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. 475518, (Chapter Published), DOI 10.1007/9783030451684_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 483573, (Chapter Published), DOI 10.1007/9783030396398_6 .
Abstract
Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete infsup condition require a socalled pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis. 
U. Wilbrandt, StokesDarcy 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 10.1007/9783030029043 .

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 10.1007/9783030234362 .
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. 257/1257/11 (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 DarwinHowieWhelan 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 modelbased geometry reconstruction of semiconductor QDs, involving machine learning techniques. 
W. Dreyer, P.É. Druet, P. Gajewski, C. Guhlke, Analysis of improved NernstPlanckPoisson 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. 119/1119/68, DOI 10.1007/s00033020013415 .
Abstract
We consider an improved NernstPlanckPoisson 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 convectiondiffusionreaction equations for the constituents of the mixture, of the NavierStokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, crossdiffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a globalintime 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 gradientrobust wellbalanced 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 wellbalanced scheme  a gradientrobust scheme  is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradientrobustness means that arbitrary gradient fields in the momentum balance are wellbalanced by the discrete pressure gradient  if there is enough mass in the system to compensate the force. The scheme is asymptoticpreserving in the sense that it degenerates for low Mach numbers to a recent infsup stable and pressurerobust discretization for the incompressible Stokes equations. The convergence of the coupled FEMFVM 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 nearlyhydrostatic low Mach number flows. Numerical examples also suggest that a straightforward 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. 112997/1112997/20, 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 residualbased VMS methods and two types of projectionbased 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 residualbased VMS methods, in particular when used with a pair of infsup 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. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated driftdiffusion 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 driftdiffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log ^{c}/_{1c}. 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, Driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, Journal of Computational Electronics, 19 (2020), pp. 11641174, DOI 10.1007/s10825020015056 .
Abstract
We present an electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi 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 ScharfetterGummel scheme. Using pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage 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. 105546/1105546/16, 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 timeaveraged streamwise and verticalwise 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 rootmeansquare 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 timedependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogenladen aerosols in and around agricultural buildings. 
C.K. Macnamara, A. Caiazzo, I. RamisConde, 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 individualbased model which allows one to simulate the behaviour of, and spatiotemporal 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 bloodvessel network or along the striations of fibrous tissue. 
L.G. Ramos, R. Kehl, R. Nabben, Projections, deflation and multigrid for nonsymmetric matrices, SIAM Journal on Matrix Analysis and Applications, 41 (2020), pp. 83105.

D. Frerichs, Ch. Merdon, Divergencepreserving reconstructions on polygons and a really pressurerobust 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 divergencefree discretisations for the incompressible Stokes problem may suffer from a lack of pressurerobustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergencefree virtual element methods (VEM) on polygonal meshes are not really pressurerobust as long as the righthand side is not discretised in a careful manner. To be able to evaluate the righthand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L^{2} bestapproximation does not preserve the divergence and so destroys the orthogonality between divergencefree testfunctions and possibly eminent gradient forces in the righthand side. To repair this orthogonality and restore pressurerobustness another divergencepreserving reconstruction is suggested based on RaviartThomas 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 highorder methods on polygonal or polyhedral meshes. 
J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrodeelectrolyte interfaces: The differential capacitance, Journal of The Electrochemical Society, 167 (2020), pp. 106512/1106512/15, DOI 10.1149/19457111/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 noninteracting 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, Pressurerobustness in quasioptimal a priori estimates for the Stokes problem, Electronic Transactions on Numerical Analysis, 52 (2020), pp. 281294, DOI 10.1553/etna_vol52s281 .

N. Alia, M. Pylvänäinen, V.V. Visuri, V. John, S. Ollila, Vibrations of a laboratoryscale gasstirred ladle with two eccentric nozzles and multiple sensors, Journal of Iron and Steel Research, International, 26 (2019), pp. 10311040, DOI 10.1007/s4224301900241x .

R. Kehl, R. Nabben, D.B. Szyld, Adaptive multilevel Krylov methods, Electronic Transactions on Numerical Analysis, 51 (2019), pp. 512528, DOI 10.1553/etna_vol51s512 .

A. Stephan, H. Stephan, Memory equations as reduced Markov processes, Discrete and Continuous Dynamical Systems, 39 (2019), pp. 21332155, 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 oneway 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 yttriastabilised zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions, Journal of Solid State Electrochemistry, 23 (2019), pp. 29072926, DOI 10.1007/s10008019043569 .
Abstract
A continuum model for yttriastabilised zirconia (YSZ) in the framework of nonequilibrium thermodynamics is developed. Particular attention is given to i) modeling of the YSZmetalgas 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 ScharfetterGummel 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 airhalf 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, Stochasticdeterministic population balance modeling and simulation of a fluidized bed crystallizer experiment, Chemical Engineering Sciences, 208 (2019), pp. 115102/1115102/14, DOI 10.1016/j.ces.2019.07.020 .

N.R. Gauger, A. Linke, P. Schroeder, On highorder pressurerobust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, SMAI Journal of Computational Mathematics, 5 (2019), pp. 89129.
Abstract
Recently, highorder space discretisations were proposed for the numerical simulation of the incompressible NavierStokes 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 highorder space discretisations is more robust against quantitatively large and complicated pressure fields than loworder methods. Second, it is demonstrated that novel pressurerobust methods are significantly more accurate than comparable classical, nonpressurerobust space discretisations, whenever the quadratic, nonlinear convection term is a nontrivial gradient field like in certain generalised Beltrami flows at high Reynolds number. Then, pressurerobust methods even allow to halve the (formal) approximation order without compromising the accuracy. Third, classical highorder space discretisations are outperformed by pressurerobust methods whenever the boundary is not approximated with highorder accuracy. This improved accuracy of (loworder) pressurerobust mixed methods is explained in terms of a HelmholtzHodge 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 pressurerobust 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 nonmatching immersed methods, International Journal of Numerical Methods in Biomedical Engineering, 35 (2019), pp. 3264/13264/32, 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 threedimensions) and a thin vascular structure (treated as a codimension 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 hypersingular forcing terms. These terms only depends on information defined on codimension 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 convectiondiffusion equations, Computational & Applied Mathematics, 78 (2019), pp. 31173138, 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. 127.

P.L. Lederer, Ch. Merdon, J. Schöberl, Refined a posteriori error estimation for classical and pressurerobust Stokes finite element methods, Journal of Numerical Mathematics, 142 (2019), pp. 713748.
Abstract
Recent works showed that pressurerobust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergencefree reconstruction operators and results in pressureindependent 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, Reducedorder unscented Kalman filter with observations in the frequency domain: Application to computational hemodynamics, IEEE Transactions on Biomedical Engineering, 66 (2019), pp. 12691276, 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 patientspecific data. Methods: The approach combines an efficient blood flow solver for onedimensional 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 patientspecific 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 interindividual 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 KelvinHelmholtz instability problem, Computers & Mathematics with Applications. An International Journal, 77 (2019), pp. 10101028, DOI 10.1016/j.camwa.2018.10.030 .

J. DE Frutos, B. Garc'iaArchilla, V. John, J. Novo, Error analysis of non infsup stable discretizations of the timedependent NavierStokes equations with local projection stabilization, IMA Journal of Numerical Analysis, 39 (2019), pp. 17471786, DOI 10.1093/imanum/dry044 .

A. Zeghuzi, H.J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow, A. Knigge, Timedependent simulation of thermal lensing in highpower broadarea semiconductor lasers, IEEE J. Select. Topics Quantum Electron., 25 (2019), pp. 1502310/11502310/10, 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 selfheating within broadarea lasers. Although the temperature increase is small under pulsed operation, a waveguide that is formed within a fewnslong pulse can result in a transition from a gainguided to an indexguided structure, leading to near and far field narrowing. Under continuous wave operation the longitudinally varying temperature profile is obtained selfconsistently. 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 stochasticdeterministic approach, Comput. Chem. Engng., 124 (2019), pp. 350363, 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 socalled kinetic MonteCarlo 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. 25152538, DOI 10.1140/epjst/e20198001332 .
Abstract
Electrothermodynamics 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 ionsolvent 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 MaxwellStefan setting and incorporate them into the general electrothermodynamic 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 nondilute electrolyte. 
P. Farrell, D. Peschka, Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in driftdiffusion semiconductor simulations, Computers & Mathematics with Applications. An International Journal, 78 (2019), pp. 37313747, DOI 10.1016/j.camwa.2019.06.007 .
Abstract
We analyze and benchmark the error and the convergence order of finite difference, finiteelement as well as Voronoi finitevolume discretization schemes for the driftdiffusion 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 Lshaped 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. 778785, DOI 10.1016/j.electacta.2019.05.051 .

A. Linke, L.G. Rebholz, Pressureinduced locking in mixed methods for timedependent (Navier)Stokes equations, Journal of Computational Physics, 388 (2019), pp. 350356, DOI 10.1016/j.jcp.2019.03.010 .
Abstract
We consider infsup stable mixed methods for the timedependent incompressible Stokes and NavierStokes equations, extending earlier work on the steady (Navier)Stokes Problem. A locking phenomenon is identified for classical infsup stable methods like the TaylorHood or the CrouzeixRaviart 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 L^{2} convergence order for high order methods, and even a complete stall of the L^{2} convergence order for lowestorder methods on preasymptotic meshes is predicted by the analysis and practically observed. On the other hand, it is also shown that (structurepreserving) pressurerobust mixed methods do not suffer from this locking phenomenon, even if they are of lowestorder. A connection to wellbalanced 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 electrooptical and heattransport models for highpower broadarea semiconductor lasers, Optical and Quantum Electronics, 51 (2019), pp. 69/169/10, DOI 10.1007/s1108201917921 .
Abstract
In this work, we discuss the modeling of edgeemitting highpower broadarea semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple verticallateral laser crosssections with a fast dynamic electrooptical (EO) model determined on the longitudinallateral domain that is a projection of the device to the active region of the laser. Whereas the HTsolver calculates temperature and thermallyinduced refractive index changes, the EOsolver exploits these distributions and provides timeaveraged field intensities, quasiFermi potentials, and carrier densities. All these timeaveraged distributions are used repetitively by the HTsolver 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 pressurerobustness 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. 103112.

A. Linke, Ch. Merdon, Wellbalanced discretisation for the compressible Stokes problem by gradientrobustness, 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. 113121.

C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate driftdiffusion 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. 163171, DOI 10.1007/9783030436513_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. 113128, DOI https://doi.org/10.1007/9783030418007_7 .
Abstract
Algebraic flux correction (AFC) finite element discretizations of steadystate convectiondiffusionreaction 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, Multiscale modeling of electronic, optical, and transport properties of IIIN alloys and heterostructures, in: Proceedings Physics and Simulation of Optoelectronic Devices XXVIII, 11274, San Francisco, California, USA, 2020, pp. 416426, DOI 10.1117/12.2551055 .

J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar driftdiffusion simulation of Sshaped currentvoltage 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. 625633, DOI 10.1007/9783030436513_59 .
Abstract
We discretize a unipolar electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi 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 ScharfetterGummel scheme. Applying pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage 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. 10151023, DOI 10.1007/9783319964157_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. 324, DOI 10.1007/9783030234362 .

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. 183209.

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. 7383, DOI 10.1007/9783030234362 .

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. 1314, DOI 10.1109/NUSOD.2019.8807025 .

H. Si, A simple algorithm to triangulate a special class of 3D nonconvex 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. 6171, DOI 10.1007/9783030234362 .
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 stateoftheart ScharfetterGummel scheme, namely the diffusionenhanced scheme. Physically, the diffusionenhanced 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 ScharfetterGummel 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, driftdiffusion simulations of a pin device are performed. 
D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modelling charge transport in perovskite solar cells: Potentialbased and limiting ion vacancy depletion, Preprint no. 2780, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2780 .
Abstract, PDF (1067 kByte)
From MaxwellStefan diffusion and general electrostatics, we derive a driftdiffusion 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 FermiDirac, GaussFermi or Blakemore statistics) as well as limit the ion vacancy depletion (via the FermiDirac integral of order 1). The latter will be motivated by a grandcanonical 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 buoyancydriven liquid steel stirring modeled with singlephase NavierStokes 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 endproduct 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 singlephase 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 steadystate convectiondiffusionreaction 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 broadridgewaveguide lasers, Preprint no. 2764, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2764 .
Abstract, PDF (1616 kByte)
The lateral brightness achievable with highpower GaAsbased laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higherorder lateral modes. For the study of the lateralmode 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 powercurrent 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 broadarea 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 fluxcorrectedtransport 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 fluxcorrectedtransport (FEMFCT) scheme with arbitrary time steps for evolutionary convectiondiffusionreaction equations and transport equations. 
P.L. Lederer, Ch. Merdon, Guaranteed upper bounds for the velocity error of pressurerobust 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 pressurerobustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A PragerSynge type result relates the errors of divergencefree 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 pressureindependent guaranteed upper bounds for any pressurerobust (but not necessarily divergencefree) 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 pressurerobust 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 NavierStokes' equations using pressurerobust 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 residualbased 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 pressurerobust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(h^{k}+^{1}/2) error estimate in the L^{2}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 residualbased 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 lowlevel limits of the detailed theory. The theory is then compared to recent literature. 
TH. Apel, V. Kempf, A. Linke, Ch. Merdon, A nonconforming pressurerobust 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 pressurerobust, nor are they infsup stable on general anisotropic triangulations. A lack of pressurerobustness 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, infsup stable schemes can often be made pressurerobust 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 shaperegular triangulations. The novelty of the present contribution is that the reconstruction approach for the CrouzeixRaviart 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 RaviartThomas and BrezziDouglasMarini 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, Divergencepreserving reconstructions on polygons and a really pressurerobust virtual element method for the Stokes problem, Preprint no. 2683, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2683 .
Abstract, PDF (314 kByte)
Non divergencefree discretisations for the incompressible Stokes problem may suffer from a lack of pressurerobustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that also divergencefree virtual element methods (VEM) on polygonal meshes are not really pressurerobust as long as the righthand side is not discretised in a careful manner. To be able to evaluate the righthand side for the testfunctions, some explicit interpolation of the virtual testfunctions is needed that can be evaluated pointwise everywhere. The standard discretisation via an L^{2} bestapproximation does not preserve the divergence and so destroys the orthogonality between divergencefree testfunctions and possibly eminent gradient forces in the righthand side. To repair this orthogonality and restore pressurerobustness another divergencepreserving reconstruction is suggested based on RaviartThomas 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 highorder 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 (nearlyincompressible) linear elasticity are free of volumelocking and gradientrobust. While volumelocking is a wellknown problem that can be dealt with in many different discretization approaches, the concept of gradientrobustness 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 divergenceconforming discretization. As a consequence of its wellbehaved Stokes limit the method is gradientrobust and free of volumelocking. To improve computational efficiency, we additionally consider discretizations with relaxed divergenceconformity and a modification which reenables gradientrobustness, yielding a robust and quasioptimal 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 nonsymmetric secondorder elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H^{∞}angle for the H^{∞}calculus on L_{p} 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 20digit 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 thermohydraulic 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 gradientfree optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and investigate numerically the optimal positioning and spacing of multiwell systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multiwell 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 multivariable 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 multiwell 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 bagofwords with knearest neighbors and Latent Dirichlet Allocation with knearest 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 bagofwords 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 threedimensional prismatoids which can be embedded in ℝ³ A subclass of this family are twisted prisms, which includes the family of nontriangulable 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 nontriangulable 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 quasilocal numerical effective models from lowresolution 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 lowresolution measurements. We rely on recent quasilocal 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. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate driftdiffusion 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 (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

A. Caiazzo, Multiscale modeling of vascularized tissues (online talk), 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 pressurerobust virtual element method for the Stokes problem on polygonal/polyhedral meshes (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

D. Frerichs, A really pressurerobust virtual element method for the Stokes problem (online talk), 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 driftdiffusion simulation of Sshaped currentvoltage 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 Energybased mathematical methods for reactive multiphase flows: Kickoff Conference (Online Event), October 26  30, 2020.

J. Fuhrmann, Quality preserving numerical methods for electroosmotic flow (online talk), 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 insitu visualization in Julia (online talk), Julia VizCon (Online Event), March 12  19, 2020, March 15, 2020.

J. Fuhrmann, tba (online talk), Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, University of Bergen, Norway.

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

V. John, Numerical methods for convectiondominated 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 NavierStokes 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 pressurerobustness 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 GFDCFD research activities (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

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

A. Linke, Gradientrobustness: A new concept assuring accurate spatial discretizations for vectorvalued PDEs (online talk), Eindhoven University of Technology, Centre for Analysis, Scientific computing and Applications, Netherlands, June 24, 2020.

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

A. Linke, tba (online talk), Workshop on Modeling and Simulation of Transport Phenomena 2020 (Online Event), October 13  15, 2020, Technische Universität Dortmund, SchlossHotel Petry, TreisKarden, October 14, 2020.

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

CH. Merdon, Gradientrobust discretisations for compressible NavierStokes flows (online talk), Leibniz MMS Symposium on Computational Geophysics and Fluid Dynamics (Online Event), October 21, 2020, October 21, 2020.

CH. Merdon, Wellbalanced discretisation for the compressible Stokes problem by gradientrobustness (online talk), Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, University of Bergen, Norway, June 17, 2020.

O. Pártl, Mathematical modeling of nonisothermal compositional compressible fluid flow in zeolite bed and above its surface (online talk), 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 NavierStokes 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, Modelbased 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, Modelbased 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 NavierStokes equations applied to buoyancydriven 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, DFTinspired modeling of Ni YSZ H_2H_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 ringdisc 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 onedimensional hemodynamics, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 36 ``DataDriven 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 , LeibnizInstitut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

A. Caiazzo, Multiscale hybrid modeling and simulation of cancer growth within a 3D heterogeneous tissue, CanadaGermany 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 Kernelbased Methods and it's Application, October 10  14, 2019, Xi'an JiaotongLiverpool University, Suzhou, China, October 13, 2019.

P. Farrell, Highly accurate quadraturebased ScharfetterGummel 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, HelmholtzZentrum Berlin für Materialien und Energie GmbH, Institut für SiliziumPhotovoltaik, June 27, 2019.

P. Farrell, Novel schemes for driftdiffusion semiconductor problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15 ``Novel Flux Approximation Schemes for AdvectionDiffusion 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 driftdiffusion systems, MaxPlanckInstitut 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, HelmholtzZentrum Berlin für Materialien und Energie GmbH, Institut für SiliziumPhotovoltaik, 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 AdvectionDiffusion 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 , LeibnizInstitut 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 convectiondiffusion 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 convectiondiffusion equations, Workshop ''Towards Computable Flows'', April 26  27, 2019, GeorgAugustUniversität 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 convectiondominated 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 convectiondominated equations and incompressible flow problems  A never ending story?, IndoGerman 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 convectiondominated problems, PIMSGermany 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, pressurerobustness and highorder 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, pressurerobustness and highorder methods, Technische Universität Darmstadt, Fachbereich Mathematik, August 28, 2019.

A. Linke, On highorder pressurerobust space discretisations, their advantages for incompressible high Renolds number generalised Beltrami flows and beyond, PIMSGermany Workshop on Discretization of Variational Eigenvalue and Flow Problems, June 24  26, 2019, Universität Heidelberg, June 26, 2019.

A. Linke, On highorder pressurerobust 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 highorder pressurerobust 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 pressurerobustness, coherent structures and vortexdominated flows, Leibniz MMS Days 2019, March 20  22, 2019, Universität Rostock , LeibnizInstitut 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, FriedrichAlexanderUniversität ErlangenNürnberg.

A. Linke, Pressurerobustness  A new criterion for the accuracy of incompressible NavierStokes 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 AdvectionDiffusion 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, GeorgAugustUniversität Göttingen, Institut für Numerische und Angewandte Mathematik, April 27, 2019.

CH. Merdon, A gradientrobust, wellbalanced 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, Pressurerobust finite element discretisations for the NavierStokes problem, Technische Universität Dresden, Fachbereich Mathematik, April 11, 2019.

CH. Merdon, Pressurerobust mixed finite element methods and refined a posteriori error control for the Stokes problem, GeorgAugustUniversität Göttingen, Institut für Numerische und Angewandte Mathematik, January 29, 2019.

CH. Merdon, Pressurerobustness in the discretisation of the NavierStokes equations, University of Twente, Institute of Nanotechnology, Enschede, Netherlands, September 30, 2019.

CH. Merdon, Pressurerobustness in the discretisation of the NavierStokes equations  An overview, 9th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium MS FE 125 ``Divergencefree and pressurerobust discretizations for the NavierStokes 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 electrolyteelectrode 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, Pressurerobustness in quasioptimal a priori estimates for the Stokes problem, Preprint no. arXiv:1906.03009, Cornell University Library, arXiv.org, 2019.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations