@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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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} } @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 }, language = {de} } @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} } @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{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{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} } @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 }, 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} }