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 - 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 - Simsek, Beril A1 - Krause, Hans-Joachim A1 - Engelmann, Ulrich M. ED - Digel, Ilya ED - Staat, Manfred ED - Trzewik, Jürgen ED - Sielemann, Stefanie ED - Erni, Daniel ED - Zylka, Waldemar T1 - Magnetic biosensing with magnetic nanoparticles: Simulative approach to predict signal intensity in frequency mixing magnetic detection T2 - YRA MedTech Symposium (2024) N2 - Magnetic nanoparticles (MNP) are investigated with great interest for biomedical applications in diagnostics (e.g. imaging: magnetic particle imaging (MPI)), therapeutics (e.g. hyperthermia: magnetic fluid hyperthermia (MFH)) and multi-purpose biosensing (e.g. magnetic immunoassays (MIA)). What all of these applications have in common is that they are based on the unique magnetic relaxation mechanisms of MNP in an alternating magnetic field (AMF). While MFH and MPI are currently the most prominent examples of biomedical applications, here we present results on the relatively new biosensing application of frequency mixing magnetic detection (FMMD) from a simulation perspective. In general, we ask how the key parameters of MNP (core size and magnetic anisotropy) affect the FMMD signal: by varying the core size, we investigate the effect of the magnetic volume per MNP; and by changing the effective magnetic anisotropy, we study the MNPs’ flexibility to leave its preferred magnetization direction. From this, we predict the most effective combination of MNP core size and magnetic anisotropy for maximum signal generation. Y1 - 2024 SN - 978-3-940402-65-3 U6 - https://doi.org/10.17185/duepublico/81475 N1 - 4th YRA MedTech Symposium, February 1, 2024. FH Aachen, Campus Jülich SP - 27 EP - 28 PB - Universität Duisburg-Essen CY - Duisburg 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 - BOOK A1 - Laack, Walter van T1 - Schnittstelle Tod: Was lernen wir durch Corona über Leben und Tod? Y1 - 2022 SN - 978-3-936624-53-3 N1 - Siebter Tagungsband aus der Buchreihe “Schnittstelle Tod” PB - van Laack GmbH CY - Aachen ER - TY - JOUR A1 - Röthenbacher, Annika A1 - Cesari, Matteo A1 - Doppler, Christopher E.J. A1 - Okkels, Niels A1 - Willemsen, Nele A1 - Sembowski, Nora A1 - Seger, Aline A1 - Lindner, Marie A1 - Brune, Corinna A1 - Stefani, Ambra A1 - Högl, Birgit A1 - Bialonski, Stephan A1 - Borghammer, Per A1 - Fink, Gereon R. A1 - Schober, Martin A1 - Sommerauer, Michael T1 - RBDtector: an open-source software to detect REM sleep without atonia according to visual scoring criteria JF - Scientific Reports N2 - REM sleep without atonia (RSWA) is a key feature for the diagnosis of rapid eye movement (REM) sleep behaviour disorder (RBD). We introduce RBDtector, a novel open-source software to score RSWA according to established SINBAR visual scoring criteria. We assessed muscle activity of the mentalis, flexor digitorum superficialis (FDS), and anterior tibialis (AT) muscles. RSWA was scored manually as tonic, phasic, and any activity by human scorers as well as using RBDtector in 20 subjects. Subsequently, 174 subjects (72 without RBD and 102 with RBD) were analysed with RBDtector to show the algorithm’s applicability. We additionally compared RBDtector estimates to a previously published dataset. RBDtector showed robust conformity with human scorings. The highest congruency was achieved for phasic and any activity of the FDS. Combining mentalis any and FDS any, RBDtector identified RBD subjects with 100% specificity and 96% sensitivity applying a cut-off of 20.6%. Comparable performance was obtained without manual artefact removal. RBD subjects also showed muscle bouts of higher amplitude and longer duration. RBDtector provides estimates of tonic, phasic, and any activity comparable to human scorings. RBDtector, which is freely available, can help identify RBD subjects and provides reliable RSWA metrics. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-25163-9 SN - 2045-2322 VL - 12 IS - Article number: 20886 SP - 1 EP - 14 PB - Springer Nature CY - London ER - TY - CHAP A1 - Engelmann, Ulrich M. A1 - Baumann, Martin ED - Herbig, Nicola ED - Poppelreuter, Stefan T1 - Moderationsexpertise für QMBs – die Methoden T2 - Qualitätsmanagement im Gesundheitswesen N2 - Damit Sie als Moderator effektiv und professionell moderieren können, sollten Sie die entsprechenden Methoden kennen. Mit den richtigen Methoden können Sie Diskussionen leiten, Konflikte lösen, die Teilnehmer motivieren und dafür sorgen, dass die Ziele der Veranstaltung erreicht werden. Außerdem helfen sie Ihnen, eine positive Atmosphäre zu schaffen und das Interesse der Teilnehmer zu halten. In diesem zweiten Beitrag der mehrteiligen Serie lernen Sie die grundsätzlichen Methoden kennen, um erfolgreiche Teamsitzungen, Arbeitsgruppentreffen, Kick-offs und Meetings durchzuführen. Y1 - 2023 SN - 978-3-8249-0714-4 SP - Kapitel 10815 PB - TÜV-Verlag CY - Köln ET - 60. Update ER - TY - JOUR A1 - Gaigall, Daniel T1 - Rothman–Woodroofe symmetry test statistic revisited JF - Computational Statistics & Data Analysis N2 - The Rothman–Woodroofe symmetry test statistic is revisited on the basis of independent but not necessarily identically distributed random variables. The distribution-freeness if the underlying distributions are all symmetric and continuous is obtained. The results are applied for testing symmetry in a meta-analysis random effects model. The consistency of the procedure is discussed in this situation as well. A comparison with an alternative proposal from the literature is conducted via simulations. Real data are analyzed to demonstrate how the new approach works in practice. Y1 - 2020 U6 - https://doi.org/10.1016/j.csda.2019.106837 SN - 0167-9473 VL - 2020 IS - 142 SP - Artikel 106837 PB - Elsevier CY - Amsterdam ER - TY - CHAP A1 - de Honde, Lukas A1 - Porst, Dariusz A1 - Digel, Ilya ED - Fischerauer, Alice T1 - A randomized, observational thermographic study of the neck region before and after a physiotherapeutic intervention T2 - 2nd YRA MedTech Symposium 2017 : June 8th - 9th / 2017 / Hochschule Ruhr-West Y1 - 2017 SN - 978-3-9814801-9-1 U6 - https://doi.org/10.17185/duepublico/43984 N1 - A young researchers track of the 7th IEEE Workshop & SENSORICA 2017 SP - 122 EP - 123 PB - Universität Duisburg-Essen CY - Duisburg 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 -