TY - JOUR A1 - Kleefeld, Andreas A1 - Pieronek, J. T1 - Elastic transmission eigenvalues and their computation via the method of fundamental solutions JF - Applicable Analysis N2 - A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach. KW - elastic scattering KW - method of fundamental solutions KW - Interior transmission eigenvalues Y1 - 2020 U6 - https://doi.org/10.1080/00036811.2020.1721473 SN - 1563-504X VL - 100 IS - 16 SP - 3445 EP - 3462 PB - Taylore & Francis CY - London ER - TY - CHAP A1 - Mayntz, Joscha A1 - Keimer, Jona A1 - Dahmann, Peter A1 - Hille, Sebastian A1 - Stumpf, Eike A1 - Fisher, Alex A1 - Dorrington, Graham T1 - Electrical Drive and Regeneration in General Aviation Flight with Propellers T2 - Deutscher Luft- und Raumfahrtkongress 2020 N2 - Electric flight has the potential for a more sustainable and energy-saving way of aviation compared to fossil fuel aviation. The electric motor can be used as a generator inflight to regenerate energy during descent. Three different approaches to regenerating with electric propeller powertrains are proposed in this paper. The powertrain is to be set up in a wind tunnel to determine the propeller efficiency in both working modes as well as the noise emissions. Furthermore, the planned flight tests are discussed. In preparation for these tests, a yaw stability analysis is performed with the result that the aeroplane is controllable during flight and in the most critical failure case. The paper shows the potential for inflight regeneration and addresses the research gaps in the dual role of electric powertrains for propulsion and regeneration of general aviation aircraft. KW - Propeller Aerodynamics KW - Flight Tests KW - Flight Mechanics KW - Electrical Flight KW - Inflight Regeneration, Recuperation Y1 - 2022 U6 - https://doi.org/10.25967/530100 N1 - Deutscher Luft- und Raumfahrtkongress 2020, 1. - 3. September 2020, Online PB - DGLR CY - Bonn ER - TY - GEN A1 - Mayntz, Joscha A1 - Keimer, Jona A1 - Tegtmeyer, Philipp A1 - Dahmann, Peter A1 - Hille, Sebastian A1 - Stumpf, Eike A1 - Fisher, Alex A1 - Dorrington, Graham T1 - Aerodynamic Investigation on Efficient Inflight Transition of a Propeller from Propulsion to Regeneration Mode T2 - AIAA SCITECH 2022 Forum N2 - This paper discusses a new way of inflight power regeneration for electric or hybrid-electric driven general aviation aircraft with one powertrain for both configurations. Three different approaches for the shift from propulsion to regeneration mode are analyzed. Numerical cal-culation and wind tunnel results are compared and show the highest regeneration potential for the "Windmill" approach, where the propeller blades are flipped, and rotation is reversed. A combination of all regeneration approaches for a realistic flight mission is discussed. Y1 - 2021 U6 - https://doi.org/10.2514/6.2022-0546 N1 - AIAA SCITECH 2022 Forum, January 3-7, 2022, San Diego, CA & Virtual PB - AIAA CY - Reston, Va. ER - TY - JOUR A1 - Saretzki, Charlotte A1 - Bergmann, Ole A1 - Dahmann, Peter A1 - Janser, Frank A1 - Keimer, Jona A1 - Machado, Patricia A1 - Morrison, Audry A1 - Page, Henry A1 - Pluta, Emil A1 - Stübing, Felix A1 - Küpper, Thomas T1 - Are small airplanes safe with regards to COVID-19 transmission? JF - Journal of Travel Medicine Y1 - 2021 U6 - https://doi.org/10.1093/jtm/taab105 SN - 1708-8305 VL - 28 IS - 7 PB - Oxford University Press CY - Oxford ER - TY - GEN A1 - Keimer, Jona A1 - Girbig, Leo A1 - Mayntz, Joscha A1 - Tegtmeyer, Philipp A1 - Wendland, Frederik A1 - Dahman, Peter A1 - Fisher, Alex A1 - Dorrington, Graham T1 - Flight mission optimization for eco-efficiency in consideration of electric regeneration and atmospheric conditions T2 - AIAA AVIATION 2022 Forum N2 - The development and operation of hybrid or purely electrically powered aircraft in regional air mobility is a significant challenge for the entire aviation sector. This technology is expected to lead to substantial advances in flight performance, energy efficiency, reliability, safety, noise reduction, and exhaust emissions. Nevertheless, any consumed energy results in heat or carbon dioxide emissions and limited electric energy storage capabilities suppress commercial use. Therefore, the significant challenges to achieving eco-efficient aviation are increased aircraft efficiency, the development of new energy storage technologies, and the optimization of flight operations. Two major approaches for higher eco-efficiency are identified: The first one, is to take horizontal and vertical atmospheric motion phenomena into account. Where, in particular, atmospheric waves hold exciting potential. The second one is the use of the regeneration ability of electric aircraft. The fusion of both strategies is expected to improve efficiency. The objective is to reduce energy consumption during flight while not neglecting commercial usability and convenient flight characteristics. Therefore, an optimized control problem based on a general aviation class aircraft has to be developed and validated by flight experiments. The formulated approach enables a development of detailed knowledge of the potential and limitations of optimizing flight missions, considering the capability of regeneration and atmospheric influences to increase efficiency and range. Y1 - 2022 U6 - https://doi.org/10.2514/6.2022-4118 N1 - AIAA AVIATION 2022 Forum, June 27-July 1, 2022 Chicago, IL & Virtual PB - AIAA CY - Reston, Va. ER - TY - CHAP A1 - Schult, Prince Garcia A1 - Losse, Ann-Kathrin A1 - Czarnecki, Christian A1 - Sultanow, Eldar T1 - Proposing a Framework to address the Sustainable Development Goals T2 - EnviroInfo 2023 N2 - Reducing poverty, protecting the planet, and improving life on earth for everyone are the essential goals of the "2030 Agenda for Sustainable Development"committed by the United Nations (UN). Achieving those goals will require technological innovation as well as their implementation in almost all areas of our business and day-to-day life. This paper proposes a high-level framework that collects and structures different uses cases addressing the goals defined by the UN. Hence, it contributes to the discussion by proposing technical innovations that can be used to achieve those goals. As an example, the goal "Climate Actionïs discussed in detail by describing use cases related to tackling biodiversity loss in order to conservate ecosystems. Y1 - 2023 SN - 978-3-88579-736-4 U6 - https://doi.org/10.18420/env2023-022 SN - 1617-5468 N1 - EnviroInfo 2023, 11. - 23. October 2023, Garching, Germany SP - 243 EP - 249 PB - GI - Gesellschaft für Informatik CY - Bonn ER - TY - CHAP A1 - Vladova, Gergana A1 - Ullrich, André A1 - Sultanow, Eldar A1 - Tobolla, Marinho A1 - Sebrak, Sebastian A1 - Czarnecki, Christian A1 - Brockmann, Carsten T1 - Visual analytics for knowledge management T2 - INFORMATIK 2023 - Designing Futures: Zukünfte gestalten N2 - The management of knowledge in organizations considers both established long-term processes and cooperation in agile project teams. Since knowledge can be both tacit and explicit, its transfer from the individual to the organizational knowledge base poses a challenge in organizations. This challenge increases when the fluctuation of knowledge carriers is exceptionally high. Especially in large projects in which external consultants are involved, there is a risk that critical, company-relevant knowledge generated in the project will leave the company with the external knowledge carrier and thus be lost. In this paper, we show the advantages of an early warning system for knowledge management to avoid this loss. In particular, the potential of visual analytics in the context of knowledge management systems is presented and discussed. We present a project for the development of a business-critical software system and discuss the first implementations and results. Y1 - 2023 SN - 978-3-88579-731-9 U6 - https://doi.org/10.18420/inf2023_187 SN - 1617-5468 N1 - INFORMATIK 2023, 26. - 29. September 2023, Berlin SP - 1851 EP - 1870 PB - GI - Gesellschaft für Informatik CY - Bonn ER - TY - JOUR A1 - Bung, Daniel Bernhard T1 - Extreme flooding in Western Germany: some thoughts on hazards, return periods and risk JF - Hydrolink N2 - The low-pressure system Bernd involved extreme rainfalls in the Western part of Germany in July 2021, resulting in major floods, severe damages and a tremendous number of casualties. Such extreme events are rare and full flood protection can never be ensured with reasonable financial means. But still, this event must be starting point to reconsider current design concepts. This article aims at sharing some thoughts on potential hazards, the selection of return periods and remaining risk with the focus on Germany. Y1 - 2021 IS - 4 SP - 108 EP - 113 PB - International Association for Hydro-Environment Engineering and Research (IAHR) CY - Madrid ER - TY - CHAP A1 - Abele, Daniel A1 - Kleefeld, Andreas ED - Constanda, Christian T1 - New Numerical Results for the Optimization of Neumann Eigenvalues T2 - Computational and Analytic Methods in Science and Engineering N2 - We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues. Y1 - 2020 SN - 978-3-030-48185-8 (Print) SN - 978-3-030-48186-5 (Online) U6 - https://doi.org/10.1007/978-3-030-48186-5_1 SP - 1 EP - 20 PB - Birkhäuser CY - Cham ER - TY - CHAP A1 - Pieronek, Lukas A1 - Kleefeld, Andreas ED - Constanda, Christian ED - Harris, Paul T1 - The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media T2 - Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations N2 - The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach. Y1 - 2019 SN - 978-3-030-16077-7 U6 - https://doi.org/10.1007/978-3-030-16077-7_28 SP - 353 EP - 365 PB - Birkhäuser CY - Cham ER - TY - CHAP A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin ED - Brunetti, Sara ED - Frosini, Andrea ED - Rinaldi, Simone T1 - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation T2 - Discrete Geometry and Mathematical Morphology N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. Y1 - 2024 SN - 978-3-031-57793-2 U6 - https://doi.org/10.1007/978-3-031-57793-2_25 N1 - Third International Joint Conference, DGMM 2024, Florence, Italy, April 15–18, 2024 SP - 325 EP - 337 PB - Springer CY - Cham ER - TY - JOUR A1 - Ayala, Rafael Ceja A1 - Harris, Isaac A1 - Kleefeld, Andreas T1 - Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary JF - Inverse Problems and Imaging N2 - In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method. Y1 - 2024 U6 - https://doi.org/10.3934/ipi.2023051 SN - 1930-8337 SN - 1930-8345 (eISSN) VL - 18 IS - 3 SP - 708 EP - 729 PB - AIMS CY - Springfield ER - TY - JOUR A1 - Clausnitzer, Julian A1 - Kleefeld, Andreas T1 - A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a C² boundary JF - Discrete and Continuous Dynamical Systems - Series B N2 - We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach. KW - Nonlinear eigenvalue problems KW - Boundary integral equations, KW - Exponential Euler scheme, KW - Parabolic SPDEs Y1 - 2024 U6 - https://doi.org/10.3934/dcdsb.2023148 SN - 1531-3492 SN - 1553-524X (eISSN) VL - 29 IS - 4 SP - 1624 EP - 1651 PB - AIMS CY - Springfield ER - TY - JOUR A1 - Harris, Isaac A1 - Kleefeld, Andreas T1 - Analysis and computation of the transmission eigenvalues with a conductive boundary condition JF - Applicable Analysis N2 - We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown. KW - Boundary integral equations KW - Inverse spectral problem KW - Conductive boundary condition KW - Transmission eigenvalues Y1 - 2020 U6 - https://doi.org/10.1080/00036811.2020.1789598 SN - 1563-504X VL - 101 IS - 6 SP - 1880 EP - 1895 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Chwallek, Constanze A1 - Nawrath, Lara A1 - Krastina, Anzelika A1 - Bruksle, Ieva T1 - Supportive research on sustainable entrepreneurship and business practices JF - SECA Sustainable Entrepreneurship for Climate Action Y1 - 2024 SN - 978-952-316-514-4 (pdf) SN - 2954-1654 (on-line publication) IS - 3 PB - Lapland University of Applied Sciences Ltd CY - Rovaniemi ER - TY - CHAP A1 - Burgeth, Bernhard A1 - Kleefeld, Andreas A1 - Zhang, Eugene A1 - Zhang, Yue ED - Baudrier, Étienne ED - Naegel, Benoît ED - Krähenbühl, Adrien ED - Tajine, Mohamed T1 - Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification T2 - Discrete Geometry and Mathematical Morphology N2 - Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information. Y1 - 2022 SN - 978-3-031-19897-7 U6 - https://doi.org/10.1007/978-3-031-19897-7_5 N1 - Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022 N1 - Corresponding author: Andreas Kleefeld SP - 48 EP - 59 PB - Springer CY - Cham ER - TY - JOUR A1 - Kleefeld, Andreas A1 - Zimmermann, M. ED - Constanda, Christian ED - Bodmann, Bardo E.J. ED - Harris, Paul J. T1 - Computing Elastic Interior Transmission Eigenvalues JF - Integral Methods in Science and Engineering N2 - An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains. Y1 - 2022 SN - 978-3-031-07171-3 U6 - https://doi.org/10.1007/978-3-031-07171-3_10 N1 - Corresponding author: Andreas Kleefeld SP - 139 EP - 155 PB - Birkhäuser CY - Cham ER - TY - GEN A1 - Burgeth, Bernhard A1 - Kleefeld, Andreas A1 - Naegel, Benoît A1 - Perret, Benjamin T1 - Editorial — Special Issue: ISMM 2019 T2 - Mathematical Morphology - Theory and Applications N2 - This editorial presents the Special Issue dedicated to the conference ISMM 2019 and summarizes the articles published in this Special Issue. Y1 - 2020 U6 - https://doi.org/10.1515/mathm-2020-0200 SN - 2353-3390 VL - 4 IS - 1 SP - 159 EP - 161 PB - De Gruyter CY - Warschau ER - TY - JOUR A1 - Kleefeld, Andreas T1 - The hot spots conjecture can be false: some numerical examples JF - Advances in Computational Mathematics N2 - The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well. KW - Numerics KW - Boundary integral equations KW - Potential theory KW - Helmholtz equation KW - Interior Neumann eigenvalues Y1 - 2021 U6 - https://doi.org/10.1007/s10444-021-09911-5 SN - 1019-7168 VL - 47 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Martín-Vaquero, J. A1 - Kleefeld, Andreas T1 - Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes JF - Journal of Computational Physics N2 - There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost. Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different. KW - Multi-dimensional partial differential equations KW - Higher-order codes KW - Nonlinear PDEs Y1 - 2020 U6 - https://doi.org/10.1016/j.jcp.2020.109771 SN - 0021-9991 IS - 423 PB - Elsevier CY - Amsterdam ER -