Publikationen

Monografien

  • Z. Erkoç, A. Aman, U. Güdükbay, H. Si, Out-of-core constrained Delaunay tetrahedralizations for large scenes, V.A. Garanzha, L. Kamenski, H. Si, eds., 143 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2021, pp. 113--124, (Chapter Published), DOI 10.1007/978-3-030-76798-3 .

  • H. Si, On decomposition of embedded prismatoids in $R^3$ without additional points, V.A. Garanzha, L. Kamenski, H. Si, eds., 143 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2021, pp. 95--112, (Chapter Published), DOI 10.1007/978-3-030-76798-3 .

  • V.A. Garanzha, L. Kamenski, H. Si, eds., Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 10th International Conference, NUMGRID 2020 / Delaunay 130, Celebrating the 130th Anniversary of Boris Delaunay, Moscow, Russia, November 2020, 143 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2021, 417 pages, (Collection Published), DOI 10.1007/978-3-030-76798-3 .

Artikel in Referierten Journalen

  • 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), published online on 27.07.2022, 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.

  • M. Coghi, W. Dreyer, P. Gajewski, C. Guhlke, P. Friz, 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 .

  • 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, (2022), published online on 09.04.2022, 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.

  • 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.

  • 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 (published online on 07.02.2022), 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, 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.

  • D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion, Electrochimica Acta, 390 (2021), pp. 138696/1--138696/12, DOI 10.1016/j.electacta.2021.138696 .
    Abstract
    From Maxwell--Stefan diffusion and general electrostatics, we derive a drift-diffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on Fermi--Dirac, Gauss--Fermi or Blakemore statistics for example) as well as limit the ion depletion (via the Fermi--Dirac integral of order-1). The latter will be motivated by a grand-canonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion depletion.

  • D. Abdel, P. Farrell, J. Fuhrmann, Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation, Optical and Quantum Electronics, 53 (2021), pp. 163/1--163/10, DOI 10.1007/s11082-021-02803-4 .
    Abstract
    The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter-Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter-Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p-i-n device are performed.

  • L. Lilaj, H. Harthum, T. Meyer, M. Shahrayari, G. Bertalan, A. Caiazzo, J. Braun, Th. Fischer, S. Hirsch, I. Sack, Inversion-recovery MR elastography of the human brain for improved stiffness quantification near fluid-solid boundaries, Magnetic Resonance in Medicine, (2021), published online on 28.06.2021, DOI 10.1002/mrm.28898 .

  • N. Ahmed, G.R. Barrenechea, E. Burman, J. Guzmán, A. Linke, Ch. Merdon, A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation, SIAM Journal on Numerical Analysis, 59 (2021), pp. 2746--2774, DOI 10.1137/20M1351230 .
    Abstract
    Discretization of Navier--Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(hk+1/2) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.

  • TH. Apel, V. Kempf, A. Linke, Ch. Merdon, A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes, IMA Journal of Numerical Analysis, 42 (2022), pp. 392--416 (published online on 14.01.2021), DOI 10.1093/imanum/draa097 .
    Abstract
    Most classical finite element schemes for the (Navier--)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pressure-robustness may lead to large velocity errors, whenever the Stokes momentum balance is dominated by a strong and complicated pressure gradient. It is a consequence of a method, which does not exactly satisfy the divergence constraint. However, inf-sup stable schemes can often be made pressure-robust just by a recent, modified discretization of the exterior forcing term, using H(div)-conforming velocity reconstruction operators. This approach has so far only been analyzed on shape-regular triangulations. The novelty of the present contribution is that the reconstruction approach for the Crouzeix--Raviart method, which has a stable Fortin operator on arbitrary meshes, is combined with results on the interpolation error on anisotropic elements for reconstruction operators of Raviart--Thomas and Brezzi--Douglas--Marini type, generalizing the method to a large class of anisotropic triangulations. Numerical examples confirm the theoretical results in a 2D and a 3D test case.

  • D. Chaudhuri, M. O'Donovan, T. Streckenbach, O. Marquardt, P. Farrell, S.K. Patra, Th. Koprucki, S. Schulz, Multiscale simulations of the electronic structure of III-nitride quantum wells with varied indium content: Connecting atomistic and continuum-based models, Journal of Applied Physics, 129 (2021), pp. 073104/1--073104/16, DOI 10.1063/5.0031514 .

  • G. Fu, Ch. Lehrenfeld, A. Linke, T. Streckenbach, Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity, Journal of Scientific Computing, 86 (2021), DOI 10.1007/s10915-020-01396-6 .
    Abstract
    Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the concept of gradient-robustness for linear elasticity is new. We discuss both aspects and propose novel Hybrid Discontinuous Galerkin (HDG) methods for linear elasticity. The starting point for these methods is a divergence-conforming discretization. As a consequence of its well-behaved Stokes limit the method is gradient-robust and free of volume-locking. To improve computational efficiency, we additionally consider discretizations with relaxed divergence-conformity and a modification which re-enables gradient-robustness, yielding a robust and quasi-optimal discretization also in the sense of HDG superconvergence.

  • B. García-Archilla, V. John, J. Novo, On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows, Computer Methods in Applied Mechanics and Engineering, 385 (2021), pp. 114032/1--114032/54, DOI 10.1016/j.cma.2021.114032 .

  • L. Heltai, A. Caiazzo, L.O. Müller, Multiscale coupling of one-dimensional vascular models and elastic tissues, Annals of Biomedical Engineering (ABME), published online on 20.07.2021, DOI 10.1007/s10439-021-02804-0 .
    Abstract
    We present a computational multiscale model for the efficient simulation of vascularized tissues, composed of an elastic three-dimensional matrix and a vascular network. The effect of blood vessel pressure on the elastic tissue is surrogated via hyper-singular forcing terms in the elasticity equations, which depend on the fluid pressure. In turn, the blood flow in vessels is treated as a one-dimensional network. The pressure and velocity of the blood in the vessels are simulated using a high-order finite volume scheme, while the elasticity equations for the tissue are solved using a finite element method. This work addresses the feasibility and the potential of the proposed coupled multiscale model. In particular, we assess whether the multiscale model is able to reproduce the tissue response at the effective scale (of the order of millimeters) while modeling the vasculature at the microscale. We validate the multiscale method against a full scale (three-dimensional) model, where the fluid/tissue interface is fully discretized and treated as a Neumann boundary for the elasticity equation. Next, we present simulation results obtained with the proposed approach in a realistic scenario, demonstrating that the method can robustly and efficiently handle the one-way coupling between complex fluid microstructures and the elastic matrix.

  • A. Kirch, A. Fischer, M. Liero, J. Fuhrmann, A. Glitzky, S. Reineke, Electrothermal tristability causes sudden burn-in phenomena in organic LEDs, Advanced Functional Materials, published online in September 2021, DOI 10.1002/adfm.202106716 .

  • P.L. Lederer, Ch. Merdon, Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations, Journal of Numerical Mathematics, published online on 6.11.2021, DOI https://doi.org/10.1515/jnma-2021-0078 .
    Abstract
    This paper improves guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A Prager-Synge type result relates the errors of divergence-free primal and H(div)-conforming dual mixed methods (for the velocity gradient) with an equilibration constraint that needs special care when discretised. To relax the constraints on the primal and dual method, a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust (but not necessarily divergence-free) primal discretisation. Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costs of the error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1.

  • M. O'Donovan, D. Chaudhuri, T. Streckenbach, P. Farrell, S. Schulz, Th. Koprucki, From atomistic tight-binding theory to macroscale drift-diffusion: Multiscale modeling and numerical simulation of uni-polar charge transport in (In,Ga)N devices with random fluctuations, Journal of Applied Physics, 130 (2021), pp. 065702/1--065702/13, DOI 10.1063/5.0059014 .

  • D. Frerichs, V. John, On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion equations, Journal of Computational and Applied Mathematics, 393 (2021), pp. 113487/1--113487/20, DOI 10.1016/j.cam.2021.113487 .

  • U. Wilbrandt, N. Alia, V. John, Optimal control of a buoyancy-driven liquid steel stirring modeled with single-phase Navier--Stokes equations, Journal of Mathematics in Industry, 11 (2021), pp. 10/1--10/22, DOI 10.1186/s13362-021-00106-7 .
    Abstract
    Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible NavierStokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.

Beiträge zu Sammelwerken

  • 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. 648--651.

  • S. Schulz, M. O'Donovan, D. Chaudhuri, S.K. Patra, P. Farrell, O. Marquardt, T. Streckenbach, Th. Koprucki, Connecting atomistic and continuum models for (In,Ga)N quantum wells: From tight-binding energy landscapes to electronic structure and carrier transport, in: 2021 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), IEEE Conference Publications Management Group, 2021, pp. 135--136, DOI 10.1109/NUSOD52207.2021.9541461 .
    Abstract
    We present a multi-scale framework for calculating electronic and transport properties of nitride-based devices. Here, an atomistic tight-binding model is connected with continuum-based electronic structure and transport models. In a first step, the electronic structure of (In,Ga)N quantum wells is analyzed and compared between atomistic and continuum-based approaches, showing that even though the two models operate on the same energy landscape, the obtained results differ noticeably; we briefly discuss approaches to improve the agreement between the two methods. Equipped with this information, uni-polar carrier transport is investigated. Our calculations reveal that both random alloy fluctuations and quantum corrections significantly impact the transport, consistent with previous literature results.

Preprints, Reports, Technical Reports

  • P. Vágner, M. Pavelka, J. Fuhrmann, V. Klika, A multiscale thermodynamic generalization of Maxwell--Stefan diffusion equations and of the dusty gas model, Preprint no. 2947, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2947 .
    Abstract, PDF (1288 kByte)
    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.

  • V. John, P. Knobloch, O. Pártl, A numerical assessment of finite element discretizations for convection-diffusion-reaction equations satisfying discrete maximum principles, Preprint no. 2946, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2946 .
    Abstract, PDF (2756 kByte)
    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.

  • 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.

  • O. Pártl, U. Wilbrandt, J. Mura, A. Caiazzo, Reconstruction of flow domain boundaries from velocity data via multi-step optimization of distributed resistance, Preprint no. 2929, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2929 .
    Abstract, PDF (15 MByte)
    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.

  • 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.

  • A. Stephan, H. Stephan, Positivity and polynomial decay of energies for square-field operators, Preprint no. 2901, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2901 .
    Abstract, PDF (328 kByte)
    We show that for a general Markov generator the associated square-field (or carré du champs) operator and all their iterations are positive. The proof is based on an interpolation between the operators involving the generator and their semigroups, and an interplay between positivity and convexity on Banach lattices. Positivity of the square-field operators allows to define a hierarchy of quadratic and positive energy functionals which decay to zero along solutions of the corresponding evolution equation. Assuming that the Markov generator satisfies an operator-theoretic normality condition, the sequence of energies is log-convex. In particular, this implies polynomial decay in time for the energy functionals along solutions.

  • A. Jha, O. Pártl, N. Ahmed, D. Kuzmin, An assessment of solvers for algebraically stabilized discretizations of convection-diffusion-reaction equations, Preprint no. 2889, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2889 .
    Abstract, PDF (2291 kByte)
    We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and P1 or Q1 finite elements. Time integration is performed using the Crank-Nicolson method or an explicit strong stability preserving Runge-Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection-diffusion-reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance.

  • F. Galarce Marín, D. Lombardi, O. Mula, State estimation with model reduction and shape variability: Application to biomedical problems, Preprint no. 2850, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2850 .
    Abstract, PDF (3684 kByte)
    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.

  • D. Bothe, W. Dreyer, P.-É. Druet, Multicomponent incompressible fluids -- An asymptotic study, Preprint no. 2825, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2825 .
    Abstract, PDF (519 kByte)
    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.

Vorträge, Poster

  • 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.

  • 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.

  • 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 , 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, 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.

  • D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modeling and simulation of charge transport in perovskite solar cells, AMaSiS 2021: Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems (Online Event), September 6 - 9, 2021.

  • D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modeling and simulation of charge transport in perovskite solar cells, Conference ``Asymptotic Behaviors of Systems of PDEs arising in Physics and Biology: Theoretical and Numerical Points of View'', Lille, Laboratoire Paul Painlevé, France, November 16 - 19, 2021.

  • D. Abdel, P. Vágner, J. Fuhrmann, P. Farrell, Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion, SIAM Conference on Computational Science and Engineering -- CSE21 (Online Event), Texas, USA, March 1 - 5, 2021.

  • S. Katz, C$^1$ finite elements with interpolated boundary conditions and applications to the Willmore flow of graphs, DAEDALUS Research Training Group ``Interdisciplinary Welcome Week'', October 20, 2021.

  • F. Galarce Marín , Asimilación de datos de desplazamientos cerebrales usando elastografía y modelos reducidos (online talk), XIX Jornadas de Mecánica Computacional 2021, October 7 - 8, 2021, Universidad Técnica Federico Santa María, Valparaíso, Spain, October 7, 2021.

  • P. Vágner, A continuum modeling of ionic charge transport in yttria-stabilized cubic zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions (online talk), 29th Topical Meeting of the International Society of Electrochemistry (Online Event), April 18 - 21, 2021, University of Chemistry and Technology Prague, Mikulov, Czech Republic, April 20, 2021.

  • P. Vágner, Generalized Nernst--Planck--Poisson model of solid oxide YSZ LSM O_2 electrode interface (online talk), 17th Symposium on Modeling and Experimental Validation of Fuel Cells, Electrolysers and Batteries (MODVAL 17) (Online Event), April 20 - 22, 2021, EPFL-Valais/Wallis, Sion, Switzerland, April 20, 2021.

  • P. Vágner, Generalized Nernst-Planck-Poisson model of solid oxide YSZ LSM O_2 electrode interface, Joint European Thermodynamics Conference, June 14 - 18, 2021, Czech Technical University, Prague, Czech Republic, June 17, 2021.

  • P. Vágner , Generalized Nernst--Planck--Poisson model of solid oxide YSZ LSM O_2 electrode interface (online talk), 72nd Annual International Society of Electrochemistry (ISE) Meeting (Online Event), August 29 - September 3, 2021, Seoul National University, Jeju Island, Korea (Republic of), September 3, 2021.

  • P. Vágner , Generalized Nernst--Planck--Poisson model of solid oxide YSZ LSM O_2 electrode interface (online talk), AMaSiS 2021: Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems (Online Event), September 6 - 9, 2021, WIAS Berlin, September 7, 2021.

  • B. Gaudeul, J. Fuhrmann, Two entropic finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints, AMaSiS 2021: Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems (Online Event), September 6 - 9, 2021.

  • S. Katz, Modeling and discretization techniques for partial differential equations, Graduiertenkollegs 2433 DAEDALUS, November 23 - 25, 2021, Weierstrass Institute Berlin.

  • A. Caiazzo, F. Galarce Marín, J. Polzehl, I. Sack, K. Tabelow, Physics based assimilation of displacements data from magnetic resonance elastography, Kick-off Workshop of the MATH+ Thematic Einstein Semester on Mathematics of Imaging in Real-World Challenges (Hybrid Event), Berlin, October 6 - 8, 2021.

  • A. Caiazzo, Multiscale coupling of one-dimensional vascular models and elastic tissues (online talk), European Congress of Mathematics, MS-ID39: Modeling, approximation, and analysis of partial differential equations involving singular source terms (Online Event), June 20 - 26, 2021, University of Primorska, Faculty of Mathematics, Portorož, June 22, 2021.

  • P. Farrell, Y. Hadjimichael, Ch. Merdon, T. Streckenbach, Toward charge transport in bent nanowires, AMaSiS 2021: Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems (Online Event), September 6 - 9, 2021.

  • J. Fuhrmann, Quality preserving numerical methods for electrolyte modeling (online talk), Nanoscale Physics of Electrochemical and Biological Media, 748. Heraeus Seminar (Online Event), May 9 - 12, 2021, Wilhelm und Else Heraeus-Stiftung, Bad Godesberg, May 11, 2021.

  • J. Fuhrmann, Thermodynamically consistent finite volume schemes for charge transport problems, Joint European Thermodynamics Conference, June 14 - 18, 2021, Czech Technical University, Prague, Czech Republic, June 17, 2021.

  • V. John, Finite element methods respecting the discrete maximum principle for convection-diffusion equations, Berlin International Graduate School in Model and Simulation based Research (BIMoS), Technische Universität Berlin, June 7, 2021.

  • V. John, Modeling and discretization techniques for partial differential equations, Graduiertenkollegs 2433 DAEDALUS, November 23 - 25, 2021, Weierstrass Institute Berlin.

  • V. John, On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows (online talk), International Symposium on Recent Trends in Differential Equations: Theory, Computation & Application, Symposium on Recent Trends in Numerical Method for PDEs and Applications (Online Event), March 19 - 22, 2021, Indian Institute of Technology Kanpur, India, March 19, 2021.

  • V. John, Techniques for improving finite element solutions of steady-state convection-diffusion equations (online talk), BIRS-CMO Workshop ``Bound-Preserving Space and Time Discretizations for Convection-Dominated Problems'' (Online Event), August 22 - 27, 2021, Banff International Research Station for Mathematical Innovation and Discovery, Casa Matemática Oaxaca (CMO), Mexico, August 25, 2021.

  • A. Linke, On pressure-robustness,well-balanced schemes andthe spatial discretization ofhigh Reynolds number flows (online talk), GAMM 91st Annual Meetingof the International Association of Applied Mathematics and Mechanics, S18: Numerical methods of differential equations (Online Event), March 15 - 19, 2021, Universität Kassel, March 19, 2021.

  • A. Linke, On the role of the Helmholtz--Leray projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, Ecole de Recherche CIMPA & Workshop, May 31 - June 7, 2021, Nador, Morocco, June 2, 2021.

  • CH. Merdon, A novel gradient-robust, well-balanced discretisation for the compressible isothermal Navier--Stokes problem (online talk), GAMM 91st Annual Meetingof the International Association of Applied Mathematics and Mechanics, S18: Numerical methods of differential equations (Online Event), March 15 - 19, 2021, Universität Kassel, March 19, 2021.

  • CH. Merdon, Recent advances on gradient-robust discretisations for the Navier--Stokes equations (online talk), Humboldt-Universität zu Berlin, Institut für Mathematik, December 16, 2021.

  • O. Pártl, Optimal control problems for immersed resistance parameter in Stokes flow (online talk), IFIP TC 7 Conference on System Modelling and Optimization (Online Event), August 30 - September 3, 2021, Ecuadorian Mathematical Society, Research Center for Mathematical Modeling, Quito, Ecuador, September 1, 2021.

Preprints im Fremdverlag

  • 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. 2208.14217/1--2208.14217/30, 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 convection-diffusion equations, Preprint no. 2204.07480/1--2204.07480/77, Cornell University Library, arXiv.org, .

  • 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. 2206.09123, Cornell University Library, arXiv.org, 2022.

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

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

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

  • M. Coghi, W. Dreyer, P. Gajewski, C. Guhlke, P. Friz, M. Maurelli, A McKean--Vlasov SDE and particle system with interaction from reflecting boundaries, Preprint no. 2102.12315v1, Cornell University Library, arXiv.org, 2021.

  • 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, Preprint no. arXiv:2111.01644, Cornell University Library, arXiv.org, 2021.
    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.

  • V. John, P. Knobloch, On algebraically stabilized schemes for convection-diffusion-reaction problems, Preprint no. 2111.08697, Cornell University Library, arXiv.org, 2021.