@inproceedings{Faustino,
  author    = {Faustino, Nelson},
  title     = {FISCHER DECOMPOSITION FOR DIFFERENCE DIRAC OPERATORS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2955},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29551},
  pages     = {10},
  abstract  = {We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a Fischer decomposition for the discrete Laplacian. For the sake of simplicity we consider in the first part only Dirac operators which contain only forward or backward finite differences. Of course, these Dirac operators do not factorize the classic discrete Laplacian. Therefore, we will consider a different definition of a difference Dirac operator in the quaternionic case which do factorizes the discrete Laplacian.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{Bilchuk,
  author    = {Bilchuk, Irina},
  title     = {GEOMETRIC IDENTIFICATION OF OBJECTS IN CIVIL ENGINEERING APPLICATIONS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2927},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29274},
  pages     = {21},
  abstract  = {Objects for civil engineering applications can be identified with their reference in memory, their alpha-numeric name or their geometric location. Particularly in graphic user interfaces, it is common to identify objects geometrically by selection with the mouse. As the number of geometric objects in a graphic user interface grows, it becomes increasingly more important to treat the basic operations add, search and remove for geometric objects with great efficiency. Guttmann has proposed the Region-Tree (R-tree) for geometric identification in an environment which uses pages on disc as data structure. Minimal bounding rectangles are used to structure the data in such a way that neighborhood relations can be described effectively. The literature shows that the parameters which influence the efficiency of the R-trees have been studied extensively, but without conclusive results. The goal of the research which is reported in this paper is to determine reliably the parameters which significantly influence the efficiency of R-trees for geometric identification in technical drawings. In order to make this investigation conclusive, it must be performed with the best available software technology. Therefore an object-oriented software for the method is developed. This implementation is tested with technical drawings containing many thousands of geometric objects. These drawings are created automatically by a stochastic generator which is incorporated into a test bed consisting of an editor and a visualisor. This test bed is used to obtain statistics for the main factors which affect the efficiency of R-trees. The investigation shows that the following main factors which affect the efficiency can be identified reliably : number of geometric objects on the drawing the minimum und maximum number of children of a node of the tree the maximum width and height of the minimal bounding rectangles of the geometric objects relative to the size of the drawing.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@phdthesis{Haefner2006,
  author    = {H{\"a}fner, Stefan},
  title     = {Grid-based procedures for the mechanical analysis of heterogeneous solids},
  doi       = {10.25643/bauhaus-universitaet.858},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20070830-9185},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2006},
  abstract  = {The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed.},
  subject      = {B-Spline},
  language  = {en}
}
@inproceedings{BrackxDeSchepperDeSchepperetal.,
  author    = {Brackx, Fred and De Schepper, Hennie and De Schepper, Nele and Sommen, Frank},
  title     = {HERMITIAN CLIFFORD-HERMITE WAVELETS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2931},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29313},
  pages     = {13},
  abstract  = {The one-dimensional continuous wavelet transform is a successful tool for signal and image analysis, with applications in physics and engineering. Clifford analysis offers an appropriate framework for taking wavelets to higher dimension. In the usual orthogonal case Clifford analysis focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued Dirac operator ∂, defined in terms of an orthogonal basis for the quadratic space Rm underlying the construction of the Clifford algebra R0,m. An intrinsic feature of this function theory is that it encompasses all dimensions at once, as opposed to a tensorial approach with products of one-dimensional phenomena. This has allowed for a very specific construction of higher dimensional wavelets and the development of the corresponding theory, based on generalizations of classical orthogonal polynomials on the real line, such as the radial Clifford-Hermite polynomials introduced by Sommen. In this paper, we pass to the Hermitian Clifford setting, i.e. we let the same set of generators produce the complex Clifford algebra C2n (with even dimension), which we equip with a Hermitian conjugation and a Hermitian inner product. Hermitian Clifford analysis then focusses on the null solutions of two mutually conjugate Hermitian Dirac operators which are invariant under the action of the unitary group. In this setting we construct new Clifford-Hermite polynomials, starting in a natural way from a Rodrigues formula which now involves both Dirac operators mentioned. Due to the specific features of the Hermitian setting, four different types of polynomials are obtained, two types of even degree and two types of odd degree. These polynomials are used to introduce a new continuous wavelet transform, after thorough investigation of all necessary properties of the involved polynomials, the mother wavelet and the associated family of wavelet kernels.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{Jahnke,
  author    = {Jahnke, Georg},
  title     = {HISTORISCHE BAUSUBSTANZ IN MECKLENBURG},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2971},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29719},
  pages     = {11},
  abstract  = {Mit diesen Ausf{\"u}hrungen wird ein Beitrag zum weiteren Erhalt der historischen Bausubstanz in Mecklenburg aus der Sicht der Tragwerksanalyse geleistet. Dabei best{\"a}tigt es sich immer mehr, dass mit dem Modell der Geometrie, der Belastung und des Materials gleichberechtigte Modelle f{\"u}r eine wirklichkeitsnahe Einsch{\"a}tzung des Tragverhaltens eines Tragwerks vorliegen m{\"u}ssen. Es zeigt sich, dass dabei die besten Berechnungsprogramme nur die Ergebnisse liefern k{\"o}nnen, die mit den Eingabedaten zu erzielen sind. So hat sich der Forschungsschwerpunkt im Lehrgebiet Tragwerkslehre des FB Architektur an der Hochschule Wismar in den letzten Jahren auf die realistische Abbildung der Wechselwirkung zwischen der Bauaufnahme und der geometrischen Modellierung konzentriert. In diesem Bereich zeigen sich als Schwerpunkte die Wechselwirkung zwischen Sch{\"a}den und Tragwerksanalyse und die Wechselwirkung zwischen der aufgenommenen Geometrie und dem geometrischen Modell f{\"u}r die Tragwerksanalyse. Die F{\"u}lle der aufgenommenen Daten sind dabei in der Regel mehr hinderlich als ein Segen f{\"u}r die Tragwerksanalyse. Hier wurde gezeigt, welche und wie viele geometrische Daten f{\"u}r das geometrische Modell f{\"u}r die Tragwerksanalyse sinnvoll sind. Da die eigene Datenaufnahme relativ viel Zeit beansprucht, wurde eine "geistige" Bauaufnahme durchgef{\"u}hrt. Dazu wird der historische Planungsprozess in den einzelnen Formfindungsschritten nachvollzogen und in die virtuelle Realit{\"a}t {\"u}berf{\"u}hrt. Mit dieser Methode ergeben sich unterschiedliche Bauzust{\"a}nde und es lassen sich auch m{\"o}gliche Bauphasen abbilden. Die Tragwerksanalyse dieser virtuellen Realit{\"a}t zeigt dann m{\"o}gliche Schw{\"a}chen der Tragwerke und/oder die Notwendigkeit konstruktiver Ver{\"a}nderungen. Ein Vergleich der Ergebnisse der Tragwerksanalyse mit der Realit{\"a}t anhand des vorliegenden Datenbestands liefert die Grundlage f{\"u}r den aktuellen Handlungsbedarf. Da der Bauzustand eines Bauwerkes unter einer zeitlichen Ver{\"a}nderung steht, werden Methoden {\"u}berpr{\"u}ft, die es erm{\"o}glichen, einen einmal vorgelegten Datenbestand aufzubereiten und weiter zu verwalten.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@inproceedings{SchanzWuttkeDineva,
  author    = {Schanz, Tom and Wuttke, Frank and Dineva, Petia},
  title     = {HYBRID APPROACH OF WAVE NUMBER INTEGRATION-BOUNDARY INTEGRAL EQUATION METHOD FOR SITE EFFECT ESTIMATION OF A LATERALLY VARYING SEISMIC REGION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2913},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29132},
  pages     = {15},
  abstract  = {In this paper we evaluate 2D models for soil-water characteristic curve (SWCC), that incorporate the hysteretic nature of the relationship between volumetric water content Θ and suction Ψ. The models are based on nonlinear least squares estimation of the experimental data for sand. To estimate the dependent variable Θ the proposed models include two independent variables, suction and sensors reading position (depth d in the column test). The variable d represents not only the position where suction and water content are measured but also the initial suction distribution before each of the hydraulic loading test phases. Due to this the proposed 2D regression models acquire the advantage that they: (a) can be applied for prediction of Θ for any position along the column and (b) give the functional form for the scanning curves.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{Goettlicher,
  author    = {G{\"o}ttlicher, Manfred},
  title     = {HYBRID SOLID-LIQUID MODEL FOR GRANULAR MATERIAL},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2959},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29596},
  pages     = {20},
  abstract  = {Solid behavior as well as liquid behavior characterizes the flow of granular material in silos. The presented model is based on an appropriate interaction of a displacement field and a velocity field. The constitutive equations and the applied algorithm are developed from the exact solution for a standard case. The standard case evolves from a very tall vertical plane strain silo containing material that flows at a constant speed. No horizontal displacements and velocities take place. No changes regarding the field values arise in the vertical direction and in time. Tension is not allowed at any point. Coulomb friction represents the effects of the vertical walls. The interaction between the flowing material and the walls is covered by a forced boundary condition resulting in an additional matrix for the solid component as well as for the liquid component. The resulting integral equations are designed to be solved directly. Three coefficients describe the properties of the granular material. They govern elastic solid behavior in combination with viscous liquid behavior.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@phdthesis{Roessler2006,
  author    = {R{\"o}ßler, Christiane},
  title     = {Hydratation, Fließf{\"a}higkeit und Festigkeitsentwicklung von Portlandzement - Einfluss von Fließmitteln, Alkalisulfaten und des Abbindereglers},
  doi       = {10.25643/bauhaus-universitaet.799},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20070206-8425},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2006},
  abstract  = {Eine zielf{\"u}hrende Anwendung von Zusatzmitteln bei der Ausf{\"u}hrung anspruchsvoller Betonbauten setzt einen hohen Kenntnisstand bez{\"u}glich der Wirkungsmechanismen und Interaktionen der einzelnen Betonkomponenten voraus. In der vorliegenden Arbeit wurden einige Aspekte der Zementhydratation in Abh{\"a}ngigkeit von der Fließmittelzugabe diskutiert. Im Ergebnis liefern die Teile eins und zwei der vorliegenden Arbeit einen Beitrag dazu, Ver{\"a}nderungen der Fließf{\"a}higkeit von Zementleim in Abh{\"a}ngigkeit der Zementhydratation und Fließmittelzugabe besser zu verstehen. Es konnte so z.B. gezeigt werden, dass Bildung langprismatischer Kristalle (z.B. Syngenit, Gips) die Fließf{\"a}higkeit von Zementleim und Beton vermindert. Infolge anhaltender Scherung von Zementleimen / Betonen mit langprismatischen Kristallen wird ein Zuwachs an Fließf{\"a}higkeit erzielt. Elektronenmikroskopische Untersuchungen zeigen, dass dies darauf zur{\"u}ckzuf{\"u}hren ist, dass die Kristalle in eine Vorzugsorientierung relativ zur Scherbewegung rotieren. Weiterhin wurde der Mechanismus einer so genannten Zement-Fließmittel-Inkompatibilit{\"a}t aufgezeigt. Durch diese Erweiterung des Kenntnisstandes zum Einfluss von Fließmitteln auf die Zementhydratation ist es m{\"o}glich der Zement-Fließmittel-Inkompatibilit{\"a}t durch gezielte Auswahl des Zementes vorzubeugen. Dabei ist besonders darauf zu achten, dass der Zement ein ausgewogenes Verh{\"a}ltnis an zur Reaktion zur Verf{\"u}gung stehendem C3A und Menge / L{\"o}slichkeit des Abbindereglers besitzt. Fließmittel ver{\"a}ndern nicht nur die Verarbeitungseigenschaften sondern auch die Festigkeit und Dauerhaftigkeit von Zementstein und Beton. Im dritten Teil der vorliegenden Arbeit wird daher der Einfluss der Fließmittel und deren verfl{\"u}ssigender Wirkung auf die Festigkeitsentwicklung von Zementstein und C3S untersucht. Es konnte gezeigt werden, dass durch die dispergierende Wirkung der Fließmittel auch ohne Verminderung des Wasserzementwertes, eine Verdichtung des Zementsteingef{\"u}ges erzielt werden kann. Es konnte weiterhin gezeigt werden, dass durch die Erh{\"o}hung der Partikelpackungsdichte am Anfang der Hydratation die Ausbildung der festigkeitsgebenden C-S-H Phasen ver{\"a}ndert wird. Ein dichteres Verwachsen dieser nanostrukturierten C-S-H Phasen erm{\"o}glicht einen zus{\"a}tzlichen Festigkeitszuwachs.},
  subject      = {Zement},
  language  = {de}
}
@inproceedings{ErikssonKettunen,
  author    = {Eriksson, Sirkka-Liisa and Kettunen, Jarkko},
  title     = {HYPERMONOGENIC POLYNOMIALS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2950},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29509},
  pages     = {22},
  abstract  = {It is well know that the power function is not monogenic. There are basically two ways to include the power function into the set of solutions: The hypermonogenic functions or holomorphic Cliffordian functions. L. Pernas has found out the dimension of the space of homogenous holomorphic Cliffordian polynomials of degree m, but his approach did not include a basis. It is known that the hypermonogenic functions are included in the space of holomorphic Cliffordian functions. As our main result we show that we can construct a basis for the right module of homogeneous holomorphic Cliffordian polynomials of degree m using hypermonogenic polynomials and their derivatives. To that end we first recall the function spaces of monogenic, hypermonogenic and holomorphic Cliffordian functions and give the results needed in the proof of our main theorem. We list some basic polynomials and their properties for the various function spaces. In particular, we consider recursive formulas, rules of differentiation and properties of linear independency for the polynomials.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{Ostrowski,
  author    = {Ostrowski, M.},
  title     = {INTEGRATED MATHEMATICAL MODELLING AS A BASIS FOR DECISION MAKING IN WATER MANAGEMENT},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2997},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29979},
  pages     = {9},
  abstract  = {Water resources development and management is a complex problem. It includes the design and operation of single system components, often as part of larger interrelated systems and usually on the basis of river basins. While several decades ago the dominant objective was the maximization of economic benefit, other objectives have evolved as part of the sustainable development envisaged. Today, planning and operation of larger water resources systems is practically impossible without adequate computer tools, normally being one or several models, increasingly combined with data bank management systems and multi criteria assessment procedures in decision support systems. The use of models in civil engineering already has a long history when structural engineering is considered. These design support models, however, must rather be seen as expert systems made to support the engineer with his daily work. They often have no direct link to stakeholders and the decision makers community. The scale of investigation is often much larger in water resources engineering than in structural engineering which is related to different stakeholders and decision making procedures. Still, several similarities are obvious which can be summarized as the search for a compromise solution on a complex, i.e. multiobjective and interdisciplinary decision problem. While in structural engineering e.g. aestetics, stability and energy consumption might be important evaluation criteria in addition to construction and maintenance cost other or additional criteria have to be considered in water resources planning such as political, environmental and social criteria. In this respect civil engineers tend to overemphasize technical criteria. For the future the existing expert systems should be embedded into an improved decision support shell, keeping in mind that decision makers are hardly interested in numerical modelling results. The paper will introduce into the problem and demonstrate the state of the art by means of an example.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}