Universitätsbibliothek
Weimar Open Access

In this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. IGABEM is coupled with one of the gradient-free optimization methods, the Particle Swarm Optimization (PSO) for structural shape optimization problems. PSO is a straightforward method since it does not require any sensitivity analysis but it has some trade-offs with regard to the computational cost. Coupling IGA with optimization problems enables the NURBS basis functions to represent the three models: shape design, analysis and optimization models, by a definition of a set of control points to be the control variables and the optimization parameters as well which enables an easy transition between the three models. Acoustic shape optimization for various frequencies in different mediums is performed with PSO and the results are compared with the benchmark solutions from the literature for different dimensional problems proving the efficiency of the proposed approach with the following remarks: - In 2D problems, two BEM methods are used: the conventional isogeometric boundary element method (IGABEM) and the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves, where the results are generally in good agreement with the linterature with some computation advantage to XIBEM which allows coarser meshes. -In 3D axi-symmetric problems, the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models. - In fully 3D problems, a detailed comparison between two BEM methods: the conventional boundary integral equation (CBIE) and Burton-Miller (BM) is provided including the computational cost. The proposed models are enhanced with a modified collocation scheme with offsets to Greville abscissae to avoid placing collocation points at the corners. Placing collocation points on smooth surface enables accurate evaluation of normals for BM formulation in addition to straightforward prediction of jump-terms and avoids singularities in $\mathcal{O} (1/r)$ integrals eliminating the need for polar integration. Furthermore, no additional special treatment is required for the hyper-singular integral while collocating on highly distorted elements, such as those containing sphere poles. The obtained results indicate that, CBIE with PSO is a feasible alternative (except for a small number of fictitious frequencies) which is easier to implement. Furthermore, BM presents an outstanding treatment of the complicated geometry of mufflers with internal extended inlet/outlet tube as an interior 3D Helmholtz acoustic problem instead of using mixed or dual BEM.

In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.

Im Heft zum zehnjährigen Jubiläum von sub\urban mit dem Themenschwerpunkt „sub\x: Verortungen, Entortungen" veröffentlichen wir eine Debatte, die von den bisherigen in unserer Zeitschrift in dieser Rubrik geführten textlichen Diskussionen abweicht. Im Vorfeld der Planungen für unsere Jubiläumsausgabe haben wir die aktuellen Mitglieder unseres wissenschaftlichen Beirats darum gebeten, zwei grundlegende Fragen von kritischer Stadtforschung in kurzen Beiträgen zu diskutieren: Was ist Stadt? Was ist Kritik?

This article focuses on further developments of the background-oriented schlieren (BOS) technique to visualize convective indoor air flow, which is usually defined by very small density gradients. Since the light rays deflect when passing through fluids with different densities, BOS can detect the resulting refractive index gradients as integration along a line of sight. In this paper, the BOS technique is used to yield a two-dimensional visualization of small density gradients. The novelty of the described method is the implementation of a highly sensitive BOS setup to visualize the ascending thermal plume from a heated thermal manikin with temperature differences of minimum 1 K. To guarantee steady boundary conditions, the thermal manikin was seated in a climate laboratory. For the experimental investigations, a high-resolution DLSR camera was used capturing a large field of view with sufficient detail accuracy. Several parameters such as various backgrounds, focal lengths, room air temperatures, and distances between the object of investigation, camera, and structured background were tested to find the most suitable parameters to visualize convective indoor air flow. Besides these measurements, this paper presents the analyzing method using cross-correlation algorithms and finally the results of visualizing the convective indoor air flow with BOS. The highly sensitive BOS setup presented in this article complements the commonly used invasive methods that highly influence weak air flows.

The thesis addresses journalistic, administrative and judicial historical documentation to analyze the links between aridity and geographical imaginaries in the province of Catamarca (Argentina), from a historical point of view. The research aims to contribute to the understanding of the "non-hegemonic" versions of Modernity, its territoriality and the productions of geographic imaginaries that they involve. To provide a broad purpose, it raises as an object of study the ways in which "modern" practices, actors, links, discourses and expectations about the territory are mobilized when they are located in a space in "other" water conditions. those that are intended to "civilize" it. The general objective of the research is to analyze time-space controversies around water in the city and valley of Catamarca towards 19th and 20th centuries. The specific objectives derived are a) analyzing how various actors are related to waters behavior - in other words, the local water regime – in Catamarca and the meanings built around it. b) to analyze the controversies about the place of Catamarca and its water regime in the local and national geographic imaginary. c) analyze controversies in which the relationships between actors and materialities involved in modernization projects are put into discussion. These concerns by the experience of the actors and by the historical-spatial imagination of the territory, combined, led to the construction of an interdisciplinary methodology based on tools from anthropology, sociology, geography and history.