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 - Aliazizi, Fereshteh A1 - Özsoylu, Dua A1 - Bakhshi Sichani, Soroush A1 - Khorshid, Mehran A1 - Glorieux, Christ A1 - Robbens, Johan A1 - Schöning, Michael Josef A1 - Wagner, Patrick T1 - Development and Calibration of a Microfluidic, Chip-Based Sensor System for Monitoring the Physical Properties of Water Samples in Aquacultures JF - Micromachines N2 - In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems. KW - chip-based sensor setup KW - aquaculture KW - microfluidics KW - impedance spectroscopy KW - thermometry KW - electrical conductivity of liquids Y1 - 2024 U6 - https://doi.org/10.3390/mi15060755 SN - 2072-666X N1 - This article belongs to the Special Issue "Multisensor Arrays" N1 - Corresponding author: Michael J. Schöning VL - 15 IS - 6 PB - MDPI CY - Basel ER - TY - JOUR A1 - Özsoylu, Dua A1 - Aliazizi, Fereshteh A1 - Wagner, Patrick A1 - Schöning, Michael Josef T1 - Template bacteria-free fabrication of surface imprinted polymer-based biosensor for E. coli detection using photolithographic mimics: Hacking bacterial adhesion JF - Biosensors and Bioelectronics N2 - As one class of molecular imprinted polymers (MIPs), surface imprinted polymer (SIP)-based biosensors show great potential in direct whole-bacteria detection. Micro-contact imprinting, that involves stamping the template bacteria immobilized on a substrate into a pre-polymerized polymer matrix, is the most straightforward and prominent method to obtain SIP-based biosensors. However, the major drawbacks of the method arise from the requirement for fresh template bacteria and often non-reproducible bacteria distribution on the stamp substrate. Herein, we developed a positive master stamp containing photolithographic mimics of the template bacteria (E. coli) enabling reproducible fabrication of biomimetic SIP-based biosensors without the need for the “real” bacteria cells. By using atomic force and scanning electron microscopy imaging techniques, respectively, the E. coli-capturing ability of the SIP samples was tested, and compared with non-imprinted polymer (NIP)-based samples and control SIP samples, in which the cavity geometry does not match with E. coli cells. It was revealed that the presence of the biomimetic E. coli imprints with a specifically designed geometry increases the sensor E. coli-capturing ability by an “imprinting factor” of about 3. These findings show the importance of geometry-guided physical recognition in bacterial detection using SIP-based biosensors. In addition, this imprinting strategy was employed to interdigitated electrodes and QCM (quartz crystal microbalance) chips. E. coli detection performance of the sensors was demonstrated with electrochemical impedance spectroscopy (EIS) and QCM measurements with dissipation monitoring technique (QCM-D). KW - Surface imprinted polymer KW - E. coli detection KW - Photolithographic mimics KW - Master stamp KW - Quartz crystal microbalance Y1 - 2024 U6 - https://doi.org/10.1016/j.bios.2024.116491 SN - 1873-4235 (eISSN) SN - 0956-5663 N1 - Corresponding author: Michael J. Schöning VL - 261 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Karschuck, Tobias A1 - Poghossian, Arshak A1 - Ser, Joey A1 - Tsokolakyan, Astghik A1 - Achtsnicht, Stefan A1 - Wagner, Patrick A1 - Schöning, Michael Josef T1 - Capacitive model of enzyme-modified field-effect biosensors: Impact of enzyme coverage JF - Sensors and Actuators B: Chemical N2 - Electrolyte-insulator-semiconductor capacitors (EISCAP) belong to field-effect sensors having an attractive transducer architecture for constructing various biochemical sensors. In this study, a capacitive model of enzyme-modified EISCAPs has been developed and the impact of the surface coverage of immobilized enzymes on its capacitance-voltage and constant-capacitance characteristics was studied theoretically and experimentally. The used multicell arrangement enables a multiplexed electrochemical characterization of up to sixteen EISCAPs. Different enzyme coverages have been achieved by means of parallel electrical connection of bare and enzyme-covered single EISCAPs in diverse combinations. As predicted by the model, with increasing the enzyme coverage, both the shift of capacitance-voltage curves and the amplitude of the constant-capacitance signal increase, resulting in an enhancement of analyte sensitivity of the EISCAP biosensor. In addition, the capability of the multicell arrangement with multi-enzyme covered EISCAPs for sequentially detecting multianalytes (penicillin and urea) utilizing the enzymes penicillinase and urease has been experimentally demonstrated and discussed. KW - Field-effect biosensor KW - Capacitive model KW - Enzyme coverage KW - Multianalyte detection KW - Penicillin Y1 - 2024 U6 - https://doi.org/10.1016/j.snb.2024.135530 SN - 0925-4005 (Print) SN - 1873-3077 (Online) N1 - Corresponding Author: Michael J. Schöning VL - 408 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pieronek, Lukas A1 - Kleefeld, Andreas T1 - On trajectories of complex-valued interior transmission eigenvalues JF - Inverse problems and imaging : IPI N2 - This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection. KW - Interior transmission problem KW - Eigenvalue trajectories KW - Complex-valued eigenvalues Y1 - 2024 U6 - https://doi.org/10.3934/ipi.2023041 SN - 1930-8337 (Print) SN - 1930-8345 (Online) VL - 18 IS - 2 SP - 480 EP - 516 PB - AIMS CY - Springfield, Mo ER - TY - JOUR A1 - Yoshinobu, Tatsuo A1 - Miyamoto, Ko-ichiro A1 - Wagner, Torsten A1 - Schöning, Michael Josef T1 - Field-effect sensors combined with the scanned light pulse technique: from artificial olfactory images to chemical imaging technologies JF - Chemosensors N2 - The artificial olfactory image was proposed by Lundström et al. in 1991 as a new strategy for an electronic nose system which generated a two-dimensional mapping to be interpreted as a fingerprint of the detected gas species. The potential distribution generated by the catalytic metals integrated into a semiconductor field-effect structure was read as a photocurrent signal generated by scanning light pulses. The impact of the proposed technology spread beyond gas sensing, inspiring the development of various imaging modalities based on the light addressing of field-effect structures to obtain spatial maps of pH distribution, ions, molecules, and impedance, and these modalities have been applied in both biological and non-biological systems. These light-addressing technologies have been further developed to realize the position control of a faradaic current on the electrode surface for localized electrochemical reactions and amperometric measurements, as well as the actuation of liquids in microfluidic devices. KW - visualization KW - light-addressing technologies KW - scanned light pulse technique KW - field-effect structure KW - MOS KW - metal-oxide-semiconductor structure KW - catalytic metal KW - electronic nose KW - gas sensor KW - artificial olfactory image Y1 - 2024 U6 - https://doi.org/10.3390/chemosensors12020020 SN - 2227-9040 N1 - This article belongs to the Special Issue "An Exciting Journey of Chemical Sensors and Biosensors: A Theme Issue in Honor of Professor Ingemar Lundström" Corresponding author: Tatsuo Yoshinobu, Michael J. Schöning VL - 12 IS - 2 PB - MDPI CY - Basel ER -