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 - TY - CHAP A1 - Kleefeld, Andreas ED - Constanda, Christian T1 - Numerical calculation of interior transmission eigenvalues with mixed boundary conditions T2 - Computational and Analytic Methods in Science and Engineering N2 - Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme. Y1 - 2020 SN - 978-3-030-48185-8 (Hardcover) U6 - https://doi.org/10.1007/978-3-030-48186-5_9 SP - 173 EP - 195 PB - Birkhäuser CY - Cham ER - TY - JOUR A1 - Asante-Asamani, E.O. A1 - Kleefeld, Andreas A1 - Wade, B.A. T1 - A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting JF - Journal of Computational Physics N2 - A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques. KW - Exponential time differencing KW - Real distinct pole KW - Dimensional splitting KW - Reaction-diffusion systems KW - Matrix exponential Y1 - 2020 U6 - https://doi.org/10.1016/j.jcp.2020.109490 SN - 0021-9991 N1 - Corresponding author: Andreas Kleefeld VL - 415 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Breuß, Michael A1 - Kleefeld, Andreas T1 - Implicit monotone difference methods for scalar conservation laws with source terms JF - Acta Mathematica Vietnamica N2 - In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests. KW - Entropy solution KW - Source term KW - Monotone methods KW - Implicit methods KW - Finite difference methods KW - Conservation laws Y1 - 2020 U6 - https://doi.org/10.1007/s40306-019-00354-1 SN - 2315-4144 N1 - Corresponding author: Andreas Kleefeld VL - 45 SP - 709 EP - 738 PB - Springer Singapore CY - Singapore ER - TY - JOUR A1 - Harris, Isaac A1 - Kleefeld, Andreas T1 - The inverse scattering problem for a conductive boundary condition and transmission eigenvalues JF - Applicable Analysis N2 - In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues. KW - Transmission eigenvalues KW - Conductive boundary condition KW - Inverse scattering Y1 - 2018 U6 - https://doi.org/10.1080/00036811.2018.1504028 SN - 1563-504X VL - 99 IS - 3 SP - 508 EP - 529 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Fiedler, Thomas M. A1 - Orzada, Stephan A1 - Flöser, Martina A1 - Rietsch, Stefan H. G. A1 - Quick, Harald H. A1 - Ladd, Mark E. A1 - Bitz, Andreas T1 - Performance analysis of integrated RF microstrip transmit antenna arrays with high channel count for body imaging at 7 T JF - NMR in Biomedicine N2 - The aim of the current study was to investigate the performance of integrated RF transmit arrays with high channel count consisting of meander microstrip antennas for body imaging at 7 T and to optimize the position and number of transmit ele- ments. RF simulations using multiring antenna arrays placed behind the bore liner were performed for realistic exposure conditions for body imaging. Simulations were performed for arrays with as few as eight elements and for arrays with high channel counts of up to 48 elements. The B1+ field was evaluated regarding the degrees of freedom for RF shimming in the abdomen. Worst-case specific absorption rate (SARwc ), SAR overestimation in the matrix compression, the number of virtual obser- vation points (VOPs) and SAR efficiency were evaluated. Constrained RF shimming was performed in differently oriented regions of interest in the body, and the devia- tion from a target B1+ field was evaluated. Results show that integrated multiring arrays are able to generate homogeneous B1+ field distributions for large FOVs, espe- cially for coronal/sagittal slices, and thus enable body imaging at 7 T with a clinical workflow; however, a low duty cycle or a high SAR is required to achieve homoge- neous B1+ distributions and to exploit the full potential. In conclusion, integrated arrays allow for high element counts that have high degrees of freedom for the pulse optimization but also produce high SARwc , which reduces the SAR accuracy in the VOP compression for low-SAR protocols, leading to a potential reduction in array performance. Smaller SAR overestimations can increase SAR accuracy, but lead to a high number of VOPs, which increases the computational cost for VOP evaluation and makes online SAR monitoring or pulse optimization challenging. Arrays with interleaved rings showed the best results in the study. KW - body imaging at UHF MRI KW - integrated transmit coil arrays KW - VOP compression Y1 - 2021 U6 - https://doi.org/10.1002/nbm.4515 SN - 0952-3480 (ISSN) SN - 1099-1492 (eISSN) VL - 34 IS - 7 PB - Wiley CY - Weinheim ER - TY - RPRT A1 - Hoffmann, Sarah A1 - Ullrich, Anna Valentine T1 - 30 Minuten FDM für HAW. Ein Informationsformat für Forschende an HAW in NRW N2 - Wie kann man das Thema Forschungsdatenmanagement (FDM) konkret und anwendbar für Forschende gestalten, die bisher noch wenig Kontakt damit hatten? Auf diese Frage gibt das Konzept „30 Minuten FDM für HAW. Ein Informationsformat für Forschende an HAW in NRW“ eine Antwort. Es entstand als Projektarbeit im Zertifikatskurs Forschungsdatenmanagement 2023/24 Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.12569282 ER - TY - RPRT A1 - Birmans, Katrin A1 - Schick, Elena A1 - Tambornino, Philipp A1 - Ullrich, Anna Valentine T1 - Ingenieurwissenschaften im Fokus: Zugänge zu einem effektiven Forschungsdatenmanagement an HAW N2 - Im Rahmen der Love Data Week vom 12. bis 16.02.2024 haben die BMBF-Projekte FDM2_TH_Koeln der TH Köln (FK 16FDFH105) und Persist@HAW der FH Aachen (FK 16FDFH129) am 15.02.2024 gemeinsam eine Online-Veranstaltung mit dem Titel „Ingenieurwissenschaften im Fokus: Zugänge zu einem effektiven Forschungsdatenmanagement an HAW“ angeboten. Diese richtete sich an Forschende aus den Ingenieurwissenschaften, die einen ersten Zugang zum Thema Forschungsdatenmanagement (FDM) suchen und erfahren möchten, welche speziellen Angebote für die Daten aus den Ingenieurwissenschaften existieren. In der Veranstaltung wurden wesentliche Aspekte des Forschungsdatenmanagements entlang des Datenlebenszyklus beleuchtet. Ziel war es, den Teilnehmenden praxisnahe Einblicke und Hilfestellungen zu einem effektiven Umgang mit Forschungsdaten an Hochschulen für Angewandte Wissenschaften (HAW) zu bieten. Durch Beispiele und konkrete Empfehlungen wurde das Thema zugänglich gemacht. Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.12545429 N1 - Die Originalpräsentation ist über Conceptboard einsehbar: https://app.conceptboard.com/board/c651-e781-dr9h-zfyu-gkq9 ER - TY - RPRT A1 - Birmans, Katrin A1 - Tambornino, Philipp A1 - Ullrich, Anna Valentine T1 - Bevor Sie Coscine nutzen - Handreichung für Forschende an HAW N2 - Um die Forschungsdatenmanagement-Plattform Coscine optimal für Forschungsprojekte nutzen zu können, ist es sinnvoll, einige Fragen im Vorhinein zu klären. So können aufwendige Änderungen der Datenverwaltung im Nachhinein vermieden werden. Hierzu bietet die Handreichung hilfreiche Leitfragen und Erläuterungen für Forschende und FDM-Service-Personal an HAW in NRW (DH.NRW-Hochschulen). FDM-Service-Mitarbeitende können die Handreichung in ihrer Beratung zu Coscine einsetzen und mit der Eingabemaske in der Kopfzeile des Dokuments auf ihre Hochschule anpassen. Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.12158546 N1 - Die Handreichung ist im Projekt Persist@HAW (FK: 16FDFH129), gefördert vom BMBF, entstanden. ER -