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Publications

Monographs

  • R. Ahrens, Z. Lakdawala, A. Voigt, V. Wiedmeyer, V. John, S. Le Borne, K. Sundmacher, Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes, S. Heinrich, ed., Dynamic Flowsheet Simulation of Solids Processes, Springer, Cham, 2020, pp. 475--518, (Chapter Published), DOI 10.1007/978-3-030-45168-4_14 .

  • V. John, P. Knobloch, U. Wilbrandt, Finite Element Pressure Stabilizations for Incompressible Flow Problems, T. Bodnár, G. Galdi, Š. Nečasová, eds., Fluids Under Pressure, Birkhäuser, Cham, 2020, pp. pp 483-573, (Chapter Published), DOI 10.1007/978-3-030-39639-8_6 .
    Abstract
    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.

  • 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

  • A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, Th. Koprucki, Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes, Optical and Quantum Electronics, (2020), pp. 257/1--257/11 (published online on 05.05.2020), DOI 10.20347/WIAS.PREPRINT.2682 .
    Abstract
    We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin-Howie-Whelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for model-based geometry reconstruction of semiconductor QDs, involving machine learning techniques.

  • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 71 (2020), pp. 119/1--119/68, DOI 10.1007/s00033-020-01341-5 .
    Abstract
    We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a global--in--time weak solution for the full model, allowing for a general structure of the mobility tensor and for chemical reactions with highly non linear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time. With respect to our former study [DDGG16], we also essentially improve the a priori estimates, in particular concerning the relative chemical potentials.

  • M. Akbas, Th. Gallouët, A. Gassmann, A. Linke, Ch. Merdon, A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem, Computer Methods in Applied Mechanics and Engineering, 367 (2020), 113069, DOI 10.1016/j.cma.2020.113069 .
    Abstract
    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.

  • N. Ahmed, V. John, An assessment of two classes of variational multiscale methods for the simulation of incompressible turbulent flows, Computer Methods in Applied Mechanics and Engineering, 365 (2020), pp. 112997/1--112997/20, DOI https://doi.org/10.1016/j.cma.2020.112997 .
    Abstract
    A numerical assessment of two classes of variational multiscale (VMS) methods for the simulation of incompressible flows is presented. Two types of residual-based VMS methods and two types of projection-based VMS methods are included in this assessment. The numerical simulations are performed at turbulent channel flow problems with various friction Reynolds numbers. It turns out the the residual-based VMS methods, in particular when used with a pair of inf-sup stable finite elements, give usually the most accurate results for second order statistics. For this pair of finite element spaces, a flexible GMRES method with a Least Squares Commutator (LSC) preconditioner proved to be an efficient solver.

  • 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, IMA Journal of Numerical Analysis, published on 17.07.2020, DOI 10.1093/imanum/draa002 .
    Abstract
    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.

  • D.H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero, Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices, Journal of Computational Electronics, 19 (2020), pp. 1164--1174, DOI 10.1007/s10825-020-01505-6 .
    Abstract
    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.

  • 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, Computers and Electronics in Agriculture, 175 (2020), pp. 105546/1--105546/16, DOI 10.1016/j.compag.2020.105546 .
    Abstract
    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.

  • 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, Journal of Computational Science, 40 (2020), 101067, DOI 10.1016/j.jocs.2019.101067 .
    Abstract
    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.

  • L.G. Ramos, R. Kehl, R. Nabben, Projections, deflation and multigrid for non-symmetric matrices, SIAM Journal on Matrix Analysis and Applications, 41 (2020), pp. 83--105.

  • D. Frerichs, Ch. Merdon, Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem, IMA Journal of Numerical Analysis, (2020), published on 9.11.2020, DOI 10.1093/imanum/draa073 .
    Abstract
    Non divergence-free discretisations for the incompressible Stokes problem may suffer from a lack of pressure-robustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergence-free virtual element methods (VEM) on polygonal meshes are not really pressure-robust as long as the right-hand side is not discretised in a careful manner. To be able to evaluate the right-hand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L2 -bestapproximation does not preserve the divergence and so destroys the orthogonality between divergence-free testfunctions and possibly eminent gradient forces in the right-hand side. To repair this orthogonality and restore pressure-robustness another divergence-preserving reconstruction is suggested based on Raviart--Thomas approximations on local subtriangulations of the polygons. All findings are proven theoretically and are demonstrated numerically in two dimensions. The construction is also interesting for hybrid high-order methods on polygonal or polyhedral meshes.

  • J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance, Journal of The Electrochemical Society, 167 (2020), pp. 106512/1--106512/15, DOI 10.1149/1945-7111/ab9cca .
    Abstract
    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.

  • A. Linke, Ch. Merdon, M. Neilan, Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem, Electronic Transactions on Numerical Analysis, 52 (2020), pp. 281--294, DOI 10.1553/etna_vol52s281 .

  • 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 .

  • R. Kehl, R. Nabben, D.B. Szyld, Adaptive multilevel Krylov methods, Electronic Transactions on Numerical Analysis, 51 (2019), pp. 512--528, DOI 10.1553/etna_vol51s512 .

  • 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), pp. 115102/1--115102/14, 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.

  • L. Heltai, A. Caiazzo, Multiscale modeling of vascularized tissues via non-matching immersed methods, International Journal of Numerical Methods in Biomedical Engineering, 35 (2019), pp. 3264/1--3264/32, DOI 10.1002/cnm.3264 .
    Abstract
    We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two manifold) at a given pressure. We derive different variational formulations of the coupled problem, in which the effect of the vasculature can be surrogated in the elasticity equations via singular or hyper-singular forcing terms. These terms only depends on information defined on co-dimension two manifolds (such as vessel center line, cross sectional area, and mean pressure over cross section), thus drastically reducing the complexity of the computational model. We perform several numerical tests, ranging from simple cases with known exact solutions to the modeling of materials with random distributions of vessels. In the latter case, we use our immersed method to perform an in silico characterization of the mechanical properties of the effective biphasic material tissue via statistical simulations.

  • 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, DOI 10.1016/j.camwa.2018.10.030 .

  • 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), pp. 1502310/1--1502310/10, 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, Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in drift-diffusion semiconductor simulations, Computers & Mathematics with Applications. An International Journal, 78 (2019), pp. 3731--3747, 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 dynamic electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), pp. 69/1--69/10, 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

  • A. Linke, Ch. Merdon, On the significance of pressure-robustness for the space discretization of incompressible high reynolds number flows, in: Proceedings ofFinite Volumes for Complex Applications IX -- Methods, Theoretical Aspects, Examples -- FVCA 9, Bergen, Norway, June 2020, R. Klöfkorn, E. Keilegavlen, A.F. Radu, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 103--112.

  • A. Linke, Ch. Merdon, Well-balanced discretisation for the compressible Stokes problem by gradient-robustness, in: Proceedings ofFinite Volumes for Complex Applications IX -- Methods, Theoretical Aspects, Examples -- FVCA 9, Bergen, Norway, June 2020, R. Klöfkorn, E. Keilegavlen, A.F. Radu, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 113--121.

  • C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate drift-diffusion model, in: Proceedings of Finite Volumes for Complex Applications IX, Bergen, Norway, June 2020, R. Klöfkorn, F. Radu, E. Keijgavlen, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 163--171, DOI 10.1007/978-3-030-43651-3_13 .

  • A. Jha, V. John, On basic iteration schemes for nonlinear AFC discretizations, in: Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018, G.N. Barrenechea, J. Mackenzie, eds., 135 of Lecture Notes in Computational Science and Engineering, Springer, Cham, 2020, pp. 113--128, DOI https://doi.org/10.1007/978-3-030-41800-7_7 .
    Abstract
    Algebraic flux correction (AFC) finite element discretizations of steady-state convection-diffusion-reaction equations lead to a nonlinear problem. This paper presents first steps of a systematic study of solvers for these problems. Two basic fixed point iterations and a formal Newton method are considered. It turns out that the fixed point iterations behave often quite differently. Using a sparse direct solver for the linear problems, one of them exploits the fact that only one matrix factorization is needed to become very efficient in the case of convergence. For the behavior of the formal Newton method, a clear picture is not yet obtained.

  • S. Schulz, D. Chaudhuri, M. O'Donovan, S. Patra, T. Streckenbach, P. Farrell, O. Marquardt, Th. Koprucki, Multi-scale modeling of electronic, optical, and transport properties of III-N alloys and heterostructures, in: Proceedings Physics and Simulation of Optoelectronic Devices XXVIII, 11274, San Francisco, California, USA, 2020, pp. 416--426, DOI 10.1117/12.2551055 .

  • 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, in: Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 625--633, DOI 10.1007/978-3-030-43651-3_59 .
    Abstract
    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.

  • J.H.M. Ten Thije Boonkkamp, N. Kumar, B. Koren, D.A.M. caps">caps">van der Woude, A. Linke, Nonlinear flux approximation scheme for Burgers equation derived from a local BVP, in: Numerical Mathematics and Advanced Applications 2017 -- ENUMATH 2017, F.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. Pop, eds., 126 of Lecture Notes Comput. Sci. Engrg., Springer Nature Switzerland AG, Cham, 2019, pp. 1015--1023, DOI 10.1007/978-3-319-96415-7_96 .

  • 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, 2019, pp. 13--14, DOI 10.1109/NUSOD.2019.8807025 .

  • 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

  • D. Abdel, P. Farrell, J. Fuhrmann, Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation, Preprint no. 2787, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2787 .
    Abstract, PDF (682 kByte)
    The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter-Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter-Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p-i-n device are performed.

  • D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modelling charge transport in perovskite solar cells: Potential-based and limiting ion vacancy depletion, Preprint no. 2780, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2780 .
    Abstract, PDF (1067 kByte)
    From Maxwell--Stefan diffusion and general electrostatics, we derive a drift-diffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on for example Fermi--Dirac, Gauss--Fermi or Blakemore statistics) as well as limit the ion vacancy depletion (via the Fermi--Dirac integral of order -1). The latter will be motivated by a grand-canonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion vacancy depletion.

  • U. Wilbrandt, N. Alia, V. John, Optimal control of a buoyancy-driven liquid steel stirring modeled with single-phase Navier--Stokes equations, Preprint no. 2776, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2776 .
    Abstract, PDF (1469 kByte)
    Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible NavierStokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.

  • D. Frerichs, V. John, On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion-reaction equations, Preprint no. 2769, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2769 .
    PDF (1663 kByte)

  • J.-P. Köster, A. Putz, H. Wenzel, H.-J. Wünsche, M. Radziunas, H. Stephan, M. Wilkens, A. Zeghuzi, A. Knigge, Mode competition in broad-ridge-waveguide lasers, Preprint no. 2764, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2764 .
    Abstract, PDF (1616 kByte)
    The lateral brightness achievable with high-power GaAs-based laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higher-order lateral modes. For the study of the lateral-mode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing power-current characteristics that fit the data measured for 5 to 23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness 2W · mm¯¹ 1mrad¯¹ at 10MW · cm¯²2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broad-area lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam

  • V. John, P. Knobloch, Existence of solutions of a finite element flux-corrected-transport scheme, Preprint no. 2761, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2761 .
    Abstract, PDF (190 kByte)
    The existence of a solution is proved for a nonlinear finite element flux-corrected-transport (FEM-FCT) scheme with arbitrary time steps for evolutionary convection-diffusion-reaction equations and transport equations.

  • P.L. Lederer, Ch. Merdon, Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations, Preprint no. 2750, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2750 .
    Abstract, PDF (422 kByte)
    This paper improves guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A Prager-Synge type result relates the errors of divergence-free primal and H(div)-conforming dual mixed methods (for the velocity gradient) with an equilibration constraint that needs special care when discretised. To relax the constraints on the primal and dual method, a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust (but not necessarily divergence-free) primal discretisation. Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costs of the error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1.

  • N. Ahmed, G.R. Barrenechea, E. Burman, J. Guzmán, A. Linke, Ch. Merdon, A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation, Preprint no. 2740, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2740 .
    Abstract, PDF (843 kByte)
    Discretization of Navier--Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(hk+1/2) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.

  • P. Vágner, M. Pavelka, E. Oğul, Multiscale thermodynamics of charged mixtures, Preprint no. 2733, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2733 .
    Abstract, PDF (549 kByte)
    A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.

  • TH. Apel, V. Kempf, A. Linke, Ch. Merdon, A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes, Preprint no. 2702, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2702 .
    Abstract, PDF (509 kByte)
    Most classical finite element schemes for the (Navier--)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pressure-robustness may lead to large velocity errors, whenever the Stokes momentum balance is dominated by a strong and complicated pressure gradient. It is a consequence of a method, which does not exactly satisfy the divergence constraint. However, inf-sup stable schemes can often be made pressure-robust just by a recent, modified discretization of the exterior forcing term, using H(div)-conforming velocity reconstruction operators. This approach has so far only been analyzed on shape-regular triangulations. The novelty of the present contribution is that the reconstruction approach for the Crouzeix--Raviart method, which has a stable Fortin operator on arbitrary meshes, is combined with results on the interpolation error on anisotropic elements for reconstruction operators of Raviart--Thomas and Brezzi--Douglas--Marini type, generalizing the method to a large class of anisotropic triangulations. Numerical examples confirm the theoretical results in a 2D and a 3D test case.

  • D. Frerichs, Ch. Merdon, Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem, Preprint no. 2683, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2683 .
    Abstract, PDF (314 kByte)
    Non divergence-free discretisations for the incompressible Stokes problem may suffer from a lack of pressure-robustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergence-free virtual element methods (VEM) on polygonal meshes are not really pressure-robust as long as the right-hand side is not discretised in a careful manner. To be able to evaluate the right-hand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L2 -bestapproximation does not preserve the divergence and so destroys the orthogonality between divergence-free testfunctions and possibly eminent gradient forces in the right-hand side. To repair this orthogonality and restore pressure-robustness another divergence-preserving reconstruction is suggested based on Raviart--Thomas approximations on local subtriangulations of the polygons. All findings are proven theoretically and are demonstrated numerically in two dimensions. The construction is also interesting for hybrid high-order methods on polygonal or polyhedral meshes.

  • G. Fu, Ch. Lehrenfeld, A. Linke, T. Streckenbach, Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity, Preprint no. 2680, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2680 .
    Abstract, PDF (429 kByte)
    Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the concept of gradient-robustness for linear elasticity is new. We discuss both aspects and propose novel Hybrid Discontinuous Galerkin (HDG) methods for linear elasticity. The starting point for these methods is a divergence-conforming discretization. As a consequence of its well-behaved Stokes limit the method is gradient-robust and free of volume-locking. To improve computational efficiency, we additionally consider discretizations with relaxed divergence-conformity and a modification which re-enables gradient-robustness, yielding a robust and quasi-optimal discretization also in the sense of HDG superconvergence.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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

  • C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate drift-diffusion model, Finite Volumes for Complex Applications IX (Online Event), Bergen, Norway, June 15 - 19, 2020.

  • A. Caiazzo, CFD Simulation for non invasive estimation of blood pressure, Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

  • A. Caiazzo, Multiscale modeling of vascularized tissues, Virtual Physiological Human (VPH2020) -- When models, methods & experiments meet the clinic (Online Event), August 24 - 28, 2020, INRIA, Paris, France, August 28, 2020.

  • D. Frerichs, A pressure-robust virtual element method for the Stokes problem on polygonal / polyhedral meshes, Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

  • D. Frerichs, A really pressure-robust virtual element method for the Stokes problem, Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10 - 15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

  • 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, Finite Volumes for Complex Applications IX (Online Event), Bergen, Norway, June 15 - 19, 2020.

  • J. Fuhrmann, C. Guhlke, M. Landstorfer, A. Linke, Ch. Merdon, R. Müller, Quality preserving numerical methods for electroosmotic flow, Einstein Semester on Energy-based mathematical methods for reactive multiphase flows: Kick-off Conference (Online Event), October 26 - 30, 2020.

  • J. Fuhrmann, Quality preserving numerical methods for electroosmotic flow, Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10 - 15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

  • J. Fuhrmann, VTKView.jl -- vtk based in-situ visualization in Julia, Julia VizCon (Online Event), March 12 - 19, 2020, March 15, 2020.

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

  • V. John, Numerical methods for convection-dominated equations, January 27 - 30, 2020, Indian Institute of Technology Roorkee, Department of Mathematics, India.

  • V. John, On the provable convergence order for the kinetic energy of FEMs for the incompressible Navier--Stokes equations, 7th European Seminar on Computing (ESCO 2020) (Online Event), Pilsen, Czech Republic, June 8 - 12, 2020.

  • A. Linke, Ch. Merdon, On the significance of pressure-robustness for the space discretization of incompressible high reynolds number flows, Finite Volumes for Complex Applications IX (Online Event), Belgien, Norway, June 15 - 19, 2020.

  • A. Linke, An overview on the Leibniz MMS network and its GFD-CFD research activities, Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

  • A. Linke, Gradient-robustness: A new concept assuring accurate spatial discretizations for vector-valued PDEs, Workshop ``Structure, Regularity and Robustness in the Approximation of PDEs'', Università degli Studi di Milano Statale, Italy, February 10, 2020.

  • A. Linke, Gradient-robustness: A new concept assuring accurate spatial discretizations for vector-valued PDEs (online talk), Eindhoven University of Technology, Centre for Analysis, Scientific computing and Applications, Netherlands, June 24, 2020.

  • A. Linke, On pressure-robust space discretizations and incompressible high Reynolds number flows, Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10 - 15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 15, 2020.

  • A. Linke, tba, Workshop on Modeling and Simulation of Transport Phenomena 2020, October 13 - 15, 2020, Technische Universität Dortmund, Schloss-Hotel Petry, Treis-Karden, October 14, 2020.

  • CH. Merdon, A gradient-robust discretisation for the compressible Stokes problem, Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10 - 15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 2020.

  • CH. Merdon, Gradient-robust discretisations for compressible Navier--Stokes flows, Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

  • CH. Merdon, Well-balanced discretisation for the compressible Stokes problem by gradient-robustness, Finite Volumes for Complex Applications IX (Online Event), June 15 - 19, 2020, University of Bergen, Norway, June 17, 2020.

  • O. Pártl, Mathematical modeling of non-isothermal compositional compressible fluid flow in zeolite bed and above its surface, Conference on Scientific Computing (ALGORITMY 2020) (Online Event), September 10 - 15, 2020, Slovak University of Technology, Podbanské, Slovakia, September 14, 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, WIAS at Leibniz Headquarters, Berlin, June 15, 2019.

  • 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), Barcelona, 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 Anorganic 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, Braunschweig, 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, Part 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 complete 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, University of Twente, Institute of Nanotechnology, Enschede, Netherlands, September 30, 2019.

  • CH. Merdon, Pressure-robustness in the discretisation of the Navier--Stokes equations --- An overview, 9th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium MS FE 1-2-5 ``Divergence-free and pressure-robust discretizations for the Navier--Stokes equations -- Part I'', 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 course ``An Introduction to Mesh Generation Methods and Software for Scientific Computing'', BAIHANG University International Summer School 2019, July 1 - 26, 2019, Beijing, China.

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

  • 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, Braunschweig, March 12 - 13, 2019.

External Preprints

  • 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 Library, 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.

Research Groups