Publications
Articles in Refereed Journals

D. Abdel, N.E. Courtier, P. Farrell, Volume exclusion effects in perovskite charge transport modeling, Optical and Quantum Electronics, 55 (2023), pp. 884/1884/14, DOI 10.1007/s11082023051259 .
Abstract
Due to their flexible material properties, perovskite materials are a promising candidate for many semiconductor devices such as lasers, memristors, LEDs and solar cells. For example, perovskitebased solar cells have recently become one of the fastest growing photovoltaic technologies. Unfortunately, perovskite devices are far from commercialization due to challenges such as fast degradation. Mathematical models can be used as tools to explain the behavior of such devices, for example driftdiffusion equations portray the ionic and electric motion in perovskites. In this work, we take volume exclusion effects on ion migration within a perovskite crystal lattice into account. This results in the formulation of two different ionic current densities for such a driftdiffusion model  treating either the mobility or the diffusivity as densitydependent while the other quantity remains constant. The influence of incorporating each current density description into a model for a typical perovskite solar cell configuration is investigated numerically, through simulations performed using two different open source tools. 
D. Abdel, C. ChainaisHillairet, P. Farrell, M. Herda, Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells, IMA Journal of Numerical Analysis, (2023), pp. 140, DOI 10.1093/imanum/drad034 .
Abstract
In this paper, we consider a driftdiffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g. due to FermiDirac statistics). To incorporate volume exclusion effects, we rely on the FermiDirac integral of order −1 when modeling moving anionic vacancies within the perovskite layer which is sandwiched between electron and hole transport layers. After nondimensionalization, we first prove a continuous entropydissipation inequality for the model. Then, we formulate a corresponding twopoint flux finite volume scheme on Voronoi meshes and show an analogous discrete entropydissipation inequality. This inequality helps us to show the existence of a discrete solution of the nonlinear discrete system with the help of a corollary of Brouwer's fixed point theorem and the minimization of a convex functional. Finally, we verify our theoretically proven properties numerically, simulate a realistic device setup and show exponential decay in time with respect to the L^{2} error as well as a physically and analytically meaningful relative entropy. 
S. Katz, A. Caiazzo, V. John, Impact of viscosity modeling on the simulation of aortic blood flow, Journal of Computational and Applied Mathematics, 425 (2023), pp. 115036/1115036/18, DOI 10.1016/j.cam.2022.115036 .
Abstract
Modeling issues for the simulation of blood flow in an aortic coarctation are studied in this paper. From the physical point of view, several viscosity models for nonNewtonian fluids as well as a Newtonian fluid model will be considered. From the numerical point of view, two different turbulence models are utilized in the simulations. The impact of both, the physical and the numerical modeling, on clinically relevant biomarkers is investigated and compared. 
S. Katz, A. Caiazzo, B. Moreau, U. Wilbrandt, J. Brüning, L. Goubergrits, V. John, Impact of turbulence modeling on the simulation of blood flow in aortic coarctation, International Journal of Numerical Methods in Biomedical Engineering, 39 (2023), pp. e3695/1e3695/36, DOI 10.1002/cnm.3695 .
Abstract
Numerical simulations of pulsatile blood flow in an aortic coarctation require the use of turbulence modeling. This paper considers three models from the class of large eddy simulation (LES) models (Smagorinsky, Vreman, model) and one model from the class of variational multiscale models (residualbased) within a finite element framework. The influence of these models on the estimation of clinically relevant biomarkers used to assess the degree of severity of the pathological condition (pressure difference, secondary flow degree, normalized flow displacement, wall shear stress) is investigated in detail. The simulations show that most methods are consistent in terms of severity indicators such as pressure difference and stenotic velocity. Moreover, using secondorder velocity finite elements, different turbulence models might lead to considerably different results concerning other clinically relevant quantities such as wall shear stresses. These differences may be attributed to differences in numerical dissipation introduced by the turbulence models. 
F. Galarce Marín, K. Tabelow, J. Polzehl, Ch.P. Papanikas, V. Vavourakis, L. Lilaj, I. Sack, A. Caiazzo, Displacement and pressure reconstruction from magnetic resonance elastography images: Application to an in silico brain model, SIAM Journal on Imaging Sciences, 16 (2023), pp. 961027, DOI 10.1137/22M149363X .
Abstract
This paper investigates a data assimilation approach for noninvasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. Data assimilation is based on a parametrizedbackground data weak methodology, in which the state of the physical system tissue displacements and pressure fields is reconstructed from partially available data assuming an underlying poroelastic biomechanics model. For this purpose, a physicsinformed manifold is built by sampling the space of parameters describing the tissue model close to their physiological ranges, to simulate the corresponding poroelastic problem, and compute a reduced basis. Displacements and pressure reconstruction is sought in a reduced space after solving a minimization problem that encompasses both the structure of the reducedorder model and the available measurements. The proposed pipeline is validated using synthetic data obtained after simulating the poroelastic mechanics on a physiological brain. The numerical experiments demonstrate that the framework can exhibit accurate joint reconstructions of both displacement and pressure fields. The methodology can be formulated for an arbitrary resolution of available displacement data from pertinent images. It can also inherently handle uncertainty on the physical parameters of the mechanical model by enlarging the physicsinformed manifold accordingly. Moreover, the framework can be used to characterize, in silico, biomarkers for pathological conditions, by appropriately training the reducedorder model. A first application for the estimation of ventricular pressure as an indicator of abnormal intracranial pressure is shown in this contribution. 
C. ChainaisHillairet, R. Eymard, J. Fuhrmann, A monotone numerical flux for quasilinear convection diffusion equations, Mathematics of Computation, published online in June 2023, DOI 10.1090/mcom/3870 .

R. Araya, C. Cárcamo, A.H. Posa, A stabilized finite element method for the StokesTemperature coupled problem, Applied Numerical Mathematics. An IMACS Journal, 187 (2023), pp. 2449, DOI doi.org/10.1016/j.apnum.2023.02.002 .
Abstract
In this work, we introduce and analyze a new stabilized finite element scheme for the StokesTemperature coupled problem. This new scheme allows equal order of interpolation to approximate the quantities of interest, i.e. velocity, pressure, temperature, and stress. We analyze an equivalent variational formulation of the coupled problem inspired by the ideas proposed in [3]. The existence of the discrete solution is proved, decoupling the proposed stabilized scheme and using the help of continuous dependence results and Brouwer's theorem under the standard assumption of sufficiently small data. Optimal convergence is proved under classic regularity assumptions of the solution. Finally, we present some numerical examples to show the quality of our scheme, in particular, we compare our results with those coming from a standard reference in geosciences described in [38]. 
D. Budáč, V. Miloš, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Prediction of electrical conductivity of porous composites using a simplified Monte Carlo 3D equivalent electronic circuit network model: LSMYSZ case study, Electrochimica Acta, 457 (2023), pp. 142512/1142512/12, DOI doi.org/10.1016/j.electacta.2023.142512 .
Abstract
Multiphase electric charge conductors composed of materials with various properties are widely utilized in both research and industrial applications. The composite materials include porous electrodes and other components mainly applied in fuel cell and battery technologies. In this study, a simplified Monte Carlo equivalent electronic circuit (EEC) network model is presented. In comparison to similar models, the present EEC network model allows an accurate prediction of the electrical properties of such materials, thus saving timeconsuming experimental determination. The distinct feature of this EEC network model is that it requires only experimentally easily obtainable data as the input parameters: phase composition, porosity and bulk electrical conductivity of the individual constituents. During its run, the model generates a large number of artificial cubically shaped specimens based on random distribution of individual phases according to the input composition. Each of the specimens generated was modelled by a corresponding EEC network. The EEC networks were solved using Kirchhoff's laws, resulting in impedance response simulation for the prediction of composite conductivity values. The EEC network model was validated using lanthanum strontium manganite mixed with yttriastabilized zirconia. Excellent agreement was obtained between the experimentally determined and the calculated electrical conductivity for sample porosities of 0 to 60 %. Due to its variability, the EEC network model can be suitable for a wide range of practical applications. The presented approach has high potential to save an enormous amount of experimental effort, while maintaining sufficient accuracy, when designing corresponding multiphase electrode structures. 
R. Finn, M. O'Donovan, P. Farrell, J. Moatti, T. Streckenbach, Th. Koprucki, S. Schulz, Theoretical study of the impact of alloy disorder on carrier transport and recombination processes in deep UV (Al,Ga)N light emitters, Applied Physics Letters, 122 (2023), pp. 241104/1241104/7, DOI 10.1063/5.0148168 .
Abstract
Aluminum gallium nitride [(Al,Ga)N] has gained significant attention in recent years due to its potential for highly efficient light emitters operating in the deep ultraviolet (UV) range (<280 nm). However, given that current devices exhibit extremely low efficiencies, understand ing the fundamental properties of (Al,Ga)Nbased systems is of key importance. Here, using a multiscale simulation framework, we study the impact of alloy disorder on carrier transport, radiative and nonradiative recombination processes in a cplane Al 0.7 Ga0.3 N/Al0.8 Ga0.2 N quantum well embedded in a pn junction. Our calculations reveal that alloy fluctuations can open "percolative" pathways that promote transport for the electrons and holes into the quantum well region. Such an effect is neglected in conventional and widely used transport sim ulations. Moreover, we find that the resulting increased carrier density and alloy induced carrier localization effects significantly increase nonradiative AugerMeitner recombination in comparison to the radiative process. Thus, to suppress such nonradiative process and poten tially related material degradation, a careful design (wider well, multiquantum wells) of the active region is required to improve the effi ciency of deep UV light emitters. 
B. GarcíaArchilla, V. John, J. Novo, Second order error bounds for PODROM methods based on first order divided differences, Applied Mathematics Letters, 146 (2023), pp. 108836/1108836/7, DOI 10.1016/j.aml.2023.108836 .
Abstract
This note proves for the heat equation that using BDF2 as time stepping scheme in PODROM methods with snapshots based on difference quotients gives both the optimal second order error bound in time and pointwise estimates. 
B. GarcíaArchilla, V. John, J. Novo, PODROMs for incompressible flows including snapshots of the temporal derivative of the full order solution, SIAM Journal on Numerical Analysis, 61 (2023), pp. 13401368, DOI 10.1137/22M1503853 .
Abstract
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible NavierStokes equations by means of proper orthogonal decomposition (POD) methods. Our set of snapshots includes the velocity approximation at the initial time from a full order mixed finite element method (FOM) together with approximations to the time derivative at different times. The approximation at the initial velocity can be replaced by the mean value of the velocities at the different times so that when implementing the method to the fluctuations, as done mostly in practice, only approximations to the time derivatives are included in the set of snapshots. For the POD method we study the differences between projecting onto L2 and H1. In both cases pointwise in time error bounds can be proved. Including graddiv stabilization in both the FOM and the POD methods, error bounds with constants independent of inverse powers of the viscosity can be obtained. 
A. Jha, V. John, P. Knobloch, Adaptive grids in the context of algebraic stabilizations for convectiondiffusionreaction equations, SIAM Journal on Scientific Computing, 45 (2023), pp. B564B589, DOI 10.1137/21M1466360 .
Abstract
Three algebraically stabilized finite element schemes for discretizing convectiondiffusionreaction equations are studied on adaptively refined grids. These schemes are the algebraicflux correction (AFC) scheme with the Kuzmin limiter, the AFC scheme with the BarrenecheaJohnKnobloch limiter, and the recently proposed monotone upwindtype algebraically stabilizedmethod. Both conforming closure of the refined grids and grids with hanging vertices are considered.A nonstandard algorithmic step becomes necessary before these schemes can be applied on gridswith hanging vertices. The assessment of the schemes is performed with respect to the satisfactionof the global discrete maximum principle, the accuracy, e.g., smearing of layers, and the efficiency insolving the corresponding nonlinear problems. 
P. Ral, A.K. Giri, V. John, Instantaneous gelation and nonexistence of weak solutions for the OortHulstSafronov coagulation model, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 479 (2023), pp. 20220385/120220385/13, DOI 10.1098/rspa.2022.0385 .
Abstract
The possible occurrence of instantaneous gelation to the OortHulstSafronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the nonexistence of massconserving weak solutions. Finally, it is shown that for such kernels, there is no weak solution to the OHS coagulation equation at any time interval. 
V. John, P. Knobloch, U. Wilbrandt, A posteriori optimization of parameters in stabilized methods for convectiondiffusion problems  Part II, Journal of Computational and Applied Mathematics, 428 (2023), pp. 115167/1115167/17, DOI 10.1016/j.cam.2023.115167 .
Abstract
Extensions of algorithms for computing optimal stabilization parameters in finite element methods for convectiondiffusion equations are presented. These extensions reduce the dimension of the control space, in comparison to available methods, and thus address the long computing times of these methods. One method is proposed that considers only relevant mesh cells, another method that uses groups of mesh cells, and the combination of both methods is also studied. The incorporation of these methods within a gradientbased optimization procedure, via solving an adjoint problem, is explained. Numerical studies provide impressions on the gain of efficiency as well as on the loss of accuracy if control spaces with reduced dimensions are utilized. 
CH. Merdon, W. Wollner, Pressurerobustness in the context of optimal control, SIAM Journal on Control and Optimization, 61 (2023), pp. 342360, DOI 10.1137/22M1482603 .
Abstract
This paper studies the benefits of pressurerobust discretizations in the scope of optimal control of incompressible flows. Gradient forces that may appear in the data can have a negative impact on the accuracy of state and control and can only be correctly balanced if their L^{2}orthogonality onto discretely divergencefree test functions is restored. Perfectly orthogonal divergencefree discretizations or divergencefree reconstructions of these test functions do the trick and lead to much better analytic a priori estimates that are also validated in numerical examples. 
O. Pártl, U. Wilbrandt, J. Mua, A. Caiazzo, Reconstruction of flow domain boundaries from velocity data via multistep optimization of distributed resistance, Computers & Mathematics with Applications. An International Journal, 129 (2023), pp. 1133, DOI /10.1016/j.camwa.2022.11.006 .
Abstract
We reconstruct the unknown shape of a flow domain using partially available internal velocity measurements. This inverse problem is motivated by applications in cardiovascular imaging where motionsensitive protocols, such as phasecontrast MRI, can be used to recover threedimensional velocity fields inside blood vessels. In this context, the information about the domain shape serves to quantify the severity of pathological conditions, such as vessel obstructions. We consider a flow modeled by a linear Brinkman problem with a fictitious resistance accounting for the presence of additional boundaries. To reconstruct these boundaries, we employ a multistep gradientbased variational method to compute a resistance that minimizes the difference between the computed flow velocity and the available data. Afterward, we apply different postprocessing steps to reconstruct the shape of the internal boundaries. To limit the overall computational cost, we use a stabilized equalorder finite element method. We prove the stability and the wellposedness of the considered optimization problem. We validate our method on threedimensional examples based on synthetic velocity data and using realistic geometries obtained from cardiovascular imaging. 
F. Galarce Marín, D. Lombardi, O. Mula, State estimation with model reduction and shape variability: Application to biomedical problems, SIAM Journal on Scientific Computing, 44 (2022), pp. B805B833, DOI 10.1137/21M1430480 .
Abstract
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems are posed on certain organs or portions of the body which inevitably involve morphological variations. If one wants to provide fast reconstruction methods, the algorithms must take into account the geometric variability. We develop and analyze a method which allows to take this variability into account without needing any a priori knowledge on a parametrization of the geometrical variations. For this, we rely on morphometric techniques involving Multidimensional Scaling, and couple them with reconstruction algorithms that make use of reduced model spaces precomputed on a database of geometries. We prove the potential of the method on a synthetic test problem inspired from the reconstruction of blood flows and quantities of medical interest with Doppler ultrasound imaging. 
P. Vágner, M. Pavelka, J. Fuhrmann, V. Klika, A multiscale thermodynamic generalization of MaxwellStefan diffusion equations and of the dusty gas model, International Journal of Heat and Mass Transfer, 199 (2022), pp. 123405/1123405/14, DOI 10.1016/j.ijheatmasstransfer.2022.123405 .
Abstract
Despite the fact that the theory of mixtures has been part of nonequilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only diffusionlike processes take place), the question how to properly describe homogeneous mixtures that flow with multiple independent velocities that still possess some inertia (before mechanical equilibrium is reached) is still open. Moreover, the mixtures can have several temperatures before they relax to a common value. In this paper, we derive a theory of mixtures from Hamiltonian mechanics in interaction with electromagnetic fields. The resulting evolution equations are then reduced to the case with only one momentum (classical irreversible thermodynamics), providing a generalization of the MaxwellStefan diffusion equations. In a next step, we reduce that description to the mechanical equilibrium (no momentum) and derive a nonisothermal variant of the dusty gas model. These reduced equations are solved numerically, and we illustrate the results on effciency analysis, showing where in a concentration cell effciency is lost. Finally, the theory of mixtures identifies the temperature difference between constituents as a possible new source of the Soret coeffcient. For the sake of clarity, we restrict the presentation to the case of binary mixtures; the generalization is straightforward. 
M. Coghi, W. Dreyer, P.K. Friz, P. Gajewski, C. Guhlke, M. Maurelli, A McKeanVlasov SDE and particle system with interaction from reflecting boundaries, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 22512294, DOI 10.1137/21M1409421 .

D. Bothe, W. Dreyer, P.É. Druet, Multicomponent incompressible fluids  An asymptotic study, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, published online on 14.01.2022, DOI 10.1002/zamm.202100174 .
Abstract
This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure. Here we are confronted with two problems:(i) Our study shows that the physical system at hand cannot remain incompressible for arbitrary large deviations from a reference pressure unless its volume is linear in the composition. (ii) As a consequence of the 2nd law of thermodynamics, the incompressible limit implies that the molar volume becomes independent of temperature as well. Most applications, however, reveal the nonappropriateness of this property. According to our mathematical treatment, the free energy as a function of temperature and partial masses tends to a limit in the sense of epi or Gammaconvergence. In the context of the first problem, we study the mixing of two fluids to compare the linearity with experimental observations. The second problem will be treated by considering the asymptotic behavior of both a general inequality relating thermal expansion and compressibility and a PDEsystem relying on the equations of balance for partial masses, momentum and the internal energy.

B. Gaudeul, J. Fuhrmann, Entropy and convergence analysis for two finite volume schemes for a NernstPlanckPoisson system with ion volume constraints, Numerische Mathematik, 151 (2022), pp. 99149, DOI 10.1007/s0021102201279y .
Abstract
In this paper, we consider a driftdiffusion system with crosscoupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the selfconsistent electric field maintained by the ions and described by a Poisson equation. We design two finite volume schemes based on different formulations of the fluxes. We also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence proof is proposed for nondegenerate solutions. Numerical experiments show the behavior of these schemes. 
V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Generalized PoissonNernstPlanckbased physical model of the O$_2$ I LSM I YSZ electrode, Journal of The Electrochemical Society, 169 (2022), pp. 044505/1044505/17, DOI 10.1149/19457111/ac4a51 .
Abstract
The paper presents a generalized PoissonNernstPlanck model of an yttriastabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic equations with results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and O^{2} from the assumption of shared ones. Furthermore, we discern massaction kinetics models from exponential kinetics models. 
M. O'Donovan, P. Farrell, T. Streckenbach, Th. Koprucki, S. Schulz, Multiscale simulations of unipolar hole transport in (In,Ga)N quantum well systems, Optical and Quantum Electronics, 54 (2022), pp. 405/1405/23, DOI 10.1007/s11082022037522 .
Abstract
Understanding the impact of the alloy microstructure on carrier transport becomes important when designing IIInitridebased LED structures. In this work, we study the impact of alloy fluctuations on the hole carrier transport in (In,Ga)N single and multiquantum well systems. To disentangle hole transport from electron transport and carrier recombination processes, we focus our attention on unipolar (pip) systems. The calculations employ our recently established multiscale simulation framework that connects atomistic tightbinding theory with a macroscale driftdiffusion model. In addition to alloy fluctuations, we pay special attention to the impact of quantum corrections on hole transport. Our calculations indicate that results from a virtual crystal approximation present an upper limit for the hole transport in a pip structure in terms of the currentvoltage characteristics. Thus we find that alloy fluctuations can have a detrimental effect on hole transport in (In,Ga)N quantum well systems, in contrast to unipolar electron transport. However, our studies also reveal that the magnitude by which the random alloy results deviate from virtual crystal approximation data depends on several factors, e.g. how quantum corrections are treated in the transport calculations. 
A.F.M. TER Elst, A. Linke, J. Rehberg, On the numerical range of sectorial forms, Pure and Applied Functional Analysis, 7 (2022), pp. 19311940.
Abstract
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. 
M. Demir, C. Aytekin, K. Songül, Time filtered second order backward Euler method for EMAC formulation of NavierStokes equations, Journal of Mathematical Analysis and Applications, 516 (2022), pp. 126562/112656/21, DOI 10.1016/j.jmaa.2022.126562 .

D. FrerichsMihov, V. John, On a technique for reducing spurious oscillations in DG solutions of convectiondiffusion equations, Applied Mathematics Letters, 129 (2022), pp. 107969/1107969/7, DOI 10.1016/j.aml.2022.107969 .
Abstract
This note studies a generalization of a postprocessing technique and a novel method inspired by the same technique which significantly reduce spurious oscillations in discontinuous Galerkin solutions of convectiondiffusion equations in the convectiondominated regime. 
V. John, P. Knobloch, O. Pártl, A numerical assessment of finite element discretizations for convectiondiffusionreaction equations satisfying discrete maximum principles, Computational Methods in Applied Mathematics, published online on 30.09.2022, DOI 10.1515/cmam20220125 .
Abstract
Numerical studies are presented that investigate finite element methods satisfying discrete maximum principles for convectiondiffusionreaction equations. Two linear methods and several nonlinear schemes, some of them proposed only recently, are included in these studies, which consider a number of twodimensional examples. The evaluation of the results examines the accuracy of the numerical solutions with respect to quantities of interest, like layer widths, and the efficiency of the simulations. 
V. John, P. Knobloch, On algebraically stabilized schemes for convectiondiffusionreaction problems, Numerische Mathematik, 152 (2022), pp. 553585, DOI 10.1007/s00211022013259 .

V. John, B. Moreau, J. Novo, Error analysis of a SUPGstabilized PODROM method for convectiondiffusionreaction equations, Computers & Mathematics with Applications. An International Journal, 122 (2022), pp. 4860, DOI 10.1016/j.camwa.2022.07.017 .
Abstract
A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convectiondiffusionreaction equations. The streamlineupwind PetrovGalerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPGROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPGROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. Numerical studies illustrate the performance of the SUPGROM method.
Contributions to Collected Editions

C. Belponer, A. Caiazzo, L. Heltai, L.O. Müller, D. Peterseim, Multiscale and homogenized modeling of vascular tissues, in: 7th International Conference on Computational & Mathematical Biomedical Engineering (CMBE22), 27th  29th June, 2022, Milan, Italy, P. Nithiarasu, C. Vergara, eds., 1, CMBE, Cardiff, UK, 2022, pp. 2931.

F. Galarce Marín, K. Tabelow, J. Polzehl, Ch. Panagiotis, V. Vavourakis, I. Sack, A. Caiazzo, Assimilation of magnetic resonance elastography displacement data in brain tissues, in: 7th International Conference on Computational & Mathematical Biomedical Engineering (CMBE22), 27th  29th June, 2022, Milan, Italy, P. Nithiarasu, C. Vergara, eds., 2, CMBE, Cardiff, UK, 2022, pp. 648651.

Y. Hadjimichael, O. Marquardt, Ch. Merdon, P. Farrell, Band structures in highly strained 3D nanowires, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2022), Turin, Italy, 2022, J. Piprek, Bardella Paolo, eds., IEEE, 2022, pp. 119120, DOI 10.1109/NUSOD54938.2022.9894837 .

M. O'Donovan, P. Farrell, T. Streckenbach, Th. Koprucki, S. Schulz, Carrier transport in (In,Ga)N quantum well systems: Connecting atomistic tightbinding electronic structure theory to driftdiffusion simulations, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), Turin, Italy, 2022, J. Piprek, P. Bardella, eds., IEEE, 2022, pp. 9798, DOI 10.1109/NUSOD54938.2022.9894745 .
Preprints, Reports, Technical Reports

D. FrerichsMihov, L. Henning, V. John, Using deep neural networks for detecting spurious oscillations in discontinuous Galerkin solutions of convectiondominated convectiondiffusion equations, Preprint no. 2986, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2986 .
Abstract, PDF (7271 kByte)
Standard discontinuous Galerkin (DG) finite element solutions to convectiondominated convectiondiffusion equations usually possess sharp layers but also exhibit large spurious oscillations. Slope limiters are known as a postprocessing technique to reduce these unphysical values. This paper studies the application of deep neural networks for detecting mesh cells on which slope limiters should be applied. The networks are trained with data obtained from simulations of a standard benchmark problem with linear finite elements. It is investigated how they perform when applied to discrete solutions obtained with higher order finite elements and to solutions for a different benchmark problem.
Talks, Poster

S. Katz, Impact of turbulence modeling on the full and reduced simulations of aortic blood flow, 22nd Computational Fluids Conference (CFC 2023), April 25  28, 2023, International Association for Computational Mechanics (IACM), Cannes, France, April 28, 2023.

Y. Hadjimichael, An energybased finitestrain constitutive model for bent heterostructured materials, GAMM 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, May 30  June 2, 2023, Technische Universität Dresden, June 2, 2023.

D. Runge, Massconservative reduced basis approach for convectiondiffusion equations with nonlinear boundary reaction conditions, Leibniz MMS Days 2023, Leibniz Network "Mathematical Modeling and Simulation", Leibniz Institute for Agricultural Engineering and Bioeconomy Potsdam (ATB), Potsdam, April 18, 2023.

M. Demir, Subgrid artificial viscosity modelling based defectdeferred correction method for fluidfluid interaction, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), September 4  8, 2023, Instituto Superior Técnico, Lisboa, Portugal, September 7, 2023.

A. Caiazzo, Multiscale and reducedorder modeling for poroelasticity, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), September 4  8, 2023, Instituto Superior Técnico, Lisboa, Portugal.

P. Farrell, Modeling and numerical simulation of twodimensional TMDC memristive devices, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokyo, Japan, August 20  25, 2023.

P. Farrell, Modeling and numerical simulation of twodimensional TMDC memristive devices, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Japan, August 20  25, 2023.

P. Farrell, Modeling and numerical simulation of twodimensional memristive devices, 22nd European Consortium for Mathematics in Industry (ECMI) Conference on Industrial and Applied Mathematics, June 26  30, 2023, Wrocław University of Science and Technology, Poland.

P. Farrell, Device physics characterization and interpretation in perovskite and organic materials (DEPERO), October 3  5, 2023, Eidgenössische Technische Hochshcule Zürich, nanoGe, Switzerland.

D. FrerichsMihov, On deep learning techniques for solving convectiondominated convectiondiffusion equations, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium 00747 ''Analysis and Numerics on Deep Learning Based Methods for Solving PDEs'', August 20  25, 2023, Waseda University, Tokyo, Japan, August 23, 2023.

D. FrerichsMihov, Using deep learning techniques for solving convectiondominated convectiondiffusion equations, 22nd Computational Fluids Conference (CFC 2023), April 25  28, 2023, International Association for Computational Mechanics (IACM), Cannes, France, April 28, 2023.

J. Fuhrmann, Thermodynamically consistent finite volume schemes for electrolyte simulations, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), August 20  25, 2023, Waseda University, Tokyo, Japan, August 22, 2023.

J. Fuhrmann, VORONOIFVM.JL  a multiphysics finite volume solver for elliptic and parabolic systems, SIAM Conference on Computational Science and Engineering (CSE23), Minisymposium MS67 ``Research Software Engineering with Julia  Part II of II'', February 26  March 3, 2023, Society for Industrial and Applied Mathematic, Amsterdam, Netherlands, February 27, 2023.

V. John, A SUPGstabilized PODROM method for convectiondiffusionreaction problems (online talk), Numerical Analysis of Galerkin ROMs seminar series (Online Event), NA GROMS, February 28, 2023.

V. John, On slope limiters in discontinuous Galerkin discretizations of convectiondiffusion problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Minisymposium MS06 ' 'Theoretical and computational aspects of the discontinuous Galerkin method' ', September 4  8, 2023, Instituto Superior Técnico, Lisboa, Portugal, September 5, 2023.

V. John, Finite element methods respecting the discrete maximum principle for convectiondiffusion equations I, 19th Workshop on Numerical Methods for Problems with Layer Phenomena, Charles University, Faculty of Mathematics and Physics, Department of Numerical Mathematics, Prague, Czech Republic, May 26, 2023.

V. John, On recent topics in the finite element analysis of convectiondiffusion problems (online talk), Numerical Analysis Seminar (Hybrid Event), University of Waterloo, Applied Mathematics, Canada, April 11, 2023.

CH. Merdon, RaviartThomas enriched ScottVogelius finite element methods for the NavierStokes equations(online talk), City University of Hong Kong, Department of Mathematics, Hong Kong, January 18, 2023.

CH. Merdon, RaviartThomas enriched ScottVogelius FEM for the NavierStokes equations, European Finite Element Fair 2023 (EFEF2023), Department of Mathematics University of Twente (DAMUT), Enschede, Netherlands, May 10, 2023.

CH. Merdon, RaviartThomas enriched ScottVogelius finite element methods for the NavierStokes equations, GAMM 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, May 30  June 2, 2023, Technische Universität Dresden, June 2, 2023.

CH. Merdon, RaviartThomasenriched ScottVogelius finite element methods for the Stokes equations on general meshes, The 29th Biennial Numerical Analysis Conference 2023, June 27  30, 2023, University of Strathclyde, Department of Mathematics and Statistics, Glasgow, UK, June 27, 2023.

O. Pártl, Finite element methods respecting the discrete maximum principle for convectiondiffusion equations III, 19th Workshop on Numerical Methods for Problems with Layer Phenomena, Charles University, Faculty of Mathematics and Physics, Department of Numerical Mathematics, Prague, Czech Republic, May 26, 2023.

O. Pártl, Reconstruction of flow domain boundaries from velocity data via multistep optimization of distributed resistance, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), September 4  8, 2023, Instituto Superior Técnico, Lisboa, Portugal.

C. Belponer, An algorithmic approach for solving optimization problems with probabilistic/robust (probust) constraints (online talk), Winter School ``Multiple Scales in Mathematics and Engineering'', March 7  11, 2022, Universität Augsburg.

C. Belponer, Multiscale and homogenized modeling of vascular tissues, 7th International Conference on Computational and Mathematical Biomedical Engineering (CMBE22), June 27  29, 2022, Politecnico di Milano, Milan, Italy, June 27, 2022.

C. Belponer, Multiscale and homogenized modeling of vascular tissues, Workshop on Numerical Methods and Analysis in CFD, July 5  8, 2022, WIAS Berlin, July 6, 2022.

CH. Keller, J. Fuhrmann, M. Landstorfer, B. Wagner, Development of an ionchannel modelframework for invitro assisted interpretation of current voltage relations, MATH+Day 2022, Technische Universität Berlin, November 18, 2022.

F. Galarce Marin, Estimation of displacement and pressure fields from magnetic resonance elastography data in brain tissues, The SIAM Conference on Imaging Science (IS22) (Online Event), March 21  25, 2022, Society for Industrial and Applied Mathematic, Philadelphia, USA, March 22, 2022.

F. Galarce Marín, Inverse problems on nonparametric domains. Flow reconstruction from medical data using non linear dimensionality reduction, Workshop on Numerical Methods and Analysis in CFD, July 5  8, 2022, WIAS Berlin, July 7, 2022.

F. Galarce Marín, Pressure estimation in brain tissues from magnetic resonance elastography, 7th International Conference on Computational and Mathematical Biomedical Engineering (CMBE22), June 27  29, 2022, Politecnico di Milano, Milan, Italy, June 27, 2022.

F. Galarce Marín, Pressure estimation in physiological brain geometry from magnetic resonance elastography data, VPH 2022 Conference Virtual Physiological Human, September 6  9, 2022, University of Porto, Portugal, September 7, 2022.

S. Katz, Blood flow simulations and the sensitivity of quantities of interest to numerical modeling, 8th European Seminar on Computing (ESCO 2022), June 13  16, 2022, University of West Bohemia, Pilsen, Czech Republic, June 14, 2022.

S. Katz, Blood flow simulations and the sensitivity of quantities of interest to numerical modeling, Leibniz MMS Days 2022; Parallel Session on Computational and Geophysical Fluid Dynamics, April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 26, 2022.

CH. Merdon, Infsup stabilized ScottVogelius pairs on general simplicial grids by RaviartThomas enrichment, Workshop on Numerical Methods and Analysis in CFD, July 5  8, 2022, WIAS Berlin, July 7, 2022.

A. Caiazzo, Displacement & pressure reconstruction from MRE images in an in silico brain model, ISMRM Workshop on Magnetic Resonance Elastography, Charité, Berlin, August 25  26, 2022.

P. Farrell, Datadriven solutions of illposed inverse problems arising from doping reconstruction in semiconductors, AI4Science 2022 : AI for Science, NASSMA Workshop, Rabat, Morocco, December 12  16, 2022.

D. FrerichsMihov, A really pressurerobust virtual element method for the Stokes problem, 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 22), June 5  9, 2022, Nordic Association of Computational Mechanics, Oslo, Norway, June 7, 2022.

D. FrerichsMihov, On reducing spurious oscillations in discontinuous Galerkin methods for convectiondiffusion equations, Workshop on Numerical Methods and Analysis in CFD, July 5  8, 2022, WIAS Berlin, July 6, 2022.

D. FrerichsMihov, On reducing spurious oscillations in discontinuous Galerkin methods for convectiondiffusion equations, Leibniz MMS Days 2022; Parallel Session on Computational and Geophysical Fluid Dynamics, April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 26, 2022.

J. Fuhrmann, The Julia Programming Language: an overview, Leibniz MMS Days 2022, April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 27, 2022.

J. Fuhrmann, The Julia programming language: An overview (hybrid talk), Leibniz Network ''Mathematical Modeling and Simulation'' (Hybrid Event), April 25  27, 2022, Potsdam Institute for Climate Impact Research, April 26, 2022.

J. Fuhrmann, n.n., 1st MaRDI Workshop on Scientific Computing, October 26  28, 2022, Westfälische WilhelmsUniversität Münster.

J. Fuhrmann , tba, 31st Topical Meeting of the International Society of Electrochemistry Meeting topic: "Theory and Computation in Electrochemistry: Seeking Synergies in Methods, Materials and Systems", May 15  19, 2022, RheinischWestfälische Technische Hochschule, May 16, 2022.

V. John, Finite element methods respecting the discrete maximum principle for convectiondiffusion equations I, International Conference on Boundary and Interior Layers, November 28  December 2, 2022, Universidad de Buenos Aires, Argentina, December 1, 2022.

V. John, On the optimization of stabilization parameters, 18th Workshop on Numerical Methods for Problems with Layer Phenomena, March 24  26, 2022, FernUniversität in Hagen, March 25, 2022.

V. John, Finite element methods respecting the discrete maximum principle for convectiondiffusion equations I, Chemnitz Finite Element Symposium 2022, September 15  17, 2022, Universität der Bundeswehr München, Herrsching, September 16, 2022.

CH. Merdon, A gradientrobust wellbalanced scheme for the compressible NavierStokes problem, 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 22), MS142: Structurepreserving Finite Element Methods in Computational Fluid Dynamics, June 5  9, 2022, Nordic Association of Computational Mechanics, Oslo, Norway, June 7, 2022.

CH. Merdon, A novel gradientrobust, wellbalanced discretisation for the compressible Stokes problem (hybrid talk), Leibniz Network ''Mathematical Modeling and Simulation'', Parallel Session on Computational and Geophysical Fluid Dynamics (Hybrid Event), April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 26, 2022.

CH. Merdon, Recent advances for pressurerobust discretisations of the incompressible NavierStokes equations (online talk), SIAM Annual Meeting 2022, MS87: ``Recent Developments in Mathematical Analysis and Numerics for Incompressible Flow and Related Problems (Hybrid Event)'', July 11  15, 2022, David L. Lawrence Convention Center, Pennsylvania, USA, July 14, 2022.

CH. Merdon, Recent advances in pressurerobust finite element methods (online talk), 15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics (Online Event), July 31  August 5, 2022, Japan Convention Services, Congress Secretariat, Yokohama, Japan, August 2, 2022.

O. Pártl, Reconstruction of flow domain boundaries from velocity data via multistep optimization of distributed resistance, Workshop on Numerical Methods and Analysis in CFD, July 5  8, 2022, WIAS Berlin, July 8, 2022.

U. Wilbrandt, ParMooN  Recent developments and application, Leibniz MMS Days (Hybrid Event), Potsdam, April 25  27, 2022.
External Preprints

R. Araya, A. Caiazzo, F. Chouly, Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche, Preprint no. hal04077986, Hyper Articles en Ligne (HAL), 2023.
Abstract
We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Wellposedness of the discrete problem and optimal convergence rates are established, and illustrated with various numerical experiments. 
R. Finn, M. O'Donovan, P. Farrell, J. Moatti, T. Streckenbach, Th. Koprucki, S. Schulz, Theoretical study of the impact of alloy disorder on carrier transport and recombination processes in deep UV (Al, Ga)N light emitters, Preprint no. hal04037215, Hyper Articles en Ligne (HAL), 2023.
Abstract
Aluminium gallium nitride ((Al,Ga)N) has gained significant attention in recent years due to its potential for highly efficient light emitters operating in the deep ultraviolet (UV) range (< 280 nm). However, given that current devices exhibit extremely low efficiencies, understanding the fundamental properties of (Al,Ga)Nbased systems is of key importance. Here, using a multiscale simulation framework, we study the impact of alloy disorder on carrier transport, radiative and nonradiative recombination processes in a cplane Al0.7Ga0.3N/Al0.8Ga0.2N quantum well embedded in a pin junction. Our calculations reveal that alloy fluctuations can open "percolative" pathways that promote transport for the electrons and holes into the quantum well region. Such an effect is neglected in conventional, and widely used transport simulations. Moreover, we find also that the resulting increased carrier density and alloy induced carrier localization effects significantly increase nonradiative AugerMeitner recombination in comparison to the radiative process. Thus, to avoid such nonradiative process and potentially related material degradation, a careful design (wider well, multi quantum wells) of the active region is required to improve the efficiency of deep UV light emitters. 
B. GarcíaArchilla, V. John, S. Katz, J. Novo, PODROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure, Preprint no. arXiv:2304.08313, Cornell University, 2023, DOI 10.48550/arXiv.2304.08313 .
Abstract
Reduced order methods (ROMs) for the incompressible NavierStokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed finite element method (FOM). In addition, the set of snapshots contains the mean velocity of the FOM. Both the FOM and the PODROM are equipped with a graddiv stabilization. A velocity error analysis for this method can be found already in the literature. The present paper studies two different procedures to compute approximations to the pressure and proves error bounds for the pressure that are independent of inverse powers of the viscosity. Numerical studies support the analytic results and compare both methods. 
B. Spetzler, D. Abdel, F. Schwierz, M. Ziegler, P. Farrell, The role of mobile point defects in twodimensional memristive devices, Preprint no. arXiv:2304.06527, Cornell University, 2023, DOI 10.48550/arXiv.2304.06527 .
Abstract
Twodimensional (2D) layered transition metal dichalcogenides (TMDCs) are promising memristive materials for neuromorphic computing systems as they could solve the problem of the excessively high energy consumption of conventional von Neumann computer architectures. Despite extensive experimental work, the underlying switching mechanisms are still not understood, impeding progress in material and device functionality. This study reveals the dominant role of mobile defects in the switching dynamics of 2D TMDC materials. The switching process is governed by the formation and annihilation dynamics of a local vacancy depletion zone. Moreover, minor changes in the interface potential barriers cause fundamentally different device behavior previously thought to originate from multiple mechanisms. The key mechanisms are identified with a charge transport model for electrons, holes, and ionic point defects, including imagechargeinduced Schottky barrier lowering (SBL). The model is validated by comparing simulations to measurements for various 2D MoS2based devices, strongly corroborating the relevance of vacancies in TMDC devices and offering a new perspective on the switching mechanisms. The insights gained from this study can be used to extend the functional behavior of 2D TMDC memristive devices in future neuromorphic computing applications. 
P. Farrell, J. Moatti, M. O'Donovan, S. Schulz, Th. Koprucki, Importance of satisfying thermodynamic consistency in light emitting diode simulations, Preprint no. hal04012467, Hyper Articles en Ligne (HAL), 2023.
Abstract
We show the importance of using a thermodynamically consistent flux discretization when describing driftdiffusion processes within light emitting diode simulations. Using the classical ScharfetterGummel scheme with FermiDirac statistics is an example of such an inconsistent scheme. In this case, for an (In,Ga)N multi quantum well device, the Fermi levels show steep gradients on one side of the quantum wells which are not to be expected. This result originates from neglecting diffusion enhancement associated with FermiDirac statistics in the numerical flux approximation. For a thermodynamically consistent scheme, such as the SEDAN scheme, the spikes in the Fermi levels disappear. We will show that thermodynamic inconsistency has far reaching implications on the currentvoltage curves and recombination rates. 
S. Katz, A. Caiazzo, B. Moreau, U. Wilbrandt, J. Brüning, L. Goubergrits, V. John, Impact of turbulence modeling on the simulation of blood flow in aortic coarctation, Preprint no. arXiv:2208.14217, Cornell University, 2022, DOI 10.48550/arXiv.2208.14217 .

G.R. Barrenechea, V. John, P. Knobloch, Finite element methods respecting the discrete maximum principle for convectiondiffusion equations, Preprint no. arXiv:2204.07480, Cornell University, 2022, DOI 10.48550/arXiv.2204.07480 .

B. GarcíaArchilla, V. John, J. Novo, PODROMs for incompressible flows including snapshots of the temporal derivative of the full order solution, Preprint no. arXiv:2206.09123, Cornell University, 2022, DOI 10.48550/arXiv.2206.09123 .

A. Jha, V. John, P. Knobloch, Adaptive grids in the context of algebraic stabilizations for convectiondiffusionreaction equations, Preprint no. arXiv:2007.08405, Cornell University, 2022, DOI 10.48550/arXiv.2007.08405 .

M. O'Donovan, P. Farrell, J. Moatti, T. Streckenbach, Th. Koprucki, S. Schulz, Impact of random alloy fluctuations on the carrier distribution in multicolor (In,Ga)N/GaN quantum well systems, Preprint no. arXiv.2209.11657, Cornell University, 2022, DOI 10.48550/arXiv.2209.11657 .
Abstract
In this work, we study the impact that random alloy fluctuations have on the distribution of electrons and holes across the active region of a (In,Ga)N/GaN multiquantum well based light emitting diode (LED). To do so, an atomistic tightbinding model is employed to account for alloy fluctuations on a microscopic level and the resulting tightbinding energy landscape forms input to a driftdiffusion model. Here, quantum corrections are introduced via localization landscape theory and we show that when neglecting alloy disorder our theoretical framework yields results similar to commercial software packages that employ a selfconsistent SchroedingerPoissondriftdiffusion solver. Similar to experimental studies in the literature, we have focused on a multiquantum well system where two of the three wells have the same In content while the third well differs in In content. By changing the order of wells in this multicolor quantum well structure and looking at the relative radiative recombination rates of the different emitted wavelengths, we (i) gain insight into the distribution of carriers in such a system and (ii) can compare our findings to trends observed in experiment. Our results indicate that the distribution of carriers depends significantly on the treatment of the quantum well microstructure. When including random alloy fluctuations and quantum corrections in the simulations, the calculated trends in the relative radiative recombination rates as a function of the well ordering are consistent with previous experimental studies. The results from the widely employed virtual crystal approximation contradict the experimental data. Overall, our work highlights the importance of a careful and detailed theoretical description of the carrier transport in an (In,Ga)N/GaN multiquantum well system to ultimately guide the design of the active region of IIINbased LED structures. 
P. Ral, A.K. Giri, V. John, Instantaneous gelation and nonexistence for the OortHulstSafronov coagulation model, Preprint no. arXiv:2206.02035, Cornell University, 2022, DOI 10.48550/arXiv.2206.02035 .

N. Ahmed, V. John, X. Li, Ch. Merdon, Infsup stabilized ScottVogelius pairs on general simplicial grids for NavierStokes equations, Preprint no. arXiv:2212.10909, Cornell University, 2022, DOI 10.48550/arXiv.2212.10909 .

V. John, X. Li, Ch. Merdon, H. Rui, Infsup stabilized ScottVogelius pairs on general simplicial grids by RaviartThomas enrichment, Preprint no. arXiv:2206.01242, Cornell University, 2022, DOI 10.48550/arXiv.2206.01242 .
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