@article{KleefeldPieronek2020,
  author    = {Kleefeld, Andreas and Pieronek, J.},
  title     = {Elastic transmission eigenvalues and their computation via the method of fundamental solutions},
  series = {Applicable Analysis},
  volume    = {100},
  journal   = {Applicable Analysis},
  number    = {16},
  publisher = {Taylore \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2020.1721473},
  pages     = {3445 -- 3462},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@incollection{AbeleKleefeld2020,
  author    = {Abele, Daniel and Kleefeld, Andreas},
  title     = {New Numerical Results for the Optimization of Neumann Eigenvalues},
  series = {Computational and Analytic Methods in Science and Engineering},
  booktitle = {Computational and Analytic Methods in Science and Engineering},
  editor    = {Constanda, Christian},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-48185-8 (Print)},
  doi       = {10.1007/978-3-030-48186-5_1},
  pages     = {1 -- 20},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@misc{BurgethKleefeldNaegeletal.2020,
  author    = {Burgeth, Bernhard and Kleefeld, Andreas and Naegel, Beno{\^i}t and Perret, Benjamin},
  title     = {Editorial — Special Issue: ISMM 2019},
  series = {Mathematical Morphology - Theory and Applications},
  volume    = {4},
  journal   = {Mathematical Morphology - Theory and Applications},
  number    = {1},
  publisher = {De Gruyter},
  address   = {Warschau},
  issn      = {2353-3390},
  doi       = {10.1515/mathm-2020-0200},
  pages     = {159 -- 161},
  year      = {2020},
  abstract  = {This editorial presents the Special Issue dedicated to the conference ISMM 2019 and summarizes the articles published in this Special Issue.},
  language  = {en}
}
@article{MartinVaqueroKleefeld2020,
  author    = {Mart{\´i}n-Vaquero, J. and Kleefeld, Andreas},
  title     = {Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes},
  series = {Journal of Computational Physics},
  journal   = {Journal of Computational Physics},
  number    = {423},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109771},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@incollection{Kleefeld2020,
  author    = {Kleefeld, Andreas},
  title     = {Numerical calculation of interior transmission eigenvalues with mixed boundary conditions},
  series = {Computational and Analytic Methods in Science and Engineering},
  booktitle = {Computational and Analytic Methods in Science and Engineering},
  editor    = {Constanda, Christian},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-48185-8 (Hardcover)},
  doi       = {10.1007/978-3-030-48186-5_9},
  pages     = {173 -- 195},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{AsanteAsamaniKleefeldWade2020,
  author    = {Asante-Asamani, E.O. and Kleefeld, Andreas and Wade, B.A.},
  title     = {A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting},
  series = {Journal of Computational Physics},
  volume    = {415},
  journal   = {Journal of Computational Physics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109490},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{BreussKleefeld2020,
  author    = {Breuß, Michael and Kleefeld, Andreas},
  title     = {Implicit monotone difference methods for scalar conservation laws with source terms},
  series = {Acta Mathematica Vietnamica},
  volume    = {45},
  journal   = {Acta Mathematica Vietnamica},
  publisher = {Springer Singapore},
  address   = {Singapore},
  issn      = {2315-4144},
  doi       = {10.1007/s40306-019-00354-1},
  pages     = {709 -- 738},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{KetelhutBrueggeGoelletal.2020,
  author    = {Ketelhut, Maike and Br{\"u}gge, G. M. and G{\"o}ll, Fabian and Braunstein, Bjoern and Albracht, Kirsten and Abel, Dirk},
  title     = {Adaptive iterative learning control of an industrial robot during neuromuscular training},
  series = {IFAC PapersOnLine},
  volume    = {53},
  journal   = {IFAC PapersOnLine},
  number    = {2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {2405-8963},
  doi       = {10.1016/j.ifacol.2020.12.741},
  pages     = {16468 -- 16475},
  year      = {2020},
  abstract  = {To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.},
  language  = {en}
}
@phdthesis{Achtsnicht2020,
  author    = {Achtsnicht, Stefan},
  title     = {Multiplex-Magnetdetektion von superparamagnetischen Beads zur Identifizierung von Trinkwasserkontaminationen},
  doi       = {10.18154/RWTH-2020-12052},
  pages     = {144 Seiten},
  year      = {2020},
  abstract  = {Die qualitative und quantitative Detektion von Zielsubstanzen innerhalb einer w{\"a}ssrigen Probe ist f{\"u}r viele Fragestellungen von Interesse, etwa bei der Detektion von Kontaminationen in Trinkwasser in Krisensituationen. Hierbei ist es nicht nur wichtig, dass Pathogene m{\"o}glichst sensitiv detektiert werden k{\"o}nnen, sondern auch, dass die Analyse schnell erfolgt, um Betroffenen im Katastrophenfall z{\"u}gig sicheres Trinkwasser zu Verf{\"u}gung stellen zu k{\"o}nnen. Da bei einem solchen Szenario nicht von einer in der N{\"a}he befindlichen funktionierenden Laborinfrastruktur ausgegangen werden kann, ist es wichtig, dass die Messung direkt vor Ort erfolgen kann. Im Rahmen dieser Arbeit wurde untersucht, ob eine derartige Schnellanalytik mithilfe von superparamagnetischen Beads (MBs) und der magnetischen Frequenzmischtechnik m{\"o}glich ist. Dabei werden die MBs mit Hilfe von prim{\"a}ren Antik{\"o}rpern an die Zielsubstanz gebunden und mit sekund{\"a}ren Antik{\"o}rpern an die Poren-Oberfl{\"a}che eines Polyethylen-Filters fixiert (Sandwich-Immunoassay). So kann die Quantifizierung der Zielsubstanz auf eine magnetische Messung der immobilisierten MB-Marker zur{\"u}ckgef{\"u}hrt werden. Die magnetische Frequenzmischtechnik basiert auf der Anregung der Probe mit Magnetfeldern zweier verschiedener Frequenzen. Die durch die nichtlineare Magnetisierungsform der superparamagnetischen MBs entstehenden Mischfrequenzen werden typischerweise mithilfe einer zweistufigen Lock-in-Detektion analysiert (analoge Demodulation), die in einem Magnetreader als Handheldger{\"a}t realisiert wurde. Zus{\"a}tzlich zu dieser Technik wurde das Prinzip der direkten Digitalisierung des gesamten Antwortsignals mit anschließender Fourier-Analyse der erzeugten Mischfrequenzen experimentell umgesetzt, um die Amplituden und Phasen mehrerer Mischfrequenzen simultan zu erfassen. Eine M{\"o}glichkeit zur Sensitivit{\"a}tssteigerung ist die magnetische Aufkonzentration, indem vor der magnetischen Analyse eine Separation der MBs aus einem gr{\"o}ßeren Probenvolumen mittels magnetischem Feldgradienten durchgef{\"u}hrt wird. Zur Charakterisierung verschiedener kommerzieller MBs hinsichtlich ihrer magnetischen Separierbarkeit wurde ein Aufbau zur Messung ihrer magnetophoretischen Beweglichkeiten realisiert und ihre Geschwindigkeiten im Gradientenfeld mikroskopisch gemessen.Da eine Probe oftmals nicht nur auf eine einzige Zielsubstanz, sondern simultan auf mehrere verschiedene Pathogene hin untersucht werden soll, wurden verschiedene Ans{\"a}tze entwickelt und getestet, die einen solchen multiparametrischen magnetischen Immunoassay erm{\"o}glichen. Einerseits wurde eine r{\"a}umliche Separation der Bindungsbereiche f{\"u}r verschiedene Zielsubstanzen realisiert, die sequentiell ausgewertet werden k{\"o}nnen. Andererseits wurde die Unterscheidung von verschiedenen Zielsubstanzen anhand der Charakteristika der an sie gebundenen, verschieden funktionalisierten MB-Typen untersucht. F{\"u}r eine solche Unterscheidung wurde zum einen die Anregefrequenz der magnetischen Frequenzmischtechnik w{\"a}hrend einer Messung variiert. Damit konnte gezeigt werden, dass sich verschiedene MB-Sorten anhand der Phase ihrer Frequenzmischsignale voneinander unterscheiden lassen. Weiterhin wurde gezeigt, dass sich der Signalverlauf einer bin{\"a}ren Mischung zweier verschiedener MB-Typen als gradueller {\"U}bergang der Verl{\"a}ufe der beiden reinen MB-L{\"o}sungen ergibt. Eine weitere Analysemethode f{\"u}r einen multiparametrischen Immunoassay besteht darin, ein zus{\"a}tzliches einstellbares statisches magnetisches Offsetfeld zu verwenden. Hierf{\"u}r wurden mehrere Aufbauten auf Basis von Permanent- und Elektromagneten simuliert, konstruiert und charakterisiert. Mithilfe von Simulationen konnte gezeigt werden, dass eine auf diesem Verfahren beruhende Unterscheidung f{\"u}r MBs mit unterschiedlichen magnetischen Partikelmomenten m{\"o}glich ist. Als direkte Anwendung des hier entwickelten Magnetreaders in Zusammenspiel mit der digitalen Demodulation wurde ein magnetischer Assay gegen die B-Untereinheit des Choleratoxins in Trinkwasser mit einem niedrigen Detektionslimit von 0,2 ng/ml demonstriert.},
  language  = {de}
}
@article{Gaigall2020,
  author    = {Gaigall, Daniel},
  title     = {Rothman-Woodroofe symmetry test statistic revisited},
  series = {Computational Statistics \& Data Analysis},
  volume    = {2020},
  journal   = {Computational Statistics \& Data Analysis},
  number    = {142},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-9473},
  doi       = {10.1016/j.csda.2019.106837},
  pages     = {Artikel 106837},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}