TY - THES A1 - Legatiuk, Anastasiia T1 - Discrete potential and function theories on a rectangular lattice and their applications N2 - 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. KW - Diskrete Funktionentheorie KW - Diskrete Potentialtheorie KW - Diskrete Fundamentallösung KW - Transmissionsaufgabe KW - Discrete potential theory KW - Discrete function theory KW - Transmission problem KW - Discrete fundamental solution Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20221220-48654 ER - TY - JOUR A1 - Legatiuk, Dmitrii T1 - Mathematical Modelling by Help of Category Theory: Models and Relations between Them JF - mathematics N2 - 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. KW - Kategorientheorie KW - Modellierung KW - Modellierungsmethode KW - OA-Publikationsfonds2021 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210817-44844 UR - https://www.mdpi.com/2227-7390/9/16/1946?type=check_update&version=1 VL - 2021 IS - volume 9, issue 16, article 1946 PB - MDPI CY - Basel ER - TY - JOUR A1 - Legatiuk, Dmitrii A1 - Weisz-Patrault, Daniel T1 - 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 JF - Computational Methods and Function Theory N2 - 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. KW - Angewandte Mathematik KW - Finite-Elemente-Methode KW - Rissausbreitung KW - Modellierung KW - Bruchmechanik KW - fracture mechanics KW - crack propagation KW - coupling KW - energetic approach Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210805-44763 UR - https://link.springer.com/article/10.1007/s40315-021-00403-7 VL - 2021 SP - 1 EP - 23 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Legatiuk, Anastasiia A1 - Gürlebeck, Klaus A1 - Hommel, Angela T1 - Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice JF - Mathematical Methods in the Applied Sciences N2 - 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. KW - diskrete Fourier-Transformation KW - Laplace-Operator KW - discrete fourier transform KW - discrete fundamental solution KW - laplace operator KW - rectangular lattice Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45829 UR - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7747 VL - 2021 SP - 1 EP - 23 PB - Wiley CY - Chichester ER - TY - JOUR A1 - Cerejeiras, Paula A1 - Kähler, Uwe A1 - Legatiuk, Anastasiia A1 - Legatiuk, Dmitrii T1 - Discrete Hardy Spaces for Bounded Domains in Rn JF - Complex Analysis and Operator Theory N2 - 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. KW - Dirac-Operator KW - Randwertproblem KW - Funktionentheorie KW - discrete Dirac operator KW - discrete monogenic functions KW - discrete boundary value problems Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210804-44746 UR - https://link.springer.com/article/10.1007/s11785-020-01047-6 VL - 2021 IS - Volume 15, article 4 SP - 1 EP - 32 PB - Springer CY - Heidelberg ER - TY - THES A1 - Hamzah, Abdulrazzak T1 - Lösung von Randwertaufgaben der Bruchmechanik mit Hilfe einer approximationsbasierten Kopplung zwischen der Finite-Elemente-Methode und Methoden der komplexen Analysis N2 - Das Hauptziel der vorliegenden Arbeit war es, eine stetige Kopplung zwischen der ananlytischen und numerischen Lösung von Randwertaufgaben mit Singularitäten zu realisieren. Durch die inter-polationsbasierte gekoppelte Methode kann eine globale C0 Stetigkeit erzielt werden. Für diesen Zweck wird ein spezielle finite Element (Kopplungselement) verwendet, das die Stetigkeit der Lösung sowohl mit dem analytischen Element als auch mit den normalen CST Elementen gewährleistet. Die interpolationsbasierte gekoppelte Methode ist zwar für 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 Instabilitäten zu bewältigen, wurde eine approximationsbasierte Kopplungsmethode entwickelt und untersucht. Die Stabilität 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 günstigeren Konditionszahl in der Abhängigkeit von der Anzahl der Kopplungsknoten auf dem Interface aufgewiesen. Um die dazu gehörigen numerischen Instabilitäten ausschließen zu können wird das Basissystem mit Hilfe vom Gram-Schmidtschen Orthogonalisierungsverfahren auf beiden Intervallen orthogonalisiert. Das orthogonale Basissystem lässt sich auf dem Intervall [−2π,2π] mit expliziten Formeln schreiben. Die Methode des konsistentes Sampling, die häufig in der Nachrichtentechnik verwendet wird, wurde zur Realisierung von der approximationsbasierten Kopplung herangezogen. Eine Beschränkung dieser Methode ist es, dass die Anzahl der Sampling-Basisfunktionen muss gleich der Anzahl der Wiederherstellungsbasisfunktionen sein. Das hat dazu geführt, dass das eingeführt Basissys-tem (mit 2 n Basisfunktionen) nur mit n Basisfunktion verwendet werden kann. Zur Lösung diese Problems wurde ein alternatives Basissystems (Variante 2) vorgestellt. Für die Verwendung dieses Basissystems ist aber eine Transformationsmatrix M nötig 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 für die beiden Varianten hergeleitet und grafisch (für n = 5) dargestellt und wurde gezeigt, dass diese Funktionen die Anforderungen an den Formfunktionen erfüllen und können somit für die FE- Approximation verwendet werden. Anhand numerischer Simulationen, die mit der Variante 1 (mit Orthogonalisierung auf dem Intervall [−2π,2π]) durchgeführt wurden, wurden die grundlegenden Fragen (Beispielsweise: Stetigkeit der Verformungen auf dem Interface ΓAD, Spannungen auf dem analytischen Gebiet) über- prüft. KW - Mathematik KW - Bruchmechanik KW - Näherungsverfahren Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20200211-40936 ER - TY - THES A1 - Al-Yasiri, Zainab Riyadh Shaker T1 - Function Theoretic Methods for the Analytical and Numerical Solution of Some Non-linear Boundary Value Problems with Singularities N2 - 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. N2 - Die p-Laplace-Gleichung ist eine nichtlineare Verallgemeinerung der wohlbekannten Laplace-Gleichung Die p-Laplace-Gleichung wird häufig als Referenzbeispiel für spezielle Typen von Nichtlinearitäten benutzt und kann daher auch als Brücke zwischen sehr allgemeinen nichtlinearen partiellen Differentialgleichungen und der linearen Laplace-Gleichung gesehen werden. Sie ist darüber hinaus auch das mathematische Modell für eine Reihe praxisrelevanter Probleme, wie z.B. in der Theorie nicht-newtonscher Flüssigkeiten, der Strömungsmechanik, der Durchfeuchtung von Schütt- dämmen und auch ein wichtiges Werkzeug zur Behandlung spezieller Probleme der Bildrekonstruktion und Bildverarbeitung. Das Ziel dieser Arbeit ist es, die p-Laplace-Gleichung sowohl für 1 < p < 2 als auch ür 2 < p < 3 zu lösen. Strenge Lösungen werden unter Benutzung der Clifford- Analysis konstruiert. Die Idee ist dabei, einen hyperkomplexen Integraloperator und funktionentheoretische Methoden auf die p-Laplace-Gleichung anzuwenden und diese Gleichung dadurch in eine p-Dirac-Gleichung zu transformieren, die dann besser gelöst werden kann. Es werden spezielle Randwertprobleme für die p-Laplace-Gleichung in Dirichlet-Probleme für die p-Dirac-Gleichung transformiert und dabei die Ordnung der Differentialgleichung reduziert. Die Randwertprobleme für die p-Dirac-Gleichung werden mit Hilfe des Banachschen Fixpunktprinzips iterativ analytisch gelöst. Durch Anwendung operator-theoretischer Methoden kann die Existenz und Eindeutigkeit der Lösung in bestimmten Sobolev-Räumen nachgewiesen werden. Darüber hinaus wird eine Finite Differenzenmethode auf einem gleichmäßigen Gitter in der Ebene angewandt, um die Fundamentallösung des diskreten Laplace- Operators numerisch zu berechnen. In der Folge werden daraus Fundamentallösungen des diskreten Cauchy-Riemann-Operators und seines adjungierten Operators erzeugt. Auf dieser Grundlage werden über Faltungen mit den Fundamentallösungen diskrete Teodorescu-Operatoren definiert, die rechtsinvers zum diskreten Cauchy-Riemann- Operator bzw. zum adjungierten diskreten Cauchy-Riemann-Operator sind. Weiterhin werden diskrete Randoperatoren, die analog zum Cauchyschen Integraloperator sind, eingeführt. Alle vorgenannten Operatoren werden in einer neuen Version einer diskreten Borel-Pompeiu-Formel zusammengeführt und bilden die Grundlage für eine diskrete Operatorenrechnung. Diese Untersuchungen erweitern bekannte Resultate auf wesentlich größere Funktionenklassen als bisher möglich waren. Die diskrete Opera- torenrechnung wird benutzt, um die diskretisierten Randwertprobleme für die p-Dirac- Gleichung numerisch zu lösen. Numerische Resultate werden vorgestellt und diskutiert. Dabei wird auf Vor- und Nachteile der entwickelten Methode eingegangen. KW - discrete function theory KW - finite difference methods KW - p-Laplace equation KW - Finite-Differenzen-Methode Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20190506-38987 ER - TY - JOUR A1 - Gürlebeck, Klaus A1 - Legatiuk, Dmitrii A1 - Nilsson, Henrik A1 - Smarsly, Kay T1 - Conceptual modelling: Towards detecting modelling errors in engineering applications JF - Mathematical Methods in Applied Sciences N2 - 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. KW - Angewandte Mathematik KW - Angewandte Informatik KW - Ingenieurwissenschaften KW - Modellierung KW - engineering KW - abstraction KW - modelling KW - formal approaches KW - type theory Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20200110-40614 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5934 SP - 1 EP - 10 ER - TY - THES A1 - Hommel, Angela T1 - Diskret holomorphe Funktionen und deren Bedeutung bei der Lösung von Differenzengleichungen N2 - Auf der Grundlage diskreter Cauchy-Riemann Operatoren werden diskret holomorphe Funktionen definiert und detailliert studiert. Darauf aufbauend wird die Lösung von Differenzengleichungen mit Hilfe der diskret holomorphen Funktionen beschrieben. KW - Differenzengleichung KW - Holomorphe Funktion Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20180827-37846 ER - TY - THES A1 - Nguyen, Thai Cuong T1 - Flächen zweiter Ordnung - Dächer müssen nicht eben sein N2 - 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 alltäglichen Leben vorgestellt. KW - Quadrik KW - Quadrik KW - Kegelschnitt KW - Flächen zweiter Ordnung KW - Hauptachsentransformation Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20181024-37496 ER - TY - THES A1 - Tschernyschkow, Anton T1 - Instationäre Wärmeleitung in geschichteten Wänden N2 - Analytische Lösung der Wärmeleitungsgleichung für inhomogene Medien um ortsveränderliche Materialeigenschaften zuzulassen, womit die sprunghafte Änderung der Stoffkennwerte näherungsweise erfasst werden kann. Dazu ist ein Sturm-Liouville-Problem zu lösen. KW - Wärmeleitung KW - Wärmeübertragung KW - Wand KW - Bauphysik KW - Mathematik KW - analytische Lösung KW - geschichtete Wände KW - mehrschichtige Wände KW - Wärmeleitungsgleichung KW - eindimensionale Wärmeleitung Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170914-36014 ER - TY - CHAP A1 - Volkov, Andrey A1 - Kirschke, Heiko A1 - Chelyshkov, Pavel A1 - Sedov, Artem A1 - Lysenko, Denis ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - THE CRITERIA’S SET WITH INVARIANT DESIGN BUILDING ELEMENTS ON THE BASE OF THREE IMPUTATIONS: “CONVENIENCE”, “SAFETY” AND “ENERGY-EFFICIENCY” T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27956 SN - 1611-4086 ER - TY - CHAP A1 - Jahr, Katrin A1 - Schlich, Robert A1 - Dragos, Kosmas A1 - Smarsly, Kay ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - DECENTRALIZED AUTONOMOUS FAULT DETECTION IN WIRELESS STRUCTURAL HEALTH MONITORING SYSTEMS USING STRUCTURAL RESPONSE DATA T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28031 SN - 1611-4086 ER - TY - CHAP A1 - Almamou, Abd Albasset A1 - Gebhardt, Thomas A1 - Bock, Sebastian A1 - Hildebrand, Jörg A1 - Schwarz, Willfried ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - QUALITY CONTROL OF CONSTRUCTED MODELS USING 3D POINT CLOUD T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27944 SN - 1611-4086 ER - TY - CHAP A1 - Vasileva, Iuliia ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - THE PROBLEM OF PARTIAL REINFORCING AN INTERFACE CRACK EDGE BY A RIGID PATCH PLATE UNDER IN-PLANE AND ANTIPLANE LOADS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28242 SN - 1611-4086 ER - TY - CHAP A1 - Wiggenbrock, Jens A1 - Smarsly, Kay ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - A GENERIC FRAMEWORK SUPPORTING DISTRIBUTED COMPUTING IN ENGINEERING APPLICATIONS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28260 SN - 1611-4086 ER - TY - CHAP ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar T1 - Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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! KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren KW - Building Information Modeling KW - Optimization in engineering applications KW - Data, information and knowledge modeling in civil engineering KW - Function theoretic methods and PDE in engineering sciences KW - Mathematical methods for (robotics and) computer vision KW - Numerical modeling in engineering Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150828-24515 SN - 1611-4086 ER - TY - THES A1 - Nguyen, Manh Hung T1 - µ-Hyperholomorphic Function Theory in R³: Geometric Mapping Properties and Applications N2 - 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. KW - mathematics KW - harmonic KW - quaternion KW - elasticity KW - geometry KW - Mathematik Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150817-24477 ER - TY - CHAP A1 - Kersten, Jens A1 - Rodehorst, Volker ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - TOWARDS STEREO VISION- AND LASER SCANNER-BASED UAS POSE ESTIMATION T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28072 SN - 1611-4086 ER - TY - CHAP A1 - Alalade, Muyiwa A1 - Kafle, Binod A1 - Wuttke, Frank A1 - Lahmer, Tom ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - CALIBRATION OF CYCLIC CONSTITUTIVE MODELS FOR SOILS BY OSCILLATING FUNCTIONS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - 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. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27932 SN - 1611-4086 ER -