Publications

Monographs

  • U. Wilbrandt, Stokes--Darcy Equations -- Analytic and Numerical Analysis, D. Bresch, V. John, M. Hieber, I. Kukavica, J. Robinson, Y. Shibata, eds., Lecture Notes in Mathematical Fluid Mechanics, Birkhäuser, Basel, 2019, 212 pages, (Monograph Published), DOI 10.1007/978-3-030-02904-3 .

  • V.A. Garanzha, L. Kamenski, H. Si, eds., Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, Celebrating the 150th Anniversary of G.F. Voronoi, Moscow, Russia, December 2018, 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, 319 pages, (Collection Published), DOI 10.1007/978-3-030-23436-2 .

Articles in Refereed Journals

  • N. Alia, M. Pylvänäinen, V.-V. Visuri, V. John, S. Ollila, Vibrations of a laboratory-scale gas-stirred ladle with two eccentric nozzles and multiple sensors, Journal of Iron and Steel Research, International, 26 (2019), pp. 1031--1040, DOI 10.1007/s42243-019-00241-x .

  • A. Stephan, H. Stephan, Memory equations as reduced Markov processes, Discrete and Continuous Dynamical Systems, 39 (2019), pp. 2133--2155, DOI 10.3934/dcds.2019089 .
    Abstract
    A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along one-way loops. Typically, the arising Markov process does not have the detailed balance property. The method leads to a more realisitc modeling of memory equations. Moreover, it carries over the large number of investigation tools for Markov processes to memory equations, like the calculation of the equilibrium state, the asymptotic behavior and so on. The method can be used for an approximative solution of some degenerate memory equations like delay differential equations.

  • P. Vágner, C. Guhlke, V. Miloš, R. Müller, J. Fuhrmann, A continuum model for yttria-stabilised zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions, Journal of Solid State Electrochemistry, 23 (2019), pp. 2907--2926, DOI 10.1007/s10008-019-04356-9 .
    Abstract
    A continuum model for yttria-stabilised zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to i) modeling of the YSZ-metal-gas triple phase boundary, ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations.
    The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

  • C. Bartsch, V. Wiedmeyer, Z. Lakdawala, R.I.A. Patterson, A. Voigt, K. Sundmacher, V. John, Stochastic-deterministic population balance modeling and simulation of a fluidized bed crystallizer experiment, Chemical Engineering Sciences, 208 (2019), 115102, DOI 10.1016/j.ces.2019.07.020 .

  • N.R. Gauger, A. Linke, P. Schroeder, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, SMAI Journal of Computational Mathematics, 5 (2019), pp. 89--129.
    Abstract
    Recently, high-order space discretisations were proposed for the numerical simulation of the incompressible Navier--Stokes equations at high Reynolds numbers, even for complicated domains from simulation practice. Although the overall spatial approximation order of the algorithms depends on the approximation quality of the boundary (often not better than third order), competitively accurate and efficient results were reported. In this contribution, first, a possible explanation for this somewhat surprising result is proposed: the velocity error of high-order space discretisations is more robust against quantitatively large and complicated pressure fields than low-order methods. Second, it is demonstrated that novel pressure-robust methods are significantly more accurate than comparable classical, non-pressure-robust space discretisations, whenever the quadratic, nonlinear convection term is a nontrivial gradient field like in certain generalised Beltrami flows at high Reynolds number. Then, pressure-robust methods even allow to halve the (formal) approximation order without compromising the accuracy. Third, classical high-order space discretisations are outperformed by pressure-robust methods whenever the boundary is not approximated with high-order accuracy. This improved accuracy of (low-order) pressure-robust mixed methods is explained in terms of a Helmholtz--Hodge projector, which cancels out the nonlinear convection term in any generalised Beltrami flow, since it is a gradient field. The numerical results are illustrated by a novel numerical analysis for pressure-robust and classical space discretisations. Further, the relevance of these results is discussed for flows that are not of Beltrami type.

  • A. Jha, V. John, A study of solvers for nonlinear AFC discretizations of convection-diffusion equations, Computational & Applied Mathematics, 78 (2019), pp. 3117--3138, DOI 10.1016/j.camwa.2019.04.020 .

  • V. Klika , M. Pavelka , P. Vágner, M. Grmela, Dynamic maximum entropy reduction, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 21 (2019), pp. 1--27.

  • P.L. Lederer, Ch. Merdon, J. Schöberl, Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods, Journal of Numerical Mathematics, 142 (2019), pp. 713--748.
    Abstract
    Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in pressure-independent velocity error estimates which are robust with respect to small viscosities. In this paper we develop a posteriori error control which reflects this robustness.

  • L.O. Müller, A. Caiazzo, P.J. Blanco, Reduced-order unscented Kalman filter with observations in the frequency domain: Application to computational hemodynamics, IEEE Transactions on Biomedical Engineering, 66 (2019), pp. 1269--1276, DOI 10.1109/TBME.2018.2872323 .
    Abstract
    Objective: The aim of this work is to assess the potential of the reduced order unscented Kalman filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. Methods: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameter after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. Results: First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. Conclusion: Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). Significance: The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data.

  • P.W. Schroeder, V. John, P.L. Lederer, Ch. Lehrenfeld, G. Lube, J. Schöberl, On reference solutions and the sensitivity of the 2D Kelvin--Helmholtz instability problem, Computers & Mathematics with Applications. An International Journal, 77 (2019), pp. 1010--1028.

  • J. DE Frutos, B. Garc'ia-Archilla, V. John, J. Novo, Error analysis of non inf-sup stable discretizations of the time-dependent Navier--Stokes equations with local projection stabilization, IMA Journal of Numerical Analysis, 39 (2019), pp. 1747--1786, DOI 10.1093/imanum/dry044 .

  • A. Zeghuzi, H.-J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow, A. Knigge, Time-dependent simulation of thermal lensing in high-power broad-area semiconductor lasers, IEEE J. Select. Topics Quantum Electron., 25 (2019), 1502310, DOI 10.1109/JSTQE.2019.2925926 .
    Abstract
    We propose a physically realistic and yet numerically applicable thermal model to account for short and long term self-heating within broad-area lasers. Although the temperature increase is small under pulsed operation, a waveguide that is formed within a few-ns-long pulse can result in a transition from a gain-guided to an index-guided structure, leading to near and far field narrowing. Under continuous wave operation the longitudinally varying temperature profile is obtained self-consistently. The resulting unfavorable narrowing of the near field can be successfully counteracted by etching trenches.

  • C. Bartsch, V. John, R.I.A. Patterson, Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach, Comput. Chem. Engng., 124 (2019), pp. 350--363, DOI 10.1016/j.compchemeng.2019.01.012 .
    Abstract
    A coupled solver for population balance systems is presented, where the flow, temperature, and concentration equations are solved with finite element methods, and the particle size distribution is simulated with a stochastic simulation algorithm, a so-called kinetic Monte-Carlo method. This novel approach is applied for the simulation of an axisymmetric model of a tubular flow crystallizer. The numerical results are compared with experimental data.

  • W. Dreyer, C. Guhlke, R. Müller, The impact of solvation and dissociation on the transport parameters of liquid electrolytes: Continuum modeling and numerical study, European Physical Journal Special Topics, 227 (2019), pp. 2515--2538, DOI 10.1140/epjst/e2019-800133-2 .
    Abstract
    Electro-thermodynamics provides a consistent framework to derive continuum models for electrochemical systems. For the application to a specific experimental system, the general model must be equipped with two additional ingredients: a free energy model to calculate the chemical potentials and a kinetic model for the kinetic coefficients. Suitable free energy models for liquid electrolytes incorporating ion-solvent interaction, finite ion sizes and solvation already exist and have been validated against experimental measurements. In this work, we focus on the modeling of the mobility coefficients based on Maxwell--Stefan setting and incorporate them into the general electro-thermodynamic framework. Moreover, we discuss the impact of model parameter on conductivity, transference numbers and salt diffusion coefficient. In particular, the focus is set on the solvation of ions and incomplete dissociation of a non-dilute electrolyte.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Computers & Mathematics with Applications. An International Journal, published online on 18.06.2019, DOI 10.1016/j.camwa.2019.06.007 .
    Abstract
    We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.

  • J. Fuhrmann, C. Guhlke, Ch. Merdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Electrochimica Acta, 317 (2019), pp. 778--785, DOI 10.1016/j.electacta.2019.05.051 .

  • A. Linke, L.G. Rebholz, Pressure-induced locking in mixed methods for time-dependent (Navier--)Stokes equations, Journal of Computational Physics, 388 (2019), pp. 350--356, DOI 10.1016/j.jcp.2019.03.010 .
    Abstract
    We consider inf-sup stable mixed methods for the time-dependent incompressible Stokes and Navier--Stokes equations, extending earlier work on the steady (Navier-)Stokes Problem. A locking phenomenon is identified for classical inf-sup stable methods like the Taylor-Hood or the Crouzeix-Raviart elements by a novel, elegant and simple numerical analysis and corresponding numerical experiments, whenever the momentum balance is dominated by forces of a gradient type. More precisely, a reduction of the L2 convergence order for high order methods, and even a complete stall of the L2 convergence order for lowest-order methods on preasymptotic meshes is predicted by the analysis and practically observed. On the other hand, it is also shown that (structure-preserving) pressure-robust mixed methods do not suffer from this locking phenomenon, even if they are of lowest-order. A connection to well-balanced schemes for (vectorial) hyperbolic conservation laws like the shallow water or the compressible Euler equations is made.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s11082-019-1792-1 .
    Abstract
    In this work, we discuss the modeling of edge-emitting high-power broad-area semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple vertical-lateral laser cross-sections with a fast dynamic electro-optical (EO) model determined on the longitudinal-lateral domain that is a projection of the device to the active region of the laser. Whereas the HT-solver calculates temperature and thermally-induced refractive index changes, the EO-solver exploits these distributions and provides time-averaged field intensities, quasi-Fermi potentials, and carrier densities. All these time-averaged distributions are used repetitively by the HT-solver for the generation of the heat sources entering the HT problem solved in the next iteration step.

Contributions to Collected Editions

  • N. Lei, W. Chen, Z. Luo, H. Si, X. Gu, Secondary power Diagram, dual of secondary polytope, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 3--24, DOI 10.1007/978-3-030-23436-2 .

  • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Models and numerical methods for electrolyte flows, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 183--209.

  • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Voronoi finite volumes and pressure robust finite elements for electrolyte models with finite ion sizes, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 73--83, DOI 10.1007/978-3-030-23436-2 .

  • TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019), J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2019, pp. 13--14 (appeared online 22.08.2019), DOI 10.1109/NUSOD.2019.8807025 .

  • A. Linke, Nonlinear flux approximation scheme for burgers equation derived from a local BVP, in: Numerical Mathematics and Advanced Applications 2017, Proceedings of ENUMATH 2017, F.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. Pop, eds., Springer, Berlin et al., 2019.

  • H. Si, A simple algorithm to triangulate a special class of 3D non-convex polyhedra without Steiner points, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 61--71, DOI 10.1007/978-3-030-23436-2 .

Preprints, Reports, Technical Reports

  • A.F.M. TER Elst, A. Linke, J. Rehberg, On the numerical range of sectorial forms, Preprint no. 2667, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2667 .
    Abstract, PDF (245 kByte)
    We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H-angle for the H-calculus on Lp for all p ∈ (1, ∞) if the coefficients are real valued.

  • J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices, Preprint no. 2660, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2660 .
    Abstract, PDF (1456 kByte)
    We discretize a unipolar electrothermal drift-diffusion model for organic semiconductor devices with Gauss--Fermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized Scharfetter-Gummel scheme. Applying path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, only recently observed experimentally.

  • H. Stephan, Millions of Perrin pseudoprimes including a few giants, Preprint no. 2657, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2657 .
    Abstract, PDF (244 kByte)
    The calculation of many and large Perrin pseudoprimes is a challenge. This is mainly due to their rarity. Perrin pseudoprimes are one of the rarest known pseudoprimes. In order to calculate many such large numbers, one needs not only a fast algorithm but also an idea how most of them are structured to minimize the amount of numbers one have to test. We present a quick algorithm for testing Perrin pseudoprimes and develop some ideas on how Perrin pseudoprimes might be structured. This leads to some conjectures that still need to be proved.
    We think that we have found well over 90% of all 20-digit Perrin pseudoprimes. Overall, we have been able to calculate over 9 million Perrin pseudoprimes with our method, including some very large ones. The largest number found has 1436 digits. This seems to be a breakthrough, compared to the previously known just over 100,000 Perrin pseudoprimes, of which the largest have 20 digits.
    In addition, we propose two sequences that do not provide any pseudoprimes up to 1,000,000,000 at all.

  • L. Blank, E. Meneses Rioseco, U. Wilbrandt, A. Caiazzo, Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers, Preprint no. 2656, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2656 .
    Abstract, PDF (20 MByte)
    Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermo-hydraulic interaction between tightly deployed geothermal wells in heterogeneous temperature and permeability fields is key for a maximum sustainable use of geothermal resources. Motivated by the geological settings of the Upper Jurassic aquifer in the Greater Munich region, we develop a computational model based on finite element analysis and gradient-free optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and investigate numerically the optimal positioning and spacing of multi-well systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multi-well arrangements provides significant amounts of energy to meet heat demand in highly urbanized regions. Our results show that taking into account heterogeneous permeability structures and variable reservoir temperature may drastically affect the results in the optimal configuration. We demonstrate that the proposed numerical framework is able to efficiently handle generic geometrical and geologocal configurations, and can be thus flexibly used in the context of multi-variable optimization problems. Hence, this numerical framework can be used to assess the extractable geothermal energy from heterogeneous deep geothermal reservoirs by the optimized deployment of smart multi-well systems.

  • D. Janke, A. Caiazzo, N. Ahmed, N. Alia, O. Knoth, B. Moreau, U. Wilbrandt, D. Willink, Th. Amon, V. John, On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn, Preprint no. 2644, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2644 .
    Abstract, PDF (5234 kByte)
    Two transient open source solvers, OpenFOAM and ParMooN, are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a 1:100 scaled wind tunnel model. Both solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for time-averaged stream-wise and vertical-wise velocities. In particular, the air exchange was predicted with high accuracy by both solvers with relative errors less than 5 % compared to the experimental results. With respect to the turbulent quantities, good agreements at the second (downwind) half of the barn inside and especially outside the barn could be achieved, where both codes accurately predicted the flow separation and the root-mean-square velocities. Deviations between simulations and experimental results regarding turbulent quantities could be observed in the first part of the barn, due to different inlet conditions between the experimental setup and the numerical simulations. Both solvers proved to be promising tools for the accurate prediction of time-dependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogen-laden aerosols in and around agricultural buildings.

  • M. Akbas, Th. Gallouët, A. Gassmann, A. Linke, Ch. Merdon, A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem, Preprint no. 2641, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2641 .
    Abstract, PDF (445 kByte)
    A novel notion for constructing a well-balanced scheme --- a gradient-robust scheme --- is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient --- if there is enough mass in the system to compensate the force. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM-FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straight-forward extension to barotropic situations with nonlinear equations of state is feasible.

  • J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance, Preprint no. 2640, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2640 .
    Abstract, PDF (3691 kByte)
    We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter $d^facet to 0$ we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit $L^Debye << d^facet$ , an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.

  • D.H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero, Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices, Preprint no. 2630, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2630 .
    Abstract, PDF (2299 kByte)
    We present an electrothermal drift-diffusion model for organic semiconductor devices with Gauss-Fermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized Scharfetter-Gummel scheme. Using path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, which were only recently observed experimentally.

  • M. Lübbering, J. Kunkel, P. Farrell, What company does my news article refer to? Tackling multiclass problems with topic modeling, Preprint no. 2621, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2621 .
    Abstract, PDF (354 kByte)
    While it is technically trivial to search for the company name to predict the company a new article refers to, it often leads to incorrect results. In this article, we compare the two approaches bag-of-words with k-nearest neighbors and Latent Dirichlet Allocation with k-nearest neighbor by assessing their applicability for predicting the S&P 500 company which is mentioned in a business news article or press release. Both approaches are evaluated on a corpus of 13k documents containing 84% news articles and 16% press releases. While the bag-of-words approach yields accurate predictions, it is highly inefficient due to its gigantic feature space. The Latent Dirichlet Allocation approach, on the other hand, manages to achieve roughly the same prediction accuracy (0.58 instead of 0.62) but reduces the feature space by a factor of seven.

  • C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul, A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated drift-diffusion model, Preprint no. 2620, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2620 .
    Abstract, PDF (2725 kByte)
    In this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log c/1-c. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.

  • H. Si, On decomposition of embedded prismatoids in $R^3$ without additional points, Preprint no. 2602, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2602 .
    Abstract, PDF (10 MByte)
    This paper considers three-dimensional prismatoids which can be embedded in ℝ³ A subclass of this family are twisted prisms, which includes the family of non-triangulable Scönhardt polyhedra [12, 10]. We call a prismatoid decomposable if it can be cut into two smaller prismatoids (which have smaller volumes) without using additional points. Otherwise it is indecomposable. The indecomposable property implies the non-triangulable property of a prismatoid but not vice versa.
    In this paper we prove two basic facts about the decomposability of embedded prismatoid in ℝ³ with convex bases. Let P be such a prismatoid, call an edge interior edge of P if its both endpoints are vertices of P and its interior lies inside P. Our first result is a condition to characterise indecomposable twisted prisms. It states that a twisted prism is indecomposable without additional points if and only if it allows no interior edge. Our second result shows that any embedded prismatoid in ℝ³ with convex base polygons can be decomposed into the union of two sets (one of them may be empty): a set of tetrahedra and a set of indecomposable twisted prisms, such that all elements in these two sets have disjoint interiors.

  • C.K. Macnamara, A. Caiazzo, I. Ramis-Conde, M.A.J. Chaplain, Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure, Preprint no. 2597, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2597 .
    Abstract, PDF (1351 kByte)
    The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue.

  • V. John, P. Knobloch, U. Wilbrandt, Finite element pressure stabilizations for incompressible flow problems, Preprint no. 2587, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2587 .
    Abstract, PDF (2101 kByte)
    Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis.

  • A. Caiazzo, R. Maier, D. Peterseim, Reconstruction of quasi-local numerical effective models from low-resolution measurements, Preprint no. 2577, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2577 .
    Abstract, PDF (1550 kByte)
    We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on low-resolution measurements. We rely on recent quasi-local numerical effective models that, in contrast to conventional homogenized models, are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that the identification of the matrix representation of these effective models is possible. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.

Talks, Poster

  • V. John, Algebraic finite element stabilizations for convection-diffusion equations, Indian Institute of Technology Roorkee, Department of Mathematics, India, January 24, 2020.

  • A. Linke, On pressure-robustness, well-balanced schemes and teh spatial discretization of hight Reynolds number flows, 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2020), Section S18 ``Numerical methods of differential equations'', March 16 - 20, 2020, Universität Kassel, March 17, 2020.

  • H. Si, Adaptive exponential time integration of the Navier--Stokes equations, 3rd AIAA Sonic Boom Prediction Workshop, January 5 - 10, 2020, American Institute of Aeronautics and Astronautics SciTech Forum, Orlando, Florida, USA, January 10, 2020.

  • A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, ``Microscopy Conference 2019'', Poster session IM 4, Berlin, September 1 - 5, 2019.

  • A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19 - 30, 2019.

  • N. Alia, M.J. Arenas Jaén, Revealing secrets of industrial processes with Math, Lange Nacht der Wissenschaften (Long Night of the Sciences) 2019, Leibniz-Gemeinschaft Berlin.

  • N. Alia, On the simulation and optimization of the Navier--Stokes equations applied to buoyancy-driven liquid steel stirring, Workshop on Mathematics and Materials Science for Steel Production and Manufacturing, June 4 - 5, 2019, Thon Hotel Høyers, Skien, Norway, June 4, 2019.

  • P. Vágner, M. Pavelka, Dielectric polarization in GENERIC, Joint European Thermodynamics Conference (JETC 2019), Spain, May 21 - 24, 2019.

  • P. Vágner, DFT-inspired modeling of Ni YSZ H_2-H_2O electrode surface, University of Chemistry and Technology, Chemie und Technologie, Prague, Czech Republic, November 29, 2019.

  • P. Vágner, Dielectric polarization in GENERIC, Conference to celebrate 80th jubilee of Miroslav Grmela, May 18 - 19, 2019, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Prague, Czech Republic, May 18, 2019.

  • P. Vágner, Thermodynamic modeling of the YSZ metal gas electrode interface dynamics, University of Chemistry and Technology, Institute of Anorgani-Technology, Prague, Czech Republic, July 15, 2019.

  • P.P. Bawol , Ch. Merdon, H. Baltruschat, J. Fuhrmann, Rotating ring-disc electrode simulations: A comparison of classical finite differences to fully implicit finite volume scheme, ModVal 2019 - 16th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, March 12 - 13, 2019.

  • A. Caiazzo, Data assimilation in one-dimensional hemodynamics, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 36: Data-Driven Computational Fluid Dynamics (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 1, 2019.

  • A. Caiazzo, Geothermal reservoir: Modeling, simulation and optimization for district heating in hot sedimentary acquires, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

  • A. Caiazzo, Multiscale hybrid modeling and simulation of cancer growth within a 3D heterogeneous tissue, Canada-Germany Workshop Mathematical Biology and Numerics, June 24 - 26, 2019, Universität Heidelberg, June 26, 2019.

  • P. Farrell, Creating anisotropic meshes by combining RBFs and HDE, International Conference of Kernel-based Methods and it's Application, October 10 - 14, 2019, Xi'an Jiaotong-Liverpool University, Suzhou, China, October 13, 2019.

  • P. Farrell, Highly accurate quadrature-based Scharfetter-Gummel schemes for charge transport in degenerates, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 19, 2019.

  • P. Farrell, Konjugierte Gradienten, Technische Universität Bergakademie Freiberg, Fakultät Mathematik und Informatik, November 27, 2019.

  • P. Farrell, Modeling and simulation of charge carrier transport in semiconductors and electrolytes, Part II, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institut für Silizium-Photovoltaik, June 27, 2019.

  • P. Farrell, Novel schemes for drift-diffusion semiconductor problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • P. Farrell, Simulating semiconductor devices in a physically correct and stable way, Technische Universität Bergakademie Freiberg, Fakultät Mathematik und Informatik, November 27, 2019.

  • P. Farrell, Solving PDEs numerically, University of Exeter, Department of Mathematics, UK, April 11, 2019.

  • J. Fuhrmann, A. Linke, Ch. Merdon, R. Müller, Induced charge electroosmotic flow including finite ion size effects, 13th International Symposium on Electrokinetics (ELKIN), Cambridge, USA, June 12 - 14, 2019.

  • J. Fuhrmann, Entwicklung von Policies und Richtlinien für Forschungssoftware, deRSE19 - Konferenz für ForschungssoftwareentwicklerInnen in Deutschland, June 4 - 6, 2019, Albert Einstein Wissenschaftspark Potsdam.

  • J. Fuhrmann, Finite volume methods for degenerate drift-diffusion systems, Max-Planck-Institut für Eisenforschung GmbH, Defektchemie und Spektroskopie, Düsseldorf, October 14, 2019.

  • J. Fuhrmann, Induced charge electroosmotic flow including finite ion size effects, 13th International Symposium on Electrokinetics (ELKIN), June 12 - 14, 2019, Massachusetts Institute of Technology, Cambridge, USA, June 12, 2019.

  • J. Fuhrmann, Modeling and simulation of charge carrier transport in semiconductors and electrolytes, Pat I, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institut für Silizium-Photovoltaik, June 27, 2019.

  • J. Fuhrmann, Modified exponential fitting schemes for degenerate semiconductors and electrolytes, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • J. Fuhrmann, The Julia programming language in applications for electrochemical systems simulation, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 21, 2019.

  • J. Fuhrmann, Working with Julia: Plotting, packages and active documents, Leibniz MMS Summer School 2019, October 28 - November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach.

  • V. John, Algebraic finite element stabilizations for convection-diffusion equations, Workshop on Computational Modeling and Numerical Analysis (WCMNA 2019), February 25 - 28, 2019, Laboratório Nacional de Computação Científica, Petrópolis, Brazil, February 26, 2019.

  • V. John, Algebraic finite element stabilizations for convection-diffusion equations, Workshop ''Towards Computable Flows'', April 26 - 27, 2019, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, April 26, 2019.

  • V. John, Finite element methods for incompressible flows, Workshop on Computational Modeling and Numerical Analysis (WCMNA 2019), February 25 - 28, 2019, Laboratório Nacional de Computação Científica, Petrópolis, Brazil.

  • V. John, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, Conference on Applied Mathematics, August 19 - 21, 2019, Lahore University of Management Sciences, Pakistan, August 19, 2019.

  • V. John, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, Indo-German Conference on Computational Mathematics (IGCM), December 2 - 4, 2019, Indian Institute of Science, Department of Computer and Data Sciences, Bangalore, India, December 3, 2019.

  • V. John, On $L^2(Omega)$ estimates for finite element methods for evolutionary convection-dominated problems, PIMS-Germany Workshop on Discretization of Variational Eigenvalue and Flow Problems, June 24 - 26, 2019, Universität Heidelberg, June 25, 2019.

  • V. John, Variational Multiscale (VMS) methods for the simulation of turbulent incompressible flows, University of Groningen, Bernoulli Institute, Computational Mechanics & Numerical Mathematics, Netherlands, September 23, 2019.

  • V. John, Variational Multiscale (VMS) methods for the simulation of turbulent incompressible flows, Indian Institute of Science, Department of Computational and Data Science, Bangalore, India, November 28, 2019.

  • A. Linke, An introduction to the Julia programming languarge, Leibniz MMS Summer School 2019, October 28 - November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach, October 28, 2019.

  • A. Linke, On high Reynolds number flows, pressure-robustness and high-order methods, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

  • A. Linke, On high Reynolds number flows, pressure-robustness and high-order methods, Technische Universität Darmstadt, Fachbereich Mathematik, August 28, 2019.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Renolds number generalised Beltrami flows and beyond, PIMS-Germany Workshop on Discretization of Variational Eigenvalue and Flow Problems, June 24 - 26, 2019, Universität Heidelberg, June 26, 2019.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, Conference ``POEMs --- POlytopal Element Methods in Mathematics and Engineering'', April 29 - May 3, 2019, CIRM - Luminy, Centre International de Rencontres Mathématiques, Marseille, France, April 29, 2019.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 23: Recent Advances in Numerical Simulation of Incompressible Flows (Part 3), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • A. Linke, On pressure-robustness, coherent structures and vortex-dominated flows, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

  • A. Linke, On the occacion of the 60th birthday of Prof. Bänsch: Workshop ``Numerical Analysis and Scientific Computing'', November 22 - 23, 2019, Friedrich-Alexander-Universität Erlangen-Nürnberg.

  • A. Linke, Pressure-robustness -- A new criterion for the accuracy of incompressible Navier--Stokes solvers at high Reynolds number and beyond, 4th Annual SU2 Developers Meeting, May 8 - 10, 2019, Villa Monastero, Varenna, Italy, May 9, 2019.

  • A. Linke, Robust discretization of advective linear transport, based on a complexte flux scheme and entropy principles, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 1), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • A. Linke , Towards a pressure robust computation of computable flows, Workshop ''Towards Computable Flows'', April 26 - 27, 2019, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, April 27, 2019.

  • CH. Merdon, A gradient-robust, well-balanced discretisation for the compressible barotropic Stokes problem, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 23: Recent Advances in Numerical Simulation of Incompressible Flows (Part 1), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 1, 2019.

  • CH. Merdon, Pressure-robust finite element discretisations for the Navier--Stokes problem, Technische Universität Dresden, Fachbereich Mathematik, April 11, 2019.

  • CH. Merdon, Pressure-robust mixed finite element methods and refined a posteriori error control for the Stokes problem, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 29, 2019.

  • CH. Merdon, Pressure-robustness in the discretisation of the Navier--Stokes equations, Univeristy of Twente, Institute of Nanotechnology, Enschede, Netherlands, September 30, 2019.

  • CH. Merdon, Pressure-robustness in the discretisation of the Navier--Stokes equations --- An overview, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

  • H. Si, An introduction to mesh generation methods and softwares for scientific computing, December 15 - 26, 2019, Zhejiang University, Center for Engineering & Scientific Computation, Hangzhou, China.

  • H. Si, An introduction to unstructured mesh generation and adaptation, Universidad de Chile, Department of Computer Science, Santiago, Chile, April 28, 2019.

  • H. Si, Instructor for the cours ``An Introduction to Mesh Generation Methods and Software for Scientific Computing'', BAIHANG International Summer School 2019, July 1 - 26, 2019, Beihang University, China.

  • H. Si, Unstructured mesh generation and its applications, BeiHang University, School of Mathematics and Systems Science, Beijing, China, November 22, 2019.

  • H. Si, n.n., Winter School 2019, December 16 - 26, 2019, Zhejiang University, Hangzhou, China.

  • P. Vágner, A detailed double layer model of solid oxide cell electrolyte-electrode interface, ModVal 2019 - 16th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, March 12 - 13, 2019.

External Preprints

  • M. Akbas, Th. Gallouët, A. Gassmann, A. Linke, Ch. Merdon, A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem, Preprint no. arXiv:1911.01295, Cornell University Library, arXiv.org, 2019.

  • J. Fuhrmann, C. Guhlke, Ch. Merdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Preprint no. arXiv:1901.06941, Cornell University, 2019, DOI 10.1016/j.electacta.2019.05.051 .

  • A. Linke, Ch. Merdon, M. Neilan, Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem, Preprint no. arXiv:1906.03009, Cornell University Library, arXiv.org, 2019.