1007/s11785-020-01047-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44746},
  pages     = {1 -- 32},
  abstract  = {Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in Rn. On this way, discrete Stokes' formula, discrete Borel-Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.},
  subject      = {Dirac-Operator},
  language  = {en}
}
@phdthesis{Legatiuk,
  author    = {Legatiuk, Anastasiia},
  title     = {Discrete potential and function theories on a rectangular lattice and their applications},
  doi       = {10.25643/bauhaus-universitaet.4865},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221220-48654},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The growing complexity of modern engineering problems necessitates development of advanced numerical methods. In particular, methods working directly with discrete structures, and thus, representing exactly some important properties of the solution on a lattice and not just approximating the continuous properties, become more and more popular nowadays. Among others, discrete potential theory and discrete function theory provide a variety of methods, which are discrete counterparts of the classical continuous methods for solving boundary value problems. A lot of results related to the discrete potential and function theories have been presented in recent years. However, these results are related to the discrete theories constructed on square lattices, and, thus, limiting their practical applicability and potentially leading to higher computational costs while discretising realistic domains. This thesis presents an extension of the discrete potential theory and discrete function theory to rectangular lattices. As usual in the discrete theories, construction of discrete operators is strongly influenced by a definition of discrete geometric setting. For providing consistent constructions throughout the whole thesis, a detailed discussion on the discrete geometric setting is presented in the beginning. After that, the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, which is the core of the discrete potential theory, its numerical analysis, and practical calculations are presented. By using the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, the discrete potential theory is then constructed for interior and exterior settings. Several discrete interior and exterior boundary value problems are then solved. Moreover, discrete transmission problems are introduced and several numerical examples of these problems are discussed. Finally, a discrete fundamental solution of the discrete Cauchy-Riemann operator on a rectangular lattice is constructed, and basics of the discrete function theory on a rectangular lattice are provided. This work indicates that the discrete theories provide solution methods with very good numerical properties to tackle various boundary value problems, as well as transmission problems coupling interior and exterior problems. The results presented in this thesis provide a basis for further development of discrete theories on irregular lattices.},
  subject      = {Diskrete Funktionentheorie},
  language  = {en}
}
@phdthesis{Hommel,
  author    = {Hommel, Angela},
  title     = {Diskret holomorphe Funktionen und deren Bedeutung bei der L{\"o}sung von Differenzengleichungen},
  doi       = {10.25643/bauhaus-universitaet.3784},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180827-37846},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Auf der Grundlage diskreter Cauchy-Riemann Operatoren werden diskret holomorphe Funktionen definiert und detailliert studiert. Darauf aufbauend wird die L{\"o}sung von Differenzengleichungen mit Hilfe der diskret holomorphen Funktionen beschrieben.},
  subject      = {Differenzengleichung},
  language  = {de}
}
@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}
}
@masterthesis{Nguyen,
  type      = {Bachelor Thesis},
  author    = {Nguyen, Thai Cuong},
  title     = {Fl{\"a}chen zweiter Ordnung - D{\"a}cher m{\"u}ssen nicht eben sein},
  doi       = {10.25643/bauhaus-universitaet.3749},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20181024-37496},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {47},
  abstract  = {In dieser Arbeit geht es um die Quadriken in der Ebene und im Raum. Dabei werden die Transformation in die Normalform und die Klassifikation untersucht. Aus den geometrischen Eigenschaften werden einige Anwendungsbeispiele der Quadriken in der Technik und dem allt{\"a}glichen Leben vorgestellt.},
  subject      = {Quadrik},
  language  = {de}
}
@phdthesis{AlYasiri2017,
  author    = {Al-Yasiri, Zainab Riyadh Shaker},
  title     = {Function Theoretic Methods for the Analytical and Numerical Solution of Some Non-linear Boundary Value Problems with Singularities},
  doi       = {10.25643/bauhaus-universitaet.3898},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190506-38987},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {164},
  year      = {2017},
  abstract  = {The p-Laplace equation is a nonlinear generalization of the well-known Laplace equation. It is often used as a model problem for special types of nonlinearities, and therefore it can be seen as a bridge between very general nonlinear equations and the linear Laplace equation, too. It appears in many problems for instance in the theory of non-Newtonian fluids and fluid dynamics or in rockfill dam problems, as well as in special problems of image restoration and image processing. The aim of this thesis is to solve the p-Laplace equation for 1 < p < 2, as well as for 2 < p < 3 and to find strong solutions in the framework of Clifford analysis. The idea is to apply a hypercomplex integral operator and special function theoretic methods to transform the p-Laplace equation into a p-Dirac equation. We consider boundary value problems for the p-Laplace equation and transfer them to boundary value problems for a p-Dirac equation. These equations will be solved iteratively by applying Banach's fixed-point principle. Applying operator-theoretical methods for the p-Dirac equation, the existence and uniqueness of solutions in certain Sobolev spaces will be proved. In addition, using a finite difference approach on a uniform lattice in the plane, the fundamental solution of the Cauchy-Riemann operator and its adjoint based on the fundamental solution of the Laplacian will be calculated. Besides, we define gener- alized discrete Teodorescu transform operators, which are right-inverse to the discrete Cauchy-Riemann operator and its adjoint in the plane. Furthermore, a new formula for generalized discrete boundary operators (analogues of the Cauchy integral operator) will be considered. Based on these operators a new version of discrete Borel-Pompeiu formula is formulated and proved. This is the basis for an operator calculus that will be applied to the numerical solution of the p-Dirac equation. Finally, numerical results will be presented showing advantages and problems of this approach.},
  subject      = {Finite-Differenzen-Methode},
  language  = {en}
}
@phdthesis{Hommel1998,
  author    = {Hommel, Angela},
  title     = {Fundamentall{\"o}sungen partieller Differenzenoperatoren und die L{\"o}sung diskreter Randwertprobleme mit Hilfe von Differenzenpotentialen},
  doi       = {10.25643/bauhaus-universitaet.28},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040216-303},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {1998},
  abstract  = {Im Mittelpunkt der Dissertation steht die Theorie der Differenzenpotentiale, die eng mit der klassischen Potentialtheorie verbunden ist. Vorgestellt wird eine Methode zur L{\"o}sung von Randwertproblemen, die nicht auf der Diskretisierung einer Randintegralgleichung beruht, sondern von der {\"U}bertragung des Problems in ein Differenzenrandwertproblem ausgeht. Das diskrete Randwertproblem wird mit Hilfe einer Randreduktionsmethode auf eine Randoperatorgleichung transformiert, die detaillierter zu untersuchen ist. Voraussetzung f{\"u}r den Aufbau der Theorie ist die Existenz diskreter Fundamentall{\"o}sungen. Die Definition der Differenzenpotentiale wird von Ryabenkij {\"u}bernommen. Seine Herangehensweise f{\"u}hrt jedoch zu {\"u}berbestimmten linearen Gleichungssystemen auf dem Rand. Durch die Aufspaltung des Randpotentials in ein diskretes Einfach- und Doppelschichtpotential wird diese Schwierigkeit in der Dissertation {\"u}berwunden. Bewiesen werden Eindeutigkeits- und L{\"o}sbarkeitsaussagen f{\"u}r Differenzenrandwertprobleme. Das onvergenzverhalten der diskreten Potentiale wird im Kapitel 3 untersucht. Im Kapitel 4 werden numerische Resultate vorgestellt.},
  subject      = {Diskrete Fourier-Transformation},
  language  = {de}
}
@inproceedings{Lahmer,
  author    = {Lahmer, Tom},
  title     = {HYDRO-MECHANICAL COUPLED FIELD SYSTEM IDENTIFICATION - APPLICATION TO WATER RESERVOIRS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2865},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28650},
  pages     = {14},
  abstract  = {In this paper we present an inverse method which is capable of identifying system components in a hydro-mechanically coupled system, i.e. for fluid flow in porous media. As an example we regard water dams that were constructed more than hundred years ago but which are still in use. Over the time ageing processes have changed the condition of these dams. Within the dams fissures might have grown. The proposed method is designed to locate these fissures out of combined mechanical and hydraulic measurements. In a numerical example the fissures or damaged zones are described by a smeared crack model. The task is now to identify simultaneously the spatial distribution of Young's modulus and the hydraulic permeability due to the fact, that in regions where damages are present, the mechanical stiffness of the system is reduced and the permeability increased. The inversion is shown to be an ill-posed problem. As a consequence regularizing methods have to be applied, where the nonlinear Landweber method (a gradient type method combined with a discrepancy principle) has proven to be an efficient choice.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@masterthesis{Tschernyschkow,
  type      = {Bachelor Thesis},
  author    = {Tschernyschkow, Anton},
  title     = {Instation{\"a}re W{\"a}rmeleitung in geschichteten W{\"a}nden},
  doi       = {10.25643/bauhaus-universitaet.3601},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170914-36014},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {61},
  abstract  = {Analytische L{\"o}sung der W{\"a}rmeleitungsgleichung f{\"u}r inhomogene Medien um ortsver{\"a}nderliche Materialeigenschaften zuzulassen, womit die sprunghafte {\"A}nderung der Stoffkennwerte n{\"a}herungsweise erfasst werden kann. Dazu ist ein Sturm-Liouville-Problem zu l{\"o}sen.},
  subject      = {W{\"a}rmeleitung},
  language  = {de}
}
@inproceedings{OPUS4-2457,
  title     = {International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  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.2457},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150916-24571},
  pages     = {434},
  abstract  = {The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference!},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{OPUS4-2451,
  title     = {International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  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.2451},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150828-24515},
  pages     = {230},
  abstract  = {The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference!},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Heinrich,
  author    = {Heinrich, Timo},
  title     = {KENNZEICHNUNGSBASIERTER ZUGRIFF VON PROZESSMODELLEN AUF OBJEKTBEST{\"A}NDE DES BAUWESENS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2966},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29669},
  pages     = {13},
  abstract  = {F{\"u}r eine beherrschbare Koordination und Durchf{\"u}hrung von Planungsaufgaben in Bauprojekten wird der Planungsprozess zunehmend in formalisierten Modellen - Prozessmodellen - beschrieben. Die Produktmodellforschung ihrerseits widmet sich der Speicherung von Planungsdaten in Form von objektorientierten Modellen im Rechner. Hauptaugenmerk sind dabei die Wahrung der Konsistenz und die Modellierung von Abh{\"a}ngigkeiten innerhalb dieses Planungsmaterials. Der Bezug zu den Akteuren der Planung wird nicht direkt hergestellt. Ein formal beschriebener Planungsprozesses kann in der Praxis noch nicht derart realisiert werden, dass ein Zugriff auf Einzelobjekte des Planungsprozesses gew{\"a}hrleistet ist. Bestehende Planungsunterst{\"u}tzungs- und Workflowmanagement-Systeme abstrahieren und ordnen das Planungsmaterial nach wie vor auf Dateiebene. Der vorliegende Artikel beschreibt eine Methode f{\"u}r die geeignete Verbindung von formalisierten Prozessmodellen in der Bauplanung mit den Einzelobjekten, die in den modellorientierten Objektmengen kodiert sind. Dabei wird die Zugeh{\"o}rigkeit bestimmter Objekte zu Pl{\"a}nen und Dokumenten (zum Zwecke des Datenaustauschs) nicht l{\"a}nger durch die physische Zuordnung zu Dateien festgelegt. Es wird ein formales Beschreibungsmittel vorgestellt, welches die entsprechende Teilmengenbildung aus der Gesamtheit der Planungsobjekte erm{\"o}glicht. F{\"u}r die bisherigen Formen des Datenaustausches werden aus den Objektmodellen der Planung Teilmengen herausgel{\"o}st und physikalisch zwischen den Planern transportiert. Das neue Beschreibungsmittel hingegen erlaubt es, die Bildungsvorschrift f{\"u}r Objektteilmengen statt der Mengen selbst zwischen den Planern auszutauschen. Der Zugriff auf die konkreten Objekte findet dann direkt modellbasiert statt.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@misc{Hamzah,
  type      = {Master Thesis},
  author    = {Hamzah, Abdulrazzak},
  title     = {L{\"o}sung von Randwertaufgaben der Bruchmechanik mit Hilfe einer approximationsbasierten Kopplung zwischen der Finite-Elemente-Methode und Methoden der komplexen Analysis},
  doi       = {10.25643/bauhaus-universitaet.4093},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20200211-40936},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Das Hauptziel der vorliegenden Arbeit war es, eine stetige Kopplung zwischen der ananlytischen und numerischen L{\"o}sung von Randwertaufgaben mit Singularit{\"a}ten zu realisieren. Durch die inter-polationsbasierte gekoppelte Methode kann eine globale C0 Stetigkeit erzielt werden. F{\"u}r diesen Zweck wird ein spezielle finite Element (Kopplungselement) verwendet, das die Stetigkeit der L{\"o}sung sowohl mit dem analytischen Element als auch mit den normalen CST Elementen gew{\"a}hrleistet. Die interpolationsbasierte gekoppelte Methode ist zwar f{\"u}r beliebige Knotenanzahl auf dem Interface ΓAD anwendbar, aber es konnte durch die Untersuchung von der Interpolationsmatrix und numerische Simulationen festgestellt werden, dass sie schlecht konditioniert ist. Um das Problem mit den numerischen Instabilit{\"a}ten zu bew{\"a}ltigen, wurde eine approximationsbasierte Kopplungsmethode entwickelt und untersucht. Die Stabilit{\"a}t dieser Methode wurde anschließend anhand der Untersuchung von der Gramschen Matrix des verwendeten Basissystems auf zwei Intervallen [-π,π] und [-2π,2π] beurteilt. Die Gramsche Matrix auf dem Intervall [-2π,2π] hat einen g{\"u}nstigeren Konditionszahl in der Abh{\"a}ngigkeit von der Anzahl der Kopplungsknoten auf dem Interface aufgewiesen. Um die dazu geh{\"o}rigen numerischen Instabilit{\"a}ten ausschließen zu k{\"o}nnen wird das Basissystem mit Hilfe vom Gram-Schmidtschen Orthogonalisierungsverfahren auf beiden Intervallen orthogonalisiert. Das orthogonale Basissystem l{\"a}sst sich auf dem Intervall [-2π,2π] mit expliziten Formeln schreiben. Die Methode des konsistentes Sampling, die h{\"a}ufig in der Nachrichtentechnik verwendet wird, wurde zur Realisierung von der approximationsbasierten Kopplung herangezogen. Eine Beschr{\"a}nkung dieser Methode ist es, dass die Anzahl der Sampling-Basisfunktionen muss gleich der Anzahl der Wiederherstellungsbasisfunktionen sein. Das hat dazu gef{\"u}hrt, dass das eingef{\"u}hrt Basissys-tem (mit 2 n Basisfunktionen) nur mit n Basisfunktion verwendet werden kann. Zur L{\"o}sung diese Problems wurde ein alternatives Basissystems (Variante 2) vorgestellt. F{\"u}r die Verwendung dieses Basissystems ist aber eine Transformationsmatrix M n{\"o}tig und bei der Orthogonalisierung des Basissystems auf dem Intervall [-π,π] kann die Herleitung von dieser Matrix kompliziert und aufwendig sein. Die Formfunktionen wurden anschließend f{\"u}r die beiden Varianten hergeleitet und grafisch (f{\"u}r n = 5) dargestellt und wurde gezeigt, dass diese Funktionen die Anforderungen an den Formfunktionen erf{\"u}llen und k{\"o}nnen somit f{\"u}r die FE- Approximation verwendet werden. Anhand numerischer Simulationen, die mit der Variante 1 (mit Orthogonalisierung auf dem Intervall [-2π,2π]) durchgef{\"u}hrt wurden, wurden die grundlegenden Fragen (Beispielsweise: Stetigkeit der Verformungen auf dem Interface ΓAD, Spannungen auf dem analytischen Gebiet) {\"u}ber- pr{\"u}ft.},
  subject      = {Mathematik},
  language  = {de}
}
@article{Legatiuk,
  author    = {Legatiuk, Dmitrii},
  title     = {Mathematical Modelling by Help of Category Theory: Models and Relations between Them},
  series = {mathematics},
  volume    = {2021},
  journal   = {mathematics},
  number    = {volume 9, issue 16, article 1946},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/math9161946},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210817-44844},
  pages     = {17},
  abstract  = {The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computationbased, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios.},
  subject      = {Kategorientheorie},
  language  = {en}
}
@phdthesis{Kaemmerer1998,
  author    = {K{\"a}mmerer, Lutz},
  title     = {Mathematische Modellierung und Behandlung von Stapelproblemen},
  doi       = {10.25643/bauhaus-universitaet.27},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040216-298},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {1998},
  abstract  = {Stapelprobleme treten in der Praxis in vielf{\"a}ltiger Form auf. So finden sich Stapelprobleme in einer großen F{\"u}lle von Variationen im Logistikbereich, aber auch im Bauwesen. Zun{\"a}chst wird das klassische Turm von Hanoi Problem kurz vorgestellt. Dieses Problem wird als Stapelproblem formuliert. Weiterhin werden verzweigte Stapelproblem untersucht: Ein gegebener Stapel -- bestehend aus den Elementen v der Menge V -- soll an anderer Stelle in einer vorgeschriebenen, ver{\"a}nderten Struktur wieder aufgebaut werden. Dazu stehen Hilfsstapelpl{\"a}tze zur Verf{\"u}gung. Die Optimierung dieses Problems hinsichtlich der Anzahl der ben{\"o}tigten Hilfsstapelpl{\"a}tze ist NP-vollst{\"a}ndig. Es werden Erfahrungen mit einem Branch-and-Bound Algorithmus zur L{\"o}sung des Problems vorgestellt sowie ein heuristischer Algorithmus diskutiert. Schließlich werden verzweigte Stapelprobleme betrachtet, bei denen keine eineindeutige Zuordnung mehr von Elementen des Ausgangsstapels zu verf{\"u}gbaren Positionen im Zielstapel existiert. Hier ist schon die Bestimmung einer g{\"u}nstigsten Zuordnung in bezug auf die Anzahl ben{\"o}tigter Hilfsstapelpl{\"a}tze NP-schwer.},
  subject      = {Stapelproblem},
  language  = {de}
}
@inproceedings{SeylerSchwarz,
  author    = {Seyler, Steve and Schwarz, W.},
  title     = {MODERN PHOTOGRAMMETRY IN CIVIL ENGINEERING - EXAMPLES FOR MONITORING AND EVALUATION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.3019},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-30192},
  pages     = {13},
  abstract  = {Monitoring und Bewertung sind Hauptaufgaben im Management bzw. der Revitalisierung von Bauwerken. Unterschiedliche Verfahren k{\"o}nnen bei der Akquisition der erforderlichen geometrischen Information, wie z. B. Gr{\"o}ße oder Verformung eines Geb{\"a}udes, eingesetzt werden. Da das Potenzial der digitalen Fotografie kontinuierlich w{\"a}chst, stellt die Industriephotogrammetrie heute eine bedeutende Alternative zu den klassischen Verfahren wie Dehnmessstreifen oder anderen taktilen Sensoren dar. Moderne Industriephotogrammetrie erfasst die Bilder mittels digitaler Systeme. Dies bedeutet, dass die Information digitaler Bilder mit Hilfe der digitalen Bildverarbeitung untersucht werden muss, um die Bildkoordinaten der Messpunkte zu erhalten. Eine der Aufgaben der Bildverarbeitung f{\"u}r photogrammetrische Zwecke besteht somit darin, den Mittelpunkt von kreisf{\"o}rmigen Marken zu lokalisieren. Die modernen Operatoren liefern Subpixelgenauigkeit f{\"u}r die Koordinaten des Punktes. Das optische Messverfahren der Industriephotogrammetrie erfordert hinsichtlich der Hardware in erster Linie hochaufl{\"o}sende digitale Kameras. Dabei lassen sich die Kameras in Videokameras, HighSpeed-Kameras, intelligente Kameras sowie so genannte Consumer und Professionelle Kameras unterscheiden. Die geometrische Aufl{\"o}sung digitaler HighEnd-Kameras liegt heute bei {\"u}ber 10 Megapixel. In punkto Datentransfer zum Rechner sind verschiedene Standards am Markt verf{\"u}gbar, z. B. USB2.0, GigE-Vision, CameraLink oder Firewire. Die Wahl des Standards h{\"a}ngt immer von der spezifischen Aufgabenstellung ab, da keine der Techniken eine f{\"u}hrende Position einnimmt. Die moderne Photogrammetrie bietet viele neue M{\"o}glichkeiten f{\"u}r das Monitoring und die Bewertung von Bauwerken. Sie kann ein-, zwei-, drei- oder vierdimensionale Informationen liefern, falls erforderlich auch in Echtzeit. Als ber{\"u}hrungsloses Messverfahren ist der Einsatz der Photogrammetrie noch m{\"o}glich, wenn die taktilen Sensoren z. B. aufgrund ihres Platzbedarfes nicht mehr eingesetzt werden k{\"o}nnen. Hochaufl{\"o}sende Videokameras erlauben es, selbst dynamische Untersuchungen mit großer Pr{\"a}zision durchzuf{\"u}hren.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@phdthesis{AhmedElSayed2003,
  author    = {Ahmed El-Sayed, Ahmed Mohammed},
  title     = {One some classes and spaces of holomorphic and hyperholomorphic functions},
  doi       = {10.25643/bauhaus-universitaet.25},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040216-271},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2003},
  abstract  = {In this Thesis we study some complex and hypercomplex function spaces and classes such as hypercomplex Besov spaces, Bloch space and Op spaces as well as the class of basic sets of polynomials in several complex variables. It is shown that hyperholomorphic Besov spaces can be applied to characterize the hyperholomorphic Bloch space. Moreover, we consider BMOM and VMOM spaces.},
  subject      = {Funktionenraum},
  language  = {en}
}
@inproceedings{AlmamouGebhardtBocketal.,
  author    = {Almamou, Abd Albasset and Gebhardt, Thomas and Bock, Sebastian and Hildebrand, J{\"o}rg and Schwarz, Willfried},
  title     = {QUALITY CONTROL OF CONSTRUCTED MODELS USING 3D POINT CLOUD},
  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.2794},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27944},
  pages     = {9},
  abstract  = {Over the last decade, the technology of constructing buildings has been dramatically developed especially with the huge growth of CAD tools that help in modeling buildings, bridges, roads and other construction objects. Often quality control and size accuracy in the factory or on construction site are based on manual measurements of discrete points. These measured points of the realized object or a part of it will be compared with the points of the corresponding CAD model to see whether and where the construction element fits into the respective CAD model. This process is very complicated and difficult even when using modern measuring technology. This is due to the complicated shape of the components, the large amount of manually detected measured data and the high cost of manual processing of measured values. However, by using a modern 3D scanner one gets information of the whole constructed object and one can make a complete comparison against the CAD model. It gives an idea about quality of objects on the whole. In this paper, we present a case study of controlling the quality of measurement during the constructing phase of a steel bridge by using 3D point cloud technology. Preliminary results show that an early detection of mismatching between real element and CAD model could save a lot of time, efforts and obviously expenses.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{HammBeissertKoenig,
  author    = {Hamm, Matthias and Beißert, Ulrike and K{\"o}nig, Markus},
  title     = {SIMULATION-BASED OPTIMIZATION OF CONSTRUCTION SCHEDULES BY USING PARETO SIMULATED ANNEALING},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2849},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28499},
  pages     = {13},
  abstract  = {Within the scheduling of construction projects, different, partly conflicting objectives have to be considered. The specification of an efficient construction schedule is a challenging task, which leads to a NP-hard multi-criteria optimization problem. In the past decades, so-called metaheuristics have been developed for scheduling problems to find near-optimal solutions in reasonable time. This paper presents a Simulated Annealing concept to determine near-optimal construction schedules. Simulated Annealing is a well-known metaheuristic optimization approach for solving complex combinatorial problems. To enable dealing with several optimization objectives the Pareto optimization concept is applied. Thus, the optimization result is a set of Pareto-optimal schedules, which can be analyzed for selecting exactly one practicable and reasonable schedule. A flexible constraint-based simulation approach is used to generate possible neighboring solutions very quickly during the optimization process. The essential aspects of the developed Pareto Simulated Annealing concept are presented in detail.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{VolkovKirschkeChelyshkovetal.,
  author    = {Volkov, Andrey and Kirschke, Heiko and Chelyshkov, Pavel and Sedov, Artem and Lysenko, Denis},
  title     = {THE CRITERIA'S SET WITH INVARIANT DESIGN BUILDING ELEMENTS ON THE BASE OF THREE IMPUTATIONS: "CONVENIENCE", "SAFETY" AND "ENERGY-EFFICIENCY"},
  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.2795},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27956},
  pages     = {6},
  abstract  = {The paper deals with the formalization of the criteria for constructing building management systems. We consider three criteria - "convenience", "safety" and "energyefficiency". For each objective proposed method of calculation.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Vasileva,
  author    = {Vasileva, Iuliia},
  title     = {THE PROBLEM OF PARTIAL REINFORCING AN INTERFACE CRACK EDGE BY A RIGID PATCH PLATE UNDER IN-PLANE AND ANTIPLANE LOADS},
  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.2824},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28242},
  pages     = {5},
  abstract  = {The stress state of a piecewise-homogeneous elastic body, which has a semi-infinite crack along the interface, under in-plane and antiplane loads is considered. One of the crack edges is reinforced by a rigid patch plate on a finite interval adjacent to the crack tip. The crack edges are loaded with specified stresses. The body is stretched at infinity by specified stresses. External forces with a given principal vector and moment act on the patch plate. The problem reduces to a Riemann-Hilbert boundary-value matrix problem with a piecewise-constant coefficient for two complex potentials in the plane case and for one in the antiplane case. The complex potentials are found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the ends of the patch plate, one of which is also simultaneously the crack tip, is investigated. Stress intensity factors near the singular points are determined.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{KerstenRodehorst,
  author    = {Kersten, Jens and Rodehorst, Volker},
  title     = {TOWARDS STEREO VISION- AND LASER SCANNER-BASED UAS POSE ESTIMATION},
  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.2807},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28072},
  pages     = {7},
  abstract  = {A central issue for the autonomous navigation of mobile robots is to map unknown environments while simultaneously estimating its position within this map. This chicken-eggproblem is known as simultaneous localization and mapping (SLAM). Asctec's quadrotor Pelican is a powerful and flexible research UAS (unmanned aircraft system) which enables the development of new real-time on-board algorithms for SLAM as well as autonomous navigation. The relative UAS pose estimation for SLAM, usually based on low-cost sensors like inertial measurement units (IMU) and barometers, is known to be affected by high drift rates. In order to significantly reduce these effects, we incorporate additional independent pose estimation techniques using exteroceptive sensors. In this article we present first pose estimation results using a stereo camera setup as well as a laser range finder, individually. Even though these methods fail in few certain configurations we demonstrate their effectiveness and value for the reduction of IMU drift rates and give an outlook for further works towards SLAM.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@masterthesis{Schumann,
  type      = {Bachelor Thesis},
  author    = {Schumann, Alexander},
  title     = {Untersuchung und Beurteilung des Rissverhaltens eines Betongelenkes anhand unterschiedlicher Methoden},
  doi       = {10.25643/bauhaus-universitaet.1982},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20130722-19829},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {95},
  abstract  = {Die Bruchmechanik hat einen wichtigen Platz im modernen Bauingenieurwesen, um die Ausbreitung von Rissen in Bauteilen und ihre Gef{\"a}hrlichkeit einzusch{\"a}tzen. Dabei kommen verschiedenste Methoden zum Einsatz. In dieser Arbeit soll die Qualit{\"a}tsbewertung f{\"u}r einige dieser Methoden untersucht werden. Zu vergleichen sind u. a. die Genauigkeit, die Schnelligkeit, die Komplexit{\"a}t und die Stabilit{\"a}t. In den Vergleich sind die Finite Elemente Methode, die Extended Finite Elemente Methode und eine Kopplungsmethode (analytische L{\"o}sung f{\"u}r die Rissspitze und Finite Elemente L{\"o}sung f{\"u}r den Rest des Gebietes) einzubeziehen. Als reales Beispiel aus dem Bauingenieurwesen wird ein Betongelenk mit einem vorhandenen Riss betrachtet.},
  subject      = {Finite Elemente Methode},
  language  = {de}
}
@phdthesis{Nguyen,
  author    = {Nguyen, Manh Hung},
  title     = {µ-Hyperholomorphic Function Theory in R³: Geometric Mapping Properties and Applications},
  doi       = {10.25643/bauhaus-universitaet.2447},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150817-24477},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {155},
  abstract  = {This thesis applies the theory of \psi-hyperholomorphic functions dened in R^3 with values in the set of paravectors, which is identified with the Eucledian space R^3, to tackle some problems in theory and practice: geometric mapping properties, additive decompositions of harmonic functions and applications in the theory of linear elasticity.},
  subject      = {Mathematik},
  language  = {en}
}
@phdthesis{Bock2010,
  author    = {Bock, Sebastian},
  title     = {{\"U}ber funktionentheoretische Methoden in der r{\"a}umlichen Elastizit{\"a}tstheorie},
  doi       = {10.25643/bauhaus-universitaet.1417},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20100407-15030},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2010},
  abstract  = {Die Behandlung von geometrischen Singularit{\"a}ten bei der L{\"o}sung von Randwertaufgaben der Elastostatik stellt erh{\"o}hte Anforderungen an die mathematische Modellierung des Randwertproblems und erfordert f{\"u}r eine effiziente Auswertung speziell angepasste Berechnungsverfahren. Diese Arbeit besch{\"a}ftigt sich mit der systematischen Verallgemeinerung der Methode der komplexen Spannungsfunktionen auf den Raum, wobei der Schwerpunkt in erster Linie auf der Begr{\"u}ndung des mathematischen Verfahrens unter besonderer Ber{\"u}cksichtigung der praktischen Anwendbarkeit liegt. Den theoretischen Rahmen hierf{\"u}r bildet die Theorie quaternionenwertiger Funktionen. Dementsprechend wird die Klasse der monogenen Funktionen als Grundlage verwendet, um im ersten Teil der Arbeit ein r{\"a}umliches Analogon zum Darstellungssatz von Goursat zu beweisen und verallgemeinerte Kolosov-Muskhelishvili Formeln zu konstruieren. Im Hinblick auf die vielf{\"a}ltigen Anwendungsbereiche der Methode besch{\"a}ftigt sich der zweite Teil der Arbeit mit der lokalen und globalen Approximation von monogenen Funktionen. Hierzu werden vollst{\"a}ndige Orthogonalsysteme monogener Kugelfunktionen konstruiert, infolge dessen neuartige Darstellungen der kanonischen Reihenentwicklungen (Taylor, Fourier, Laurent) definiert werden. In Analogie zu den komplexen Potenz- und Laurentreihen auf der Grundlage der holomorphen z-Potenzen werden durch diese monogenen Orthogonalreihen alle wesentlichen Eigenschaften bez{\"u}glich der hyperkomplexen Ableitung und der monogenen Stammfunktion verallgemeinert. Anhand repr{\"a}sentativer Beispiele werden die qualitativen und numerischen Eigenschaften der entwickelten funktionentheoretischen Verfahren abschließend evaluiert. In diesem Kontext werden ferner einige weiterf{\"u}hrende Anwendungsbereiche im Rahmen der r{\"a}umlichen Funktionentheorie betrachtet, welche die speziellen Struktureigenschaften der monogenen Potenz- und Laurentreihenentwicklungen ben{\"o}tigen.},
  subject      = {Lineare Elastizit{\"a}tstheorie},
  language  = {de}
}