Publications
Articles in Refereed Journals

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), 115036, 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. 
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. 113, 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. 
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. Gajewski, C. Guhlke, P.K. Friz, 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 .

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: Proceedings of the 7th International Conference on Computational and Mathematical Biomedical Engineering (CMBE22), P. Nithiarasu, C. Vergara, eds., 1, 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: Proceedings of the 7th International Conference on Computational and Mathematical Biomedical Engineering (CMBE22), P. Nithiarasu, C. Vergara, eds., 2, pp. 648651.

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), IEEE Conference Publications Management Group, Piscataway, 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 con vectiondiffusion 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. 
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, Preprint no. 2933, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2933 .
Abstract, PDF (9978 kByte)
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. 
CH. Merdon, W. Wollner, Pressurerobustness in the context of optimal control, Preprint no. 2923, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2923 .
Abstract, PDF (4659 kByte)
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.
Talks, Poster

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.

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.

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, Leibniz MMS Days 2022; Parallel Session on Computational and Geophysical Fluid Dynamics, April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 26, 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.

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, tba, ISMRM Workshop on Magnetic Resonance Elastography, August 25  26, 2022.

P. Farrell, Datadriven solutions of illposed inverse problems arising from doping reconstruction in semiconductors, AI4Science Konferenz, 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  Part I of II (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 Network ''Mathematical Modeling and Simulation'' (Hybrid Event), April 25  27, 2022.
External Preprints

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. 2208.14217/12208.14217/30, Cornell University Library, arXiv.org, 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. 2204.07480, Cornell University Library, arXiv.org, 2022.

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

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

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 Library, arXiv.org, 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. 2206.02035, Cornell University Library, arXiv.org, 2022.

N. Ahmed, V. John, X. Li, Ch. Merdon, Infsup stabilized ScottVogelius pairs on general simplicial grids for NavierStokes equations, Preprint no. 2212.10909, Cornell University Library, arXiv.org, 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. 2206.01242, Cornell University Library, arXiv.org, 2022.
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