Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method

Well-posedness and asymptotic behaviour for linear magneto-thermo-elasticity with second sound

We consider the Cauchy problem of magneto-thermo-elasticity with second sound in three space dimensions. After proving the existence of a unique solution, we use Fourier transform and multiplier methods to show polynomial decay rates for suitable initial data. We compare the qualitative and quantitative asymptotic behaviour of magneto-thermo-elasticity with second sound with that of the classical system.publishe

Model order reduction techniques for the optimal control of parabolic partial differential equations with control and state constraints

In this thesis linear-quadratic optimal control problems for dynamical systems modeled by parabolic partial differential equations with control and state constraints are observed. Different model order reduction techniques basing on a spectral method called proper orthogonal decomposition are analyzed and both a-priori and a-posteriori error bounds are developed to quantify the arising model reduction errors efficiently. Iterative solution techniques for the coupled nonlinear optimality equations are proposed and an associated convergence analysis is provided. The theoretical findings are visualized by numerical tests which illustrate both the advantages and limits of the introduced model reduction strategies.publishe

Die Gleichungen der Magneto-Thermo-Elastizität mit "second sound"

Wir betrachten das System der Magneto-Thermo-Elastizitätsgleichungen mit "second sound" im dreidimensionalen Raum. Zunächst wird das Cauchy-Problem aus den physikalischen Grundgleichungen der Elektrodynamik, der Thermodynamik und den Elastizitätsgesetzen hergeleitet. Mit Hilfe der Theorie der Operatorhalbgruppen wird die Existenz und Eindeutigkeit von Lösungen gezeigt, anschließend werden unter geeigneten Forderungen an die Anfangsdaten polynomiale Abklingraten nachgewiesen. Das Langzeitverhalten des Systems mit "second sound" wird mit dem des klassischen Systems verglichen

POD a-posteriori error analysis for optimal control Problems with mixed control-state constraints

In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These Problems arise when a Lavrentiev regularization is utilized for state constrained linear-quadratic optimal control problems. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. Numerical examples illustrate the theoretical results. In particular, the POD Galerkin scheme is applied to a problem with state constraints

Numerical Analysis of Optimality-System POD for Constrained Optimal Control

In this work linear-quadratic optimal control problems for parabolic equa- tions with control and state constraints are considered. Utilizing a Lavrentiev regu- larization we obtain a linear-quadratic optimal control problem with mixed control- state constraints. For the numerical solution a Galerkin discretization is applied uti- lizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, com- puted on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems

Managing the ear as a donor site for composite graft in nasal reconstruction : update on technical refinements and donor site morbidity in 110 cases

Reconstruction of multilayer defects of the lower nose, using composite grafts from the ear is a widespread technique. Little information exists about important aspects of managing the ear as a donor site for composite grafts. In a retrospective study, patient data were worked up concerning special preoperative planning features (donor site, recipient site), defect closure techniques, donor site morbidity, and esthetic and functional long-term results. One hundred ten composite grafts from the auricle were harvested for different defects at the lower nose. Skin and soft-tissue defect reconstruction at the auricle was carried out by tissue advancement in 43 cases or local flaps in 66 cases. Donor site morbidity was low (5 cases of delayed wound healing, 1 abscess). No flap necrosis occurred. Long-term follow-up (2-5 years) revealed no esthetic or functional impairments. Composite graft harvesting from the auricle is safe with minimal donor site morbidity, proper implementation assumed

Three-dimensional laser surface scanning in rhinosurgery

Objective outcome analysis of nasal surgery remains difficult. Recently, evaluation of nasal shape following rhinosurgery shifted from two-dimensional evaluation to more sophisticated three-dimensional (3D) analysis techniques, including stereophotogrammetry, computed tomography, and 3D laser scanning. This article explores the feasibility of using 3D laser surface scanners as a tool for preoperative planning and quality control in rhinosurgery