Numerische Mathematik und Wissenschaftliches Rechnen

Publikationen

Artikel in Referierten Journalen

• 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. 115036/1--115036/18, 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 non-Newtonian 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. e3695/1--e3695/36, 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 (residual-based) 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 second-order 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.

• R. Araya, C. Cárcamo, A.H. Posa, A stabilized finite element method for the Stokes--Temperature coupled problem, Applied Numerical Mathematics. An IMACS Journal, 187 (2023), pp. 24--49, 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 Stokes--Temperature 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: LSM--YSZ case study, Electrochimica Acta, 457 (2023), pp. 142512/1--142512/12, 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 time-consuming 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 yttria-stabilized 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.

• P. Ral, A.K. Giri, V. John, Instantaneous gelation and non-existence of weak solutions for the Oort--Hulst--Safronov coagulation model, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 479 (2023), pp. 20220385/1--20220385/13, DOI 10.1098/rspa.2022.0385 .
  Abstract
  The possible occurrence of instantaneous gelation to the Oort--Hulst--Safronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the non-existence of mass-conserving 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 convection-diffusion problems -- Part II, Journal of Computational and Applied Mathematics, 428 (2023), pp. 115167/1--115167/17, DOI 10.1016/j.cam.2023.115167 .
  Abstract
  Extensions of algorithms for computing optimal stabilization parameters in finite element methods for convection-diffusion 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 gradient-based 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 multi-step optimization of distributed resistance, Computers & Mathematics with Applications. An International Journal, 129 (2023), pp. 11--33, 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 motion-sensitive protocols, such as phase-contrast MRI, can be used to recover three-dimensional 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 multi-step gradient-based variational method to compute a resistance that minimizes the difference between the computed flow velocity and the available data. Afterward, we apply different post-processing steps to reconstruct the shape of the internal boundaries. To limit the overall computational cost, we use a stabilized equal-order finite element method. We prove the stability and the well-posedness of the considered optimization problem. We validate our method on three-dimensional 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. B805--B833, 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 pre-computed 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 Maxwell--Stefan diffusion equations and of the dusty gas model, International Journal of Heat and Mass Transfer, 199 (2022), pp. 123405/1--123405/14, DOI 10.1016/j.ijheatmasstransfer.2022.123405 .
  Abstract
  Despite the fact that the theory of mixtures has been part of non-equilibrium 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 diffusion-like 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 Maxwell-Stefan diffusion equations. In a next step, we reduce that description to the mechanical equilibrium (no momentum) and derive a non-isothermal 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 McKean--Vlasov SDE and particle system with interaction from reflecting boundaries, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 2251--2294, 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 non-appropriateness 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 Gamma--convergence. 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 PDE-system 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 Nernst--Planck--Poisson system with ion volume constraints, Numerische Mathematik, 151 (2022), pp. 99--149, DOI 10.1007/s00211-022-01279-y .
  Abstract
  In this paper, we consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent 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 non-degenerate solutions. Numerical experiments show the behavior of these schemes.

• V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Generalized Poisson--Nernst--Planck-based physical model of the O$_2$ I LSM I YSZ electrode, Journal of The Electrochemical Society, 169 (2022), pp. 044505/1--044505/17, DOI 10.1149/1945-7111/ac4a51 .
  Abstract
  The paper presents a generalized Poisson--Nernst--Planck model of an yttria-stabilized 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 mass-action kinetics models from exponential kinetics models.

• M. O'Donovan, P. Farrell, T. Streckenbach, Th. Koprucki, S. Schulz, Multiscale simulations of uni-polar hole transport in (In,Ga)N quantum well systems, Optical and Quantum Electronics, 54 (2022), pp. 405/1--405/23, DOI 10.1007/s11082-022-03752-2 .
  Abstract
  Understanding the impact of the alloy micro-structure on carrier transport becomes important when designing III-nitride-based LED structures. In this work, we study the impact of alloy fluctuations on the hole carrier transport in (In,Ga)N single and multi-quantum well systems. To disentangle hole transport from electron transport and carrier recombination processes, we focus our attention on uni-polar (p-i-p) systems. The calculations employ our recently established multi-scale simulation framework that connects atomistic tight-binding theory with a macroscale drift-diffusion 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 p-i-p structure in terms of the current-voltage 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 uni-polar 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. 1931--1940.
  Abstract
  We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H^∞-angle for the H^∞-calculus on 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 Navier--Stokes equations, Journal of Mathematical Analysis and Applications, 516 (2022), pp. 126562/1--12656/21, DOI 10.1016/j.jmaa.2022.126562 .

• D. Frerichs-Mihov, V. John, On a technique for reducing spurious oscillations in DG solutions of convection-diffusion equations, Applied Mathematics Letters, 129 (2022), pp. 107969/1--107969/7, DOI 10.1016/j.aml.2022.107969 .
  Abstract
  This note studies a generalization of a post-processing technique and a novel method inspired by the same technique which significantly reduce spurious oscillations in discontinuous Galerkin solutions of convection-diffusion equations in the convection-dominated regime.

• V. John, P. Knobloch, O. Pártl, A numerical assessment of finite element discretizations for convection-diffusion-reaction equations satisfying discrete maximum principles, Computational Methods in Applied Mathematics, published online on 30.09.2022, DOI 10.1515/cmam-2022-0125 .
  Abstract
  Numerical studies are presented that investigate finite element methods satisfying discrete maximum principles for convection-diffusion-reaction equations. Two linear methods and several nonlinear schemes, some of them proposed only recently, are included in these studies, which consider a number of two-dimensional 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 convection-diffusion-reaction problems, Numerische Mathematik, 152 (2022), pp. 553--585, DOI 10.1007/s00211-022-01325-9 .

• V. John, B. Moreau, J. Novo, Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations, Computers & Mathematics with Applications. An International Journal, 122 (2022), pp. 48--60, DOI 10.1016/j.camwa.2022.07.017 .
  Abstract
  A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov--Galerkin (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 SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM 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 SUPG-ROM method.

Beiträge zu Sammelwerken

• 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. 29--31.

• 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. 648--651.

• 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. 119--120, 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 tight-binding electronic structure theory to drift-diffusion simulations, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), Turin, Italy, 2022, J. Piprek, P. Bardella, eds., IEEE, 2022, pp. 97--98, DOI 10.1109/NUSOD54938.2022.9894745 .

Preprints, Reports, Technical Reports

• D. Frerichs-Mihov, L. Henning, V. John, Using deep neural networks for detecting spurious oscillations in discontinuous Galerkin solutions of convection-dominated convection-diffusion 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 convection-dominated con- vection-diffusion equations usually possess sharp layers but also exhibit large spurious oscillations. Slope limiters are known as a post-processing 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 non-invasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. Data assimilation is based on a parametrized-background 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 physics-informed 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 reduced-order 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 physics-informed manifold accordingly. Moreover, the framework can be used to characterize, in silico, biomarkers for pathological conditions, by appropriately training the reduced-order 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, Pressure-robustness 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 pressure-robust 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 L²-orthogonality onto discretely divergence-free test functions is restored. Perfectly orthogonal divergence-free discretizations or divergence-free reconstructions of these test functions do the trick and lead to much better analytic a priori estimates that are also validated in numerical examples.

Vorträge, 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.

• D. Runge, Mass-conservative reduced basis approach for convection-diffusion equations with non-linear 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, Vorticity based stabilization method for Fluid-Fluid interaction problem, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), September 4 - 8, 2023, Instituto Superior Técnico, Lisboa, Portugal.

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

• D. Frerichs-Mihov, Using deep learning techniques for solving convection-dominated convection-diffusion equations, 22nd Computational Fluids Conference (CFC 2023), April 25 - 28, 2023, International Association for Computational Mechanics (IACM), Cannes, France, April 28, 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 SUPG-stabilized POD-ROM method for convection-diffusion-reaction problems (online talk), Numerical Analysis of Galerkin ROMs seminar series (Online Event), NA G-ROMS, February 28, 2023.

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

• CH. Merdon, Raviart--Thomas enriched Scott-Vogelius finite element methods for the Navier--Stokes equations(online talk), City University of Hong Kong, Department of Mathematics, Hong Kong, January 18, 2023.

• CH. Merdon, Raviart--Thomas enriched Scott--Vogelius FEM for the Navier--Stokes equations, European Finite Element Fair 2023 (EFEF2023), Department of Mathematics University of Twente (DAMUT), Enschede, Netherlands, May 10, 2023.

• O. Pártl, Reconstruction of flow domain boundaries from velocity data via multi-step 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 ion-channel model-framework for in-vitro 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 non-parametric 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, Potsdam-Institut 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, Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas 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, Data-driven solutions of ill-posed inverse problems arising from doping reconstruction in semiconductors, AI4Science Konferenz, Rabat, Morocco, December 12 - 16, 2022.

• D. Frerichs-Mihov, A really pressure-robust 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. Frerichs-Mihov, On reducing spurious oscillations in discontinuous Galerkin methods for convection-diffusion equations, Workshop on Numerical Methods and Analysis in CFD, July 5 - 8, 2022, WIAS Berlin, July 6, 2022.

• D. Frerichs-Mihov, On reducing spurious oscillations in discontinuous Galerkin methods for convection-diffusion equations, Leibniz MMS Days 2022; Parallel Session on Computational and Geophysical Fluid Dynamics, April 25 - 27, 2022, Potsdam-Institut für Klimafolgenforschung (PIK), April 26, 2022.

• J. Fuhrmann, The Julia Programming Language: an overview, Leibniz MMS Days 2022, April 25 - 27, 2022, Potsdam-Institut 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 Wilhelms-Universität 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, Rheinisch-Westfälische Technische Hochschule, May 16, 2022.

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

• CH. Merdon, A gradient-robust well-balanced scheme for the compressible Navier--Stokes problem, 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 22), MS142: Structure-preserving 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 gradient-robust, well-balanced 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, Potsdam-Institut für Klimafolgenforschung (PIK), April 26, 2022.

• CH. Merdon, Recent advances for pressure-robust discretisations of the incompressible Navier-Stokes 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 pressure-robust 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 multi-step 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.

Preprints im Fremdverlag

• R. Araya, A. Caiazzo, F. Chouly, Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche, Preprint no. hal-04077986, 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. Well-posedness 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. hal-04037215, 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 ultra-violet (UV) range (< 280 nm). However, given that current devices exhibit extremely low efficiencies, understanding the fundamental properties of (Al,Ga)N-based systems is of key importance. Here, using a multi-scale simulation framework, we study the impact of alloy disorder on carrier transport, radiative and non-radiative recombination processes in a c-plane Al0.7Ga0.3N/Al0.8Ga0.2N quantum well embedded in a p-i-n 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 non-radiative Auger-Meitner recombination in comparison to the radiative process. Thus, to avoid such non-radiative 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. García-Archilla, V. John, S. Katz, J. Novo, POD-ROMs 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 Navier--Stokes 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 POD-ROM are equipped with a grad-div 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 two-dimensional memristive devices, Preprint no. arXiv:2304.06527, Cornell University, 2023, DOI 10.48550/arXiv.2304.06527 .
  Abstract
  Two-dimensional (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 image-charge-induced Schottky barrier lowering (SBL). The model is validated by comparing simulations to measurements for various 2D MoS2-based 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. hal-04012467, Hyper Articles en Ligne (HAL), 2023.
  Abstract
  We show the importance of using a thermodynamically consistent flux discretization when describing drift-diffusion processes within light emitting diode simulations. Using the classical Scharfetter-Gummel scheme with Fermi-Dirac 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 Fermi-Dirac 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 current-voltage 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 convection-diffusion equations, Preprint no. arXiv:2204.07480, Cornell University, 2022, DOI 10.48550/arXiv.2204.07480 .

• B. García-Archilla, V. John, J. Novo, POD-ROMs 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 convection-diffusion-reaction 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 multi-color (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 multi-quantum well based light emitting diode (LED). To do so, an atomistic tight-binding model is employed to account for alloy fluctuations on a microscopic level and the resulting tight-binding energy landscape forms input to a drift-diffusion 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 self-consistent Schroedinger-Poisson-drift-diffusion solver. Similar to experimental studies in the literature, we have focused on a multi-quantum 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 multi-quantum well system to ultimately guide the design of the active region of III-N-based LED structures.

• P. Ral, A.K. Giri, V. John, Instantaneous gelation and nonexistence for the Oort--Hulst--Safronov coagulation model, Preprint no. arXiv:2206.02035, Cornell University, 2022, DOI 10.48550/arXiv.2206.02035 .

• N. Ahmed, V. John, X. Li, Ch. Merdon, Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids for Navier--Stokes equations, Preprint no. arXiv:2212.10909, Cornell University, 2022, DOI 10.48550/arXiv.2212.10909 .

• V. John, X. Li, Ch. Merdon, H. Rui, Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas enrichment, Preprint no. arXiv:2206.01242, Cornell University, 2022, DOI 10.48550/arXiv.2206.01242 .