Zugl.: Mannheim, Univ., Diss., 2007.

Zugl.: Mannheim, Univ., Diss., 2007

Zeitgenössische Fertigungstechnik ist im Begriff, einen Einfluss auf die Architekturentwicklung auszuüben wie zuletzt in der Industrialisierung des 19. Jahrhunderts. Während neue computergestützte Möglichkeiten auf breiter Basis diskutiert und erprobt werden, bleiben ihre Wurzeln und ihr Verhältnis zu früheren Fertigungstechniken im Dunkeln. Christoph Schindler betrachtet Architektur aus der Perspektive der Fertigungstechnik. Sein Ziel ist es, die von aktueller Informationstechnik getriebene gegenwärtige Forschung im Bauwesen historisch zu kontextualisieren und als Teil einer kontinuierlichen Entwicklung zu identifizieren. Im Zentrum der Arbeit steht als These das Schema eines allgemeinen technikgeschichtlichen Periodisierungsmodells, das handwerkliche, industrielle und informationstechnische Fertigung zu integrieren versucht. Grundlage dieses Periodisierungsmodells ist das Verhältnis der drei Kategorien Stoff, Energie und Information in der jeweiligen fertigungstechnischen Periode. Die Stichhaltigkeit des Modells wird anhand der Geschichte des Holzbaus überprüft, da der Holzbau wie keine andere Konstruktionsweise die Beziehungen zwischen Fertigungstechnik und Bauen umfassender über einen vergleichbar langen Zeitraum illustriert. Es wird untersucht, ob das vorgeschlagene Modell sich anhand von historischen Fakten belegen lässt – wie grundlegende Veränderungen in der Fertigungstechnik die Holzverarbeitung beeinflusst und wie diese jeweils Konstruktion und Erscheinungsbild der Holzarchitektur geprägt haben. / Contemporary production technology is about to exert an influence on the development of architecture as fundamentally as experienced during Industrialization in the 19th century. While new computer-aided methods are widely discussed and applied, their roots and relation to previous production technology remain obscure. Christoph Schindler analyzes architecture from the perspective of production technology. It aims to contextualize contemporary research in the building industry—driven by information technology—and identify it as part of a continuous development in history of technology. The thesis is built around the scheme of a periodization model, which intends to integrate fabrication within manual, industrial and information technology. It is based on the relation between the three categories matter, energy, and information in each respective period. The validity of the model is proven with help of history of timber architecture, as no other construction method illustrates the relation between processing technology, fabrication methods and architecture more comprehensively over a comparable period of time. It will be studied whether the proposed model can be circumstantiated with historical facts— how constitutive changes in process technology influenced wood processing and how they respectively coined construction and appearance of timber architecture.

Zeitgenössische Fertigungstechnik ist im Begriff, einen Einfluss auf die Architekturentwicklung auszuüben wie zuletzt in der Industrialisierung des 19. Jahrhunderts. Während neue computergestützte Möglichkeiten auf breiter Basis diskutiert und erprobt werden, bleiben ihre Wurzeln und ihr Verhältnis zu früheren Fertigungstechniken im Dunkeln. Christoph Schindler betrachtet Architektur aus der Perspektive der Fertigungstechnik. Sein Ziel ist es, die von aktueller Informationstechnik getriebene gegenwärtige Forschung im Bauwesen historisch zu kontextualisieren und als Teil einer kontinuierlichen Entwicklung zu identifizieren. Im Zentrum der Arbeit steht als These das Schema eines allgemeinen technikgeschichtlichen Periodisierungsmodells, das handwerkliche, industrielle und informationstechnische Fertigung zu integrieren versucht. Grundlage dieses Periodisierungsmodells ist das Verhältnis der drei Kategorien Stoff, Energie und Information in der jeweiligen fertigungstechnischen Periode. Die Stichhaltigkeit des Modells wird anhand der Geschichte des Holzbaus überprüft, da der Holzbau wie keine andere Konstruktionsweise die Beziehungen zwischen Fertigungstechnik und Bauen umfassender über einen vergleichbar langen Zeitraum illustriert. Es wird untersucht, ob das vorgeschlagene Modell sich anhand von historischen Fakten belegen lässt – 
wie grundlegende Veränderungen in der Fertigungstechnik die Holzverarbeitung beeinflusst und wie diese jeweils Konstruktion und Erscheinungsbild der Holzarchitektur geprägt haben. / Contemporary production technology is about to exert an influence on the development of architecture as fundamentally as experienced during Industrialization in the 19th century. While new computer-aided methods are widely discussed and applied, their roots and relation to previous production technology remain obscure. Christoph Schindler analyzes architecture from the perspective of production technology. It aims to contextualize contemporary research in the building industry—driven by information technology—and identify it as part of a continuous development in history of technology. The thesis is built around the scheme of a periodization model, which intends to integrate fabrication within manual, industrial and information technology. It is based on the relation between the three categories matter, energy, and information in each respective period. The validity of the model is proven with help of history of timber architecture, as no other construction method illustrates the relation between processing technology, fabrication methods and architecture more comprehensively over a comparable period of time. It will be studied whether the proposed model can be circumstantiated with historical facts— how constitutive changes in process technology influenced wood processing and how they respectively coined construction and appearance of timber architecture.

We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier transform and that needs a computational complexity that is bounded from above by terms that are linear in the maximum of the number of input and output data up to some logarithmic factors is called fast Fourier transform. We call the fast Fourier transform stable if the Fourier matrix of the discrete Fourier transform has a condition number near one and the fast algorithm does not corrupt this theoretical stability. We suggest to use rank-1 lattices and a generalization as spatial discretizations in order to sample multivariate trigonometric polynomials and we develop construction methods in order to determine reconstructing sampling sets, i.e., sets of sampling nodes that allow for the unique, fast, and stable reconstruction of trigonometric polynomials. The methods for determining reconstructing rank-1 lattices are component{by{component constructions, similar to the seminal methods that are developed in the field of numerical integration. During this thesis we identify a component{by{component construction of reconstructing rank-1 lattices that allows for an estimate of the number of sampling nodes M |I|\le M\le \max\left(\frac{2}{3}|I|^2,\max\{3\|\mathbf{k}\|_\infty\colon\mathbf{k}\in I\}\right) that is sufficient in order to uniquely reconstruct each multivariate trigonometric polynomial with frequencies supported on the frequency index set I. We observe that the bounds on the number M only depends on the number of frequency indices contained in I and the expansion of I, but not on the spatial dimension d. Hence, rank-1 lattices are suitable spatial discretizations in arbitrarily high dimensional problems. Furthermore, we consider a generalization of the concept of rank-1 lattices, which we call generated sets. We use a quite different approach in order to determine suitable reconstructing generated sets. The corresponding construction method is based on a continuous optimization method. Besides the theoretical considerations, we focus on the practicability of the presented algorithms and illustrate the theoretical findings by means of several examples. In addition, we investigate the approximation properties of the considered sampling schemes. We apply the results to the most important structures of frequency indices in higher dimensions, so-called hyperbolic crosses and demonstrate the approximation properties by the means of several examples that include the solution of Poisson's equation as one representative of partial differential equations.

We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier transform and that needs a computational complexity that is bounded from above by terms that are linear in the maximum of the number of input and output data up to some logarithmic factors is called fast Fourier transform. We call the fast Fourier transform stable if the Fourier matrix of the discrete Fourier transform has a condition number near one and the fast algorithm does not corrupt this theoretical stability. We suggest to use rank-1 lattices and a generalization as spatial discretizations in order to sample multivariate trigonometric polynomials and we develop construction methods in order to determine reconstructing sampling sets, i.e., sets of sampling nodes that allow for the unique, fast, and stable reconstruction of trigonometric polynomials. The methods for determining reconstructing rank-1 lattices are component{by{component constructions, similar to the seminal methods that are developed in the field of numerical integration. During this thesis we identify a component{by{component construction of reconstructing rank-1 lattices that allows for an estimate of the number of sampling nodes M |I|\le M\le \max\left(\frac{2}{3}|I|^2,\max\{3\|\mathbf{k}\|_\infty\colon\mathbf{k}\in I\}\right) that is sufficient in order to uniquely reconstruct each multivariate trigonometric polynomial with frequencies supported on the frequency index set I. We observe that the bounds on the number M only depends on the number of frequency indices contained in I and the expansion of I, but not on the spatial dimension d. Hence, rank-1 lattices are suitable spatial discretizations in arbitrarily high dimensional problems. Furthermore, we consider a generalization of the concept of rank-1 lattices, which we call generated sets. We use a quite different approach in order to determine suitable reconstructing generated sets. The corresponding construction method is based on a continuous optimization method. Besides the theoretical considerations, we focus on the practicability of the presented algorithms and illustrate the theoretical findings by means of several examples. In addition, we investigate the approximation properties of the considered sampling schemes. We apply the results to the most important structures of frequency indices in higher dimensions, so-called hyperbolic crosses and demonstrate the approximation properties by the means of several examples that include the solution of Poisson's equation as one representative of partial differential equations.