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Publications

Monographs

  • D. Peschka, M. Thomas, A. Zafferi, Reference map approach to Eulerian thermomechanics using GENERIC, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 39--70, (Chapter Published), DOI 10.1007/978-3-031-93918-1_3 .
    Abstract
    An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

  • G.R. Barrenechea, V. John, P. Knobloch, Monotone Discretizations for Elliptic Second Order Partial Differential Equations, 61 of Springer Series in Computational Mathematics, Springer, Cham, 2025, pp. 1--649, (Monograph Published), DOI 978-3-031-80684-1 .
    Abstract
    This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.

  • P. Colli, J. Sprekels, Hyperbolic relaxation of the chemical potential in the viscous Cahn--Hilliard equation, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 529--556, (Chapter Published), DOI 10.1007/978-3-031-93918-1_18 .
    Abstract
    An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

  • M. Eigel, Ch. Merdon, Chapter Eight --- A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs, F. Chouly, S.P.A. Bordas, R. Becker, P. Omnes, eds., 60 of Advances in Applied Mechanics, Elsevier, 2025, pp. 347--397, (Chapter Published), DOI 10.1016/bs.aams.2025.02.008 .

  • A. Mielke, An Eulerian formulation for dissipative materials using Lie derivatives and GENERIC, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 13--38, (Chapter Published), DOI 10.1007/978-3-031-93918-1_2 .
    Abstract
    An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

  • J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., Advances in Continuum Physics: In Memoriam Wolfgang Dreyer, 238 of Advanced Structured Materials, Springer, 2025, pp. vii--834, (Monograph Published), DOI 10.1007/978-3-031-93918-1 .

Articles in Refereed Journals

  • N. Chamakuri, V. John, N. Ranwan, Finite element analysis of a coupled Navier--Stokes flow - linear elasticity problem, Journal of Mathematical Analysis and Applications, 558 (2026), pp. 130384/1--130384/37, DOI 10.1016/j.jmaa.2025.130384 .
    Abstract
    A semi-discrete finite element approximation of a fluid-structure interaction problem is analyzed. The fluid part is modeled by the incompressible Navier--Stokes equations. Both the fluid and the solid subdomains are considered to be stationary. In the discretization of the Navier--Stokes equations, a grad-div stabilization term is included, and a special form of the convective term is used. The existence of a finite element solution is shown, a priori estimates are proved, and a finite element error estimate is derived. The dependency of the error bounds on the coefficients of the problem is tracked. Error bounds are obtained whose constants do not depend on the Reynolds number.

  • D. Abdel, M. Herda, M. Ziegler, C. Chainais-Hillairet, B. Spetzler, P. Farrell, Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models, Computers & Mathematics with Applications. An International Journal, 199 (2025), pp. 286--308, DOI 10.1016/j.camwa.2025.09.034 .
    Abstract
    In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential as components for next-generation artificial intelligence (AI) hardware and information technology. Our charge transport model describes the drift-diffusion of electrons, holes, and ionic defects self-consistently in an electric field. We incorporate two types of boundary models: ohmic and Schottky contacts. The coupled drift-diffusion partial differential equations are discretized using a physics-preserving Voronoi finite volume method. It relies on an implicit time-stepping scheme and the excess chemical potential flux approximation. We demonstrate that the fully discrete nonlinear scheme is unconditionally stable, preserving the free-energy structure of the continuous system and ensuring the non-negativity of carrier densities. Novel discrete entropy-dissipation inequalities for both boundary condition types in multiple dimensions allow us to prove the existence of discrete solutions. We perform multi-dimensional simulations to understand the impact of electrode configurations and device geometries, focusing on the hysteresis behavior in lateral 2D memristive devices. Three electrode configurations - side, top, and mixed contacts - are compared numerically for different geometries and boundary conditions. These simulations reveal the conditions under which a simplified one-dimensional electrode geometry can well represent the three electrode configurations. This work lays the foundations for developing accurate, efficient simulation tools for 2D memristive devices and memtransistors, offering tools and guidelines for their design and optimization in future applications.

  • CH. Keller, J. Fuhrmann, M. Landstorfer, B. Wagner, A model framework for ion channels with selectivity filters based on continuum non-equilibrium thermodynamics, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 27 (2025), pp. 981--1013, DOI 10.3390/e27090981 .
    Abstract
    A mathematical model framework to describe ion transport in nanopores is presented. The model is based on non-equilibrium thermodynamics and considers finite size effects, solvation phenomena as well as the electrical charges of membrane surfaces and channel proteins. Par- ticular emphasis is placed on the consistent modelling of the selectivity filter in the pore. It is treated as an embedded domain in which the constituents can change their chemical properties. The diffusion process through the filter is governed by an independent diffusion coefficient and at the interfaces, de- and resolvation reactions are introduced as Neumann interface conditions. The evolution of the molar densities is described by drift-diffusion equations, where the fluxes depend on the gradient of the chemical potentials and the electric force. The chemical potentials depend on the molar fractions and on the pressure in the electrolyte and accounts for solvation effects. The framework allows the calculation of current-voltage relations for a variety of chan- nel properties and ion concentrations. We compare our model framework to experimental results for calcium-selective ion channels and show the general validity of our approach. Our parameter studies show that calcium and sodium currents are proportional to the surface charge in the se- lectivity filter and to the diffusion coefficients of the ions. Moreover, they show that the negative charges inside the pore have a decisive influence on the selectivity of divalent over monovalent ions.

  • C. Chainais-Hillairet, R. Eymard, J. Fuhrmann, A monotone numerical flux for quasilinear convection diffusion equation, Mathematics of Computation, 93 (2024), pp. 203--231, DOI 10.1090/mcom/3870 .
    Abstract
    We propose a new numerical 2-point flux for a quasilinear convection-diffusion equation. This numerical flux is shown to be an ap- proximation of the numerical flux derived from the solution of a two-point Dirichlet boundary value problem for the projection of the continuous flux onto the line connecting neighboring collocation points. The later approach generalizes an idea first proposed by Scharfetter and Gummel [IEEE Trans. Electron Devices 16 (1969), pp. 64-77] for linear drift-diffusion equations. We establish first that the new flux satisfies sufficient properties ensuring the con- vergence of the associate finite volume scheme, while respecting the maximum principle. Then, we pay attention to the long time behavior of the scheme: we show relative entropy decay properties satisfied by the new numerical flux as well as by the generalized Scharfetter-Gummel flux. The proof of these properties uses a generalization of some discrete (and continuous) log-Sobolev inequalities. The corresponding decay of the relative entropy of the continuous solution is proved in the appendix. Some 1D numerical experiments confirm the theoretical results.

  • C.L. Manganelli, D. Spirito, P. Farrell, J. Frigerio, A. De Lacovo, D. Marian, M. Virgilio, Strain engineering in semiconductor materials, physica status solidi (RLL) -- Rapid Research Letters (pss RRL), 19 (2025), pp. 2400383/1--2400383/3, DOI 10.1002/pssr.202400383 .
    Abstract
    Strain engineering has become an essential strategy in the advancement of semiconductor technologies, providing a power- ful mean to modulate the electronic, optical, and mechanical properties of materials. By introducing controlled deformation into crystal lattices, this approach enables enhanced carrier mobility, tailored bandgap energies, and improved device perfor- mance across applications in photonics, optoelectronics, and quantum technologies.

  • M. Matthaiou, V. John, M. Zainelabdeen, Bound-preserving physics-informed neural networks for steady-state convection-diffusion-reaction problems, Computers & Mathematics with Applications. An International Journal, 199 (2025), pp. 167--183, DOI 10.1016/j.camwa.2025.09.009 .
    Abstract
    Numerical approximations of solutions of convection-diffusion-reaction problems should take only physically admissible values. Provided that bounds for the admissible values are known, this paper presents several approaches within PINNs and $hp$-VPINNs for preserving these bounds. Numerical simulations are performed for convection-dominated problems. One of the proposed approaches turned out to be superior to the other ones with respect to the accuracy of the computed solutions.

  • TH. Anandh, D. Ghose, H. Jain, P. Sunkad, S. Ganesan, V. John, Improving hp-variational physics-informed neural networks for steady-state convection-dominated problems, Computer Methods in Applied Mechanics and Engineering, 438 (2025), pp. 117797/1--117797/25, DOI 10.1016/j.cma.2025.117797 .
    Abstract
    This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature.

  • D. Brust, K. Hopf, J. Fuhrmann, A. Cheilytko, M. Wullenkord, Ch. Sattler, Transport of heat and mass for reactive gas mixtures in porous media: Modeling and application, Chemical Engineering Journal, 516 (2025), pp. 162027/1--162027/33, DOI 10.1016/j.cej.2025.162027 .
    Abstract
    We present a modeling framework for multi-component, reactive gas mixtures and heat transport in porous media based on the Maxwell--Stefan and Darcy equations for multi-component diffusion and forced, viscous flow through porous media. Analysis of the model equations reveals thermodynamic con- sistency and uniqueness of steady states, while their mathematical structure facilitates discretization via the Finite-Volume approach resulting in an open- source based implementation of the modeling framework in Julia. The model allows to impose boundary conditions that accurately reflect the conditions prevailing in a photo-thermal chemical reactor that is subsequently intro- duced as a case study for the modeling framework. Comparison of numerical with experimental results reveals good agreement. Improvement options for the physical reactor are derived from simulation results demonstrating the practical utility of the modeling framework. Additionally, the framework is used for the simulation of thermodiffusion in a ternary gas mixture and has been verified with published numerical results with very good agreement.

  • B. García-Archilla, V. John, J. Novo, POD-ROM methods: From a finite set of snapshots to continuous-in-time approximations, SIAM Journal on Numerical Analysis, 63 (2025), pp. 800-826, DOI 10.1137/24M1645681 .
    Abstract
    This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully discrete methods using first order methods in time, typically the implicit Euler time integrator. Our aim is to show which kind of error bounds can be obtained using any time integrator, both in the full order model (FOM), applied to compute the snapshots, and in the POD-ROM method. To this end, we analyze in this paper the continuous-in-time case for both the FOM and POD-ROM methods, although the POD basis is obtained from snapshots taken at a discrete (i.e., not continuous) set of times. Two cases for the set of snapshots are considered: the case in which the snapshots are based on first order divided differences in time and the case in which they are based on temporal derivatives. Optimal pointwise-in-time error bounds between the FOM and the POD-ROM solutions are proved for the L high 2 (omega) norm of the error for a semilinear reaction-diffusion model problem. The dependency of the errors on the distance in time between two consecutive snapshots and on the tail of the POD eigenvalues is tracked. Our detailed analysis allows us to show that, in some situations, a small number of snapshots in a given time interval might be sufficient to accurately approximate the solution in the full interval. Numerical studies support the error analysis.

  • F. Goth, J.P. Thiele, Foundational competencies and specializations of a research software engineer, Computing. Archives for Scientific Computing, 27 (2025), pp. 27--34, DOI 10.1109/MCSE.2025.3552156 .
    Abstract
    The term research software engineer (RSE) emerged to represent individuals working in the research community but focusing on software development. It has been widely adopted, and has several high-level definitions. However, their work varies depending on the institutional context. At one extreme, RSE roles look similar to traditional researchers. At the other extreme, they resemble an industrial software engineer. Most RSE roles inhabit the spectrum in between. Therefore, providing a straightforward, comprehensive definition of what an RSE does and what experience, skills, and competencies they require is challenging. In this summarized community article, we define the broad notion of RSEs, explore their different types of work, and define a list of competencies and values that frame their general identity. Further research and training can build upon and expand this foundation, and we expect graduates and practitioners to have a larger, more diverse set of skills than outlined here.

  • N. Jaitner, Y. Safraou, M. Anders, J. Schattenfroh, T. Meyer, B. Huang, J. Jordan, O. Boehm, A. Caiazzo, T. Schaeffter, J. Mura, J. Guo, I. Sack, Noninvasive assessment of portal pressure by combined measurement of volumetric strain and stiffness of in vivo human liver, Acta Biomaterialia, 197 (2025), pp. 312--325, DOI 10.1016/j.actbio.2025.03.016 .
    Abstract
    Liver metabolism depends on the mechanical interplay between the solid tissue matrix and blood vessels, making shear modulus and pressure important variables of hepatic homeostasis. While shear modulus can be quantified by magnetic resonance elastography (MRE), pressure is not available through noninvasive imaging. We propose combined determination of liver deformation and shear modulus using volumetric MRI and MRE for noninvasive portal pressure assessment. Volumetric MRI and multifrequency MRE were performed in five ex vivo rat livers at different portal pressures. A similar imaging protocol was used to examine eleven healthy volunteers after overnight fasting in two respiratory states and after ingestion of 1.5 L of water. Models derived from ex vivo rat data served to scale human liver volumetric strain multiplied by differential shear modulus obtained from MRE to portal pressure. After water intake, liver volume expanded by 3 % (Interquartile range [IQR], 1.3?6.0; p < 0.001) and shear modulus increased by 0.12 kPa (IQR, 0.08?0.26; p = 0.001), while deep inhalation had mixed effects (p > 0.05). Positive and negative volumetric strains were associated with stiffening and softening, respectively, leading to a consistent increase in portal pressure of 0.2 to 0.3 kPa (IQR, 0.07?0.41) for inhalation and water ingestion. In conclusion, volumetric strain analysis combined with MRE in different scenarios of in vivo liver deformation and calibration with controlled ex vivo experiments allowed assessment of portal pressure changes. In clinical applications, combined MRE and volumetric MRI after inspiration or water ingestion could provide mechanical contrast for assessing hepatic pressure-related diseases.

  • M.U. Qureshi, S. Matera, D. Runge, Ch. Merdon, J. Fuhrmann, J.-U. Repke, G. Brösigke, Reduced order CFD modeling approach based on the asymptotic expansion - An application for heterogeneous catalytic systems, Chemical Engineering Journal, 504 (2025), pp. 158684/1--158684/11, DOI 10.1016/j.cej.2024.158684 .
    Abstract
    Recent experimental techniques allow to obtain atomic scale information of heterogeneous catalysts under operando conditions, but, typically require rather complex reactor geometries. To utilize this complementary information in e.g. kinetic model development, Computational Fluid Dynamics (CFD) is needed to address the non-trivial coupling of chemical kinetics and mass transport in such chambers. However, conventional CFD approaches for solving catalytic systems have a drawback of huge computational expense, incurred by trying to solve a stiff problem. In this study, we present a reduced order approach with a significantly lower computational footprint than conventional CFD. The idea behind the approach is to estimate the solution without having to directly couple the mass transport and surface kinetics. This is achieved by a lowest-order asymptotic expansion in the catalyst sample size or, equivalently, the lateral variation of gas phase concentrations above the catalytic surface. This reduces the overall simulation time by orders of magnitude, particularly for inverse problems. We demonstrate the approach for catalytic formation of Methanol from CO2 and H2 in a two dimensional channel flow and for different applied reaction conditions, sample sizes and catalyst loadings.

  • V. John, Ch. Merdon, M. Zainelabdeen, Augmenting the grad-div stabilization for Taylor--Hood finite elements with a vorticity stabilization, Journal of Numerical Mathematics, 33 (2025), pp. 37--54, DOI 10.1515/jnma-2023-0118 .
    Abstract
    The least squares vorticity stabilization (LSVS), proposed in Ahmed et al. for the Scott--Vogelius finite element discretization of the Oseen equations, is studied as an augmentation of the popular grad-div stabilized Taylor--Hood pair of spaces. An error analysis is presented which exploits the situation that the velocity spaces of Scott--Vogelius and Taylor--Hood are identical. Convection-robust error bounds are derived under the assumption that the Scott--Vogelius discretization is well posed on the considered grid. Numerical studies support the analytic results and they show that the LSVS-grad-div method might lead to notable error reductions compared with the standard grad-div method.

  • F. Romor, G. Stabile, G. Rozza, Explicable hyper-reduced order models on nonlinearly approximated solution manifolds of compressible and incompressible Navier--Stokes equations, Journal of Computational Physics, 524 (2025), pp. 113729/1--113729/8, DOI 10.1016/j.jcp.2025.113729 .
    Abstract
    A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the reduced space needed to approximate with sufficient accuracy the solution manifold. To solve this problem, neural networks, in the form of different architectures, have been employed to perform accurate nonlinear regressions of the solution manifolds. However, the majority of the implementations are non-intrusive black-box surrogate models and only a part of them perform dimension reduction from the number of degrees of freedom of the discretized parametric models to a latent dimension. We present a new intrusive and explicable methodology for reduced-order modeling that employs neural networks for the solution manifold approximation but that does not discard the physical and numerical models underneath in the predictive/online stage. We will focus on autoencoders used to compress further the dimensionality of linear approximants of solution manifolds, achieving in the end a nonlinear dimension reduction. After having obtained an accurate nonlinear approximant, we seek for the solutions on the latent manifold with the residual-based nonlinear least-squares Petrov--Galerkin method, opportunely hyper-reduced in order to be independent of the number of degrees of freedom. New adaptive hyper-reduction strategies are developed along with the employment of local nonlinear approximants. We test our methodology on two nonlinear time dependent parametric benchmarks involving a supersonic flow past a NACA airfoil with changing Mach number and an incompressible turbulent flow around the Ahmed body with changing slant angle.

  • F. Romor, D. Torlo, G. Rozza, Friedrichs' systems discretized with the DGM: Domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions, Journal of Computational Physics, 531 (2025), pp. 113915/1--113915/40, DOI 10.1016/j.jcp.2025.113915 .
    Abstract
    Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the linearized Euler equations of gas dynamics, the equations of compressible linear elasticity and the Dirac-Klein-Gordon system. FS were studied to approximate PDEs of mixed elliptic and hyperbolic type in the same domain. For this and other reasons, the discontinuous Galerkin method (DGM) represents the most common and versatile choice of approximation space for FS in the literature. We implement a distributed memory solver for stationary FS in deal.II. Our focus is model order reduction. Since FS model hyperbolic PDEs, they often suffer from a slow Kolmogorov n-width decay. We develop and combine two approaches to tackle this problem in the context of large-scale applications. The first is domain decomposable reduced-order models (DD-ROMs). We will show that the DGM offers a natural formulation of DD-ROMs, in particular regarding interface penalties, compared to the continuous finite element method. We also develop new repartitioning strategies to obtain more efficient local approximations of the solution manifold. The second approach involves shallow graph neural networks used to infer the limit of a succession of projection-based linear ROMs corresponding to lower viscosity constants: the heuristic behind concerns the development of a multi-fidelity super-resolution paradigm to mimic the mathematical convergence to vanishing viscosity solutions while exploiting to the most interpretable and certified projection-based DD-ROMs.

Contributions to Collected Editions

  • D. Frerichs-Mihov, M. Zainelabdeen, V. John, On collocation points for physics-informed neural networks applied to convection-dominated convection-diffusion problems, in: Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1, A. Sequeira, A. Silvestre, S.S. Valtchev, J. Janela, eds., 153 of Lecture Notes in Computational Science and Engineering (LNCSE), Springer, Cham, 2025, pp. 335--344, DOI 10.1007/978-3-031-86173-4_34 .
    Abstract
    In recent years physics-informed neural networks (PINNs) for approximating the solution to (initial-)boundary value problems gained a lot of interest. PINNs are trained to minimize several residuals of the problem in collocation points. In this work we tackle convection-dominated convection-diffusion problems, whose solutions usually possess layers, which are small regions where the solution has a steep gradient. Inspired by classical Shishkin meshes, we compare hard- constrained PINNs trained with layer-adapted collocation points with ones trained with equispaced and uniformly randomly chosen points. We observe that layer-adapted points work the best for a problem with an interior layer and the worst for a problem with boundary layers. For both problems at most acceptable solutions can be obtained with PINNs.

  • M. Demir, Vorticity-based stabilization method for the rotational flow problems, in: Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1, A. Sequeira, A. Silvestre, S.S. Valtchev, J. Janela, eds., 153 of Lecture Notes in Computational Science and Engineering (LNCSE), Springer, Cham, 2025, pp. 258--267, DOI 10.1007/978-3-031-86173-4_34 .
    Abstract
    In this contribution, a subgrid artificial viscosity method for approximating solutions to the incompressible Navier?Stokes equations in a rotating frame of reference is considered. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization. Global stabilization is obtained by adding a locution via an artificial viscosity and then removing it only on the coarse mesh scale. We show that the approximate solutions of the method are unconditionally stable and optimally convergent. Several numerical tests are presented for validating the support of the derived theoretical results and demostrate the efficiency and accuracy of the method.

Preprints, Reports, Technical Reports

  • M. Heida, M. Landstorfer, Modeling of porous battery Electrodes with multiple phase transitions -- Part I: Modeling and homogenization, Preprint no. 3251, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3251 .
    Abstract, PDF (1108 kByte)
    We derive a thermodynamically consistent multiscale model for a porous intercalation battery in a half-cell configuration. Starting from microscopically resolved balance equations, the model rigorously couples cation and anion transport in the electrolyte with electron transport and solid- state diffusion in the active material through intercalation reactions. The derivation is based on non-equilibrium thermodynamics and periodic homogenization. The central novelty of this work lies in the systematic incorporation of multi-well free energy functions for intercalated cations into a homogenized DFN-type porous-electrode framework. This modeling choice leads to non-monotonic chemical potentials and enables a macroscopic descrip- tion of phase separation and multiple phase transitions within the electrode. While multi-well free energies are well established at the particle scale, their integration into homogenized porous- electrode models has so far been lacking. By extending the homogenization framework to include Cahn--Hilliard-type regularizations, phase-transition effects are retained at the electrode level. The resulting model exhibits an intrinsically coupled 3D+3D structure, in which macroscopic transport in the electrolyte is coupled to fully resolved microscopic diffusion within active parti- cles. This coupling naturally induces memory effects and time lags in the macroscopic voltage response, which cannot be captured by reduced single-scale models. Although the microscopic dynamics possess an underlying gradient-flow structure, we adopt a formal asymptotic approach to obtain a tractable DFN-type model suitable for practical simulations. This paper constitutes Part I of a three-part series and is devoted to the systematic derivation and mathematical formulation of the model. Numerical analysis, discretization strategies, simula- tion studies of transient cycling behavior, and experimental validation are deferred to Parts II and III. Part II focuses on finite C-rates, while Part III addresses open-circuit voltage conditions, where the predictive capabilities of the framework are investigated in detail.

  • M. Landstorfer, Ch. Pohl, F. Brosa Planella, K. Manmi, A model for SEI-growth based on non-equilibrium thermodynamics, Preprint no. 3250, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3250 .
    Abstract, PDF (1092 kByte)
    The growth of the solid electrolyte interphase (SEI) is a dominant degradation mechanism in lithium-ion batteries, governing capacity fade, coulombic efficiency, and long-term performance. Despite extensive experimental investigation, quantitative understanding of SEI formation and evolution remains limited by its nanoscale thickness, complex chemistry, and strong sensitivity to operating conditions. Existing zero-dimensional models capture individual rate-limiting mechanisms but typically treat the SEI as an idealized interface layer, neglecting spatially resolved transport, solvent consumption, and dynamic interface motion. In this work, we present a continuum-level model for SEI growth grounded in non-equilibrium thermodynamics. The SEI is treated as a distinct thermodynamic domain and modeled as a mixed ion - electron conductor, while the SEI - electrolyte interface is described as a moving boundary. The framework systematically derives transport laws and reaction kinetics from electrochemical poten- tials and interfacial free energies, ensuring thermodynamic consistency. A finite electrolyte reservoir is explicitly included, allowing solvent depletion to emerge naturally as a limiting mechanism for SEI growth. The general formulation consists of coupled partial differential equations for all domains and interfaces. Under open-circuit voltage conditions, the system reduces to a tractable set of ordinary differential equations describing lithium concentration in the active material, solvent concentration, and SEI thickness. Numerical simulations under charging, rest, and cycling conditions reproduce experimentally observed features such as linear and square root of time growth regimes, voltage shifts due to parasitic current consumption, capacity contributions from lithium stored in the SEI, and self- discharge during rest. Two distinct termination mechanisms - active lithium depletion and solvent exhaustion - are identified. Overall, the proposed framework unifies multiple SEI growth mechanisms within a single thermodynamically consistent model and provides a mechanistic basis for improved lifetime prediction and optimization of battery formation and operating protocols.

  • W. Kenmoe Nzali, Ch. Bayer, D. Kreher, M. Landstorfer, Volatile electricity markets and battery storage: A model-based approach for optimal control, Preprint no. 3248, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3248 .
    Abstract, PDF (1340 kByte)
    Grid connected energy storage systems provide a strategic advantage by exploiting electricity market price fluctuations, thereby significantly reducing energy consumption costs. This paper presents a general framework for minimizing electricity consumption costs by formulating the problem as a stochastic optimal control problem for a stationary battery storage device (SBSD). We propose a realistic model for electricity spot prices calibrated with real data, alongside a detailed model of battery dynamics with practical parameters. The control problem is solved in a discrete time setting by combining dynamic programming with the least squares Monte Carlo method, allowing us to approximate the value function and the optimal policy under both state of charge and voltage constraints. Using the derived optimal policy, we estimate the lower bound of electricity consumption costs across multiple price trajectories. The results demonstrate that the SBSD can substantially reduce consumption costs, with savings increasing with battery duration. After one year, a battery with 12 hours duration achieves approximately 11% cost reduction, while 24 hours battery achieves 21%, compared to a scenario without storage. Finally, we estimate the amortization time (the period required for cumulative savings to offset the initial investment). After 6.7 years for the 12 hours battery and 9.9 years for the 24 hours battery, the amortization time is reached.

  • CH. Keller, B. Wagner, A. Münch, An asymptotic model of the Poisson--Nernst--Planck--Stokes system for ion transport in narrow channels, Preprint no. 3243, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3243 .
    Abstract, PDF (1462 kByte)
    Ion transport through narrow channels is determined by the interaction between electrochemical and hydrodynamic effects, which are influenced by the channel geometry, ion concentrations, pressure and potential gradients, and surface charges. Understanding the mechanisms that control electrokinetic phenomena such as ion selectivity and flow transitions is crucial for elucidating biological functions and for further developing the design of artificial nanofluidic systems. On the continuum scale, these processes are described by the coupled Poisson-Nernst-Planck-Stokes equations (PNPS). However, direct numerical simulations in two or three dimensions are computationally intensive and provide only limited insights into the underlying physical and mathematical structure. Taking advantage of the small aspect ratio characteristic of nanopores, we derive a systematic asymptotic reduction of the PNPS boundary value problem. In contrast to existing one-dimensional reductions, which assume a Debye length much smaller than the channel radius, our analysis identifies a distinct asymptotic regime in which the Debye length is comparable to the channel width. This framework extends the applicability of reduced PNPS models and recovers previous approximations as limiting cases. The resulting model provides clarity and predictability for a wide range of settings. We demonstrate the influence of geometry and flow on ion transport in trumpet-shaped nanopores, flow transitions that occur due to electrostatic and hydrodynamic forces, and the conductivity properties of a protein-based channel.

  • O. Pártl, E. Meneses Rioseco, Computational framework for modeling, simulation, and optimization of geothermal energy production from naturally fractured reservoirs, Preprint no. 3239, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3239 .
    Abstract, PDF (51 MByte)
    We describe an open-source computational framework for the automated search for deviated multi-well lay- outs in hot fracture-controlled reservoirs that sustainably optimize geothermal energy production. This search is performed via 3D simulations of groundwater flow and heat transfer. We model the reservoirs as geologi- cally consistent, randomly generated discrete fracture networks (DFNs) in which the fractures are 2D manifolds with polygonal boundaries embedded in a 3D porous medium. The wells are modeled as line sources and sinks. The flow and heat transport in the DFN-matrix system are modeled by solving the balance equations for mass and energy, while expressing the momentum balance by the Darcy law. The spatial discretization is based on the finite element method stabilized via the algebraic flux correction. For the time discretization, we use a semi-implicit approach to enhance the solver efficiency. The optimization is performed via a gradient-free global optimization algorithm. By employing the immersed boundary method and a non-matching discretization strategy, the need for computationally expensive remeshing when altering well configurations within the reser- voir is effectively eliminated, thereby enhancing the robustness of the proposed framework and enabling fully automated optimization. We present the results of our optimization tests for randomly generated DFNs consist- ing of thousands of fractures, considering realistic values of physical parameters. To demonstrate the analytical capabilities of our open-source framework, we use it to analyze and visualize the above optimization results and the structure of the above DFNs. The developed framework was verified and validated using a set of simpli- fied yet purpose-specific fracture configurations relevant to geothermal energy extraction in naturally fractured reservoirs.

  • G. Alì, Z. Amer, P. Farrell, N. Rotundo, Classical solutions for a van Roosbroeck--Helmholtz model for a semiconductor laser diode, Preprint no. 3228, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3228 .
    Abstract, PDF (365 kByte)
    We consider a coupled light-matter model for semiconductor lasers consisting of the transient van Roosbroeck system for charge transport and a Helmholtz eigenvalue problem for the transver- sal optical field. The coupling is realized through a stimulated recombination operator in the car- rier continuity equations and a carrier-dependent dielectric function in the Helmholtz problem. In this paper, we establish, under physically relevant assumptions, local-in-time well-posedness of the coupled van Roosbroeck--Helmholtz system. The proof relies on the abstract framework of quasi-linear parabolic equations in Banach spaces developed by Kaiser, Neidhardt, and Rehberg which requires in particular a local Lipschitz continuity property of the nonlinear recombination operators. By deriving precise local Lipschitz bounds for the stimulated recombination operator, we verify the conditions needed to apply the abstract existence theorem. As a consequence, we obtain the existence and uniqueness of weak solutions to a drift-diffusion-Helmholtz model of semiconductor lasers that incorporates stimulated emission in a mathematically consistent way. To the best of our knowledge, this is the first rigorous existence and uniqueness result for the nonlinear coupling of the van Roosbroeck system with a Helmholtz eigenvalue problem under physically motivated assumptions.

  • Z. Amer, A. Avdzhieva, M. Bongarti, P. Dvurechensky, P. Farrell, U. Gotzes, F.M. Hante, A. Karsai, S. Kater, M. Landstorfer, M. Liero, D. Peschka, L. Plato, K. Spreckelsen, J. Taraz, B. Wagner, Modeling hydrogen embrittlement for pricing degradation in gas pipelines, Preprint no. 3201, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3201 .
    Abstract, PDF (12 MByte)
    This paper addresses aspects of the critical challenge of hydrogen embrittlement in the context of Germany's transition to a sustainable, hydrogen-inclusive energy system. As hydrogen infrastructure expands, estimating and pricing embrittlement become paramount due to safety, operational, and economic concerns. We present a twofold contribution: We discuss hydrogen embrittlement modeling using both continuum models and simplified approximations. Based on these models, we propose optimization-based pricing schemes for market makers, considering simplified cyclic loading and more complex digital twin models. Our approaches leverage widely-used subcritical crack growth models in steel pipelines, with parameters derived from experiments. The study highlights the challenges and potential solutions for incorporating hydrogen embrittlement into gas transportation planning and pricing, ultimately aiming to enhance the safety and economic viability of Germany's future energy infrastructure.

  • R. Araya, C. Cárcamo, A.H. Poza, A stabilized finite element method for the Navier--Stokes/Darcy coupled problem, Preprint no. 3183, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3183 .
    Abstract, PDF (2163 kByte)
    In this work, we propose, analyze, and numerically verify a new stabilized finite element method for the Navier--Stokes/Darcy coupled problem, which models a fluid flowing through a free medium into a porous medium. At the interface between both domains, we impose mass conservation, the balance of normal forces, and the well-known Beavers--Joseph--Saffman con- ditions [9]. The stabilization terms are defined using Galerkin's least-squares stabilization for the Navier--Stokes equation and Masud--Hughes stabilization [30] for the Darcy equation. This new discrete scheme employs equal-order elements to approximate the velocity and pressure of the fluid and generalizes the scheme recently analyzed for the linear case in [4]. The well-posedness of the discrete problem is established via fixed-point theorems under small data conditions, and we prove optimal error estimates in natural norms. Finally, we present numerical examples to confirm the expected theoretical convergence orders in cases where a manufactured solution is available, as well as to demonstrate the effectiveness of our scheme in a physical model with varying permeability fields.

  • M. Eigel, Ch. Merdon, A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs, Preprint no. 3174, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3174 .
    Abstract, PDF (5084 kByte)
    PDEs with random data are investigated and simulated in the field of Uncertainty Quantification (UQ), where uncertainties or (planned) variations of coefficients, forces, domains and boundary con- ditions in differential equations formally depend on random events with respect to a pre-determined probability distribution. The discretization of these PDEs typically leads to high-dimensional (determin- istic) systems, where in addition to the physical space also the (often much larger) parameter space has to be considered. A proven technique for this task is the Stochastic Galerkin Finite Element Method (SGFEM), for which a review of the state of the art is provided. Moreover, important concepts and results are summarized. A special focus lies on the a posteriori error estimation and the derivation of an adaptive algorithm that controls all discretization parameters. In addition to an explicit residual based error estimator, also an equilibration estimator with guaranteed bounds is discussed. Under cer- tain mild assumptions it can be shown that the successive refinement produced by such an adaptive algorithm leads to a sequence of approximations with guaranteed convergence to the true solution. Nu- merical examples illustrate the practical behavior for some common benchmark problems. Additionally, an adaptive algorithm for a problem with a non-affine coefficient is shown. By transforming the original PDE a convection-diffusion problem is obtained, which can be treated similarly to the standard affine case.

  • O. Pártl, E. Meneses Rioseco, Efficient numerical framework for geothermal energy production optimization in fracture-controlled reservoirs, Preprint no. 3169, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3169 .
    Abstract, PDF (3112 kByte)
    We describe an open-source numerical framework for the automated search for the placements of injection and production wells in hot fracture-controlled reservoirs that sustainably optimize geothermal energy production, where we consider deviated multiwell layouts (smart multiwell arrangement). This search is carried out via 3D simulations of groundwater flow and heat transfer. We model the reservoirs as discrete fracture networks (DFN) in which the fractures are 2D manifolds with polygonal boundaries embedded in a 3D porous medium. The wells are modeled via the immersed boundary method. The flow and heat transport in the DFN-matrix system are modeled by solving the balance equations for mass, momentum, and energy. The fully developed numerical framework combines the finite element method with semi-implicit time-stepping, algebraic flux correction, and approximation of the wells via the non-matching approach. To perform the optimization, we use various gradient- free algorithms. We present the results of verification and validation tests with DFNs of simple structure and realistic physical parameter values.

  • C. Cárcamo, P. Ciarlet Jr., AT-coercivity approach to the nonlinear Stokes equations, Preprint no. 3167, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3167 .
    Abstract, PDF (234 kByte)
    We address the nonlinear Stokes problem with Dirichlet boundary conditions, introducing additional variables into the standard formulation to accommodate solutions with reduced regularity requirements. To ground this analysis, we first review relevant preliminary results, emphasizing the significance of achieving T -coercivity in the context of nonlinear Stokes flows. We then introduce a specially designed operator T , proving its bijectivity and showing that it induces coercivity when applied to the test function space. This result provides a rigorous foundation for solving the quasi- Newtonian Stokes problem with minimal regularity constraint and also sets up the T -coercivity as an alternative to the well-posedness of the nonlinear Stokes problems.

Talks, Poster

  • A. Erhardt, Nonlinear dynamics of complex biophysical processes, Berliner Oberseminar 'Nichtlineare partielle Differentialgleichungen' (Langenbach-Seminar), WIAS, January 7, 2026.

  • D. Abdel, Charge transport in perovskite solar cells: Modelling, analysis and simulations, Workshop on Mathematical Models for Quantum and Semiclassical Dynamics, September 10 - 12, 2025, University of Florence, Department of Mathematics and Informatics Ülisse Dini", Italy, September 12, 2025.

  • D. Abdel, Charge transport in perovskite solar cells: modelling, numerical analysis and simulations, Mini-workshop ARISE, Inria center at the University of Lille, Villeneuve d'Ascq, France, June 17, 2025.

  • C. Belponer, Modelling vascularized tissues: coupling 3D elastic matrix and 1D vascular tree, COUPLED 2025, XI International Conference on Coupled Problems in Science and Engineering, May 25 - 28, 2025, CIMNE, International Centre for Numerical Methods in Engineering, Sardinien, Italy, May 27, 2025.

  • C. Belponer, Modelling vascularized tissues: coupling 3D elastic matrix and 1D vascular tree, dealii-X Research School - Digital Twins of the Human Body, December 10 - 12, 2025, International School for Advanced Studies (SISSA), Trieste, Italy, December 11, 2025.

  • Z. Elsayed Amer, Modeling and simulation of a coupled van Roosbroeck--Helmholtz System, Workshop on Mathematical Models for Quantum and Semiclassical Dynamics, September 10 - 12, 2025, University of Florence, Department of Mathematics and Informatics Ülisse Dini", Italy, September 12, 2025.

  • Z. Elsayed Amer, Numerical methods for a coupled drift-diffusion and Helmholtz model for laser applications, MESIGA25: Numerical Methods in Applied Mathematics, March 11 - 13, 2025, Institut für Mathematik der Universität Potsdam, March 12, 2025.

  • S. Katz, A. Caiazzo, Data-driven reduced-order modeling and data assimilation for cardiovascular imaging, MATH+ Day 2025, Berlin, November 17, 2025.

  • A. Erhardt, Mathematical modeling and analysis of cardiac dynamics, Kolloquium des SFB 1114, Freie Unversität Berlin, April 24, 2025.

  • Y. Hadjimichael, Strain distribution in zincblende and wurtzite nanowires bent by a one-sided stressor shell, Leibniz MMS Days 2025, March 26 - 28, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 27, 2025.

  • W. Kenmoe Nzali, D. Kreher, Ch. Bayer, M. Landstorfer, Volatile electricity market and battery storage, Vienna Congress on Mathematical Finance (VCMF 2025), Austria, July 9 - 11, 2025.

  • W. Kenmoe Nzali, D. Kreher, Ch. Bayer, M. Landstorfer, Volatile electricity market and battery storage, Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2025, Thuwal, Saudi Arabia, May 18 - 25, 2025.

  • W. Kenmoe Nzali, D. Kreher, Ch. Bayer, M. Landstorfer, Math+ Day, November 17, 2025.

  • CH. Pohl, Modeling of solid-electrolyte interphase growth with non-equilibrium thermodynamics, 248th ECS Meeting, Session 'Electrolytes & Interfaces in Li-ion Batteries and Beyond', Chicago, USA, October 12 - 16, 2025.

  • M. Demir, An evolve-filter-relax regularized reduced order model for the Boussinesq approximat, SIAM Conference on Computational Science and Engineering (CSE25), March 3 - 7, 2025, SIAM, Society for Industrial and Applied Mathematics, Fort Worth, Texas, USA.

  • CH. Keller, Die Mechanik des Lebens: Physik und Mathematik von Ionenkanälen, Mathematisch-Physikalisches Kolloquium, Technische Hochschule Nürnberg Georg-Simon-Ohm, March 25, 2025.

  • M. Zainelabdeen, Gradient-robust finite element-finite volume scheme for the compressible Navier--Stokes equations, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Minisymposium MS07 Ädvances in Numerical Methods for Problems from Fluid Mechanics", September 1 - 5, 2025, Universität Heidelberg, September 4, 2025.

  • M. Zainelabdeen, Gradient-robust finite element-finite volume scheme for the compressible Stokes equations, 21st Workshop on Numerical Methods for Problems with Layer Phenomena, April 24 - 25, 2025, University of Galway, School of Mathematical and Statistical Sciences, Ireland, April 24, 2025.

  • A. Caiazzo, Application of shape registration of aortic geometries to data assimilation and graph neural networks, COOMEDIA-Seminar, Computational mathematics for bio-medical applications, February 18 - 19, 2025, Inria, Sorbonne Université and CNRS, Paris, France, February 19, 2025.

  • A. Caiazzo, Shape-informed reduced-order modeling and graph neural networks: Application to data assimilation in aortic blood flow, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Minisymposium MS49 "PDE Models and Algorithms for Biomedical Applications", September 1 - 5, 2025, Universität Heidelberg, September 2, 2025.

  • A. Caiazzo, Shape-informed surrogate modeling and data assimilation in aortic blood flow, XI International Conference on Computational Bioengineering - ICCB 2025, Minisymposium MS02 "Cardiovascular inverse problems", September 8 - 10, 2025, Università Campus Bio-Medico di Roma, Italy, September 8, 2025.

  • C. Cárcamo, A finite element method for a perturbed Navier--Stokes problem arising form 4D-flow, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), September 1 - 5, 2025, Universität Heidelberg, September 4, 2025.

  • C. Cárcamo, A finite element method for a perturbed Navier--Stokes problem arising from 4D-flow MRI, The 30th Biennial Conference on Numerical Analysis, June 24 - 27, 2025, University of Strathclyde, Department of Mathematics and Statistics, Glasgow, UK, June 24, 2025.

  • P. Farrell, Numerische Methoden für innovative Halbleiterbauteile, Transfer Workshop: ErUM-Scientists and Industry in Dialogue, February 6 - 7, 2025, ErUM Data Hub, Aachen, February 6, 2025.

  • P. Farrell, Unravelling the mystery of enhanced open-circuit voltages in nanotextured perovskite solar cells, Kaiserslautern Applied and Industrial Mathematics Days - KLAIM 2025, October 6 - 8, 2025, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM, Kaiserslautern, October 7, 2025.

  • J. Fuhrmann, Continuum scale electrolyte simulations based on finite volume methods, Bridging the Gap II: Transitioning from Deterministic to Stochastic Interaction Modeling in Electrochemistry, September 3 - December 12, 2025, Institute for Pure and Applied Mathematics, University of California, Los Angeles, USA, October 8, 2025.

  • J. Fuhrmann, Finite volume based electrolyte simulations in the Julia programming language, Seminar: Theorie und computergestützte Modellierung von Materialien in der Energietechnik (IET-3), January 15 - 17, 2025, Forschungszentrum Jülich, Institute of Energy Technologies (IET), January 16, 2025.

  • J. Fuhrmann, LiquidElectrolytes.jl - A generalized Poisson-Nernst-Planck solver written in Juli, ModVal 2025 - 21st Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, Karlsruhe, March 10 - 12, 2025.

  • J. Fuhrmann, The Julia language: Reproducibility infrastructure and project workflows, Leibniz MMS Days 2025, March 26 - 28, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 28, 2025.

  • J. Fuhrmann, Thermodynamically consistent finite volume methods for generalized Nernst--Planck--Poisson problems, Bridging the Gap: Transitioning from Deterministic to Stochastic Interaction Modeling in Electrochemistry, September 3 - December 12, 2025, Institute for Pure and Applied Mathematics, University of California, Los Angeles, USA, September 9, 2025.

  • J. Fuhrmann, Two point flux finite volume methods for mixture flows in porous media, Mixtures: Modeling, analysis and computing, February 5 - 7, 2025, Charles University, Faculty of Mathematics and Physics, Prag, Czech Republic, February 5, 2025.

  • P. Jaap, Stochastic rounding: When 0.1 + 0.2 - 0.3 does equal zero (at least on average), JuliaCon Local Paris 2025, October 2 - 3, 2025, France, October 2, 2025.

  • P. Jaap, WIAS-PDELib: AJulia PDE solver ecosystem in a GitHub organization, deRSE25 - 5th conference for Research Software Engineering in Germany, February 25 - 27, 2025.

  • V. John, Finite element methods respecting the discrete maximum principle for convection-diffusion equations, The International Conference on Multigrid and Multiscale Methods in Computational Science (IMG) 2025, February 3 - 5, 2025, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia, February 3, 2025.

  • V. John, Prof. Dr. Lutz Tobiska - Wichtige wissenschaftliche Beiträge, Gedenkkolloquium für Prof. Dr. Herbert Goering und Prof. Dr. Lutz Tobiska, Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, November 28, 2025.

  • V. John, Some experiences in using ML techniques for the numerical solution of PDEs, Leibniz MMS Days 2025, March 26 - 27, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 27, 2025.

  • V. John, Some experiences in using machine learning techniques for the numerical solution of PDEs, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Minisymposium MS07 Ädvances in Numerical Methods for Problems from Fluid Mechanics", September 1 - 5, 2025, Universität Heidelberg, September 2, 2025.

  • V. John, Some experiences in using machine learning techniques for the numerical solution of partial differential equations, Latest Advances in Computational and Applied Mathematics (LACAM 2025), December 8 - 11, 2025, Indian Institute of Science Education and Reaseach, IISER Thiruvananthapuram, School of Mathematics, Kerala, India, December 11, 2025.

  • V. John, Some experiences in using machine learning techniques for the numerical solution of partial differential equations, Seminar of Dr. Shweta Srivastava, Assistant Professor at the School of Digital Sciences, Digital University Kerala, India, December 10, 2025.

  • V. John, Wie gut kann Physik in Simulationen widergespiegelt werden?, Reihe: Mathematische Forschung verstehen, Freie Universität Berlin, Fachbereich Mathematik und Informatik, May 14, 2025.

  • M. Landstorfer, M. Heida, Ch. Pohl, Modeling lithium-ion batteries with phase separation using non-equilibrium thermodynamics and homogenization theory, Oxford Battery Modelling Symposium (OBMS), Oxford, UK, July 24 - 25, 2025.

  • M. Landstorfer, Aspects of battery modeling with non-equilibrium thermodynamics and homogenization theory, Group Seminar: Transfer Group, May 21 - 23, 2025, Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences, Linz, Austria, May 22, 2025.

  • M. Landstorfer, Continuum thermodynamic models for electrochemical interfaces, Bridging the Gap II: Transitioning from Deterministic to Stochastic Interaction Modeling in Electrochemistry, September 3 - December 12, 2025, Institute for Pure and Applied Mathematics, University of California, Los Angeles, USA, October 8, 2025.

  • M. Landstorfer, The double layer capacitance of aqueous and aprotic electrode-electrolyte interfaces: Thermodynamic modeling and experimental data, 76th Annual Meeting of the International Society of Electrochemistry (ISE), Electrochemistry: From Basic Insights to Sustainable Technologies, September 7 - 12, 2025, International Society of Electrochemistry, Lausanne, Mainz, September 8, 2025.

  • CH. Merdon, Pressure-robust discretizations for axisymmetric flow problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Minisymposium MS07 Ädvances in Nmerical Methods for Problems from Fluid Mechanics", September 1 - 5, 2025, Universität Heidelberg, September 4, 2025.

  • CH. Merdon, Pressure-robustness for (nearly) incompressible flows, The ninth international conference on Ädvanced COmputational Methods in ENgineering and Applied Mathematics" (ACOMEN2025), MS9 Ädvanced Numerical Methods for Flow and Related Problems", September 15 - 19, 2025, Ghent University, University of Liège, Ghent, Belgium.

  • O. Pártl, Efficient numerical framework for fracture-controlled reservoir performance optimization, Leibniz MMS Days 2025, March 26 - 28, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 27, 2025.

  • O. Pártl, Geothermal well placement optimization for sustainable energy production: New computational framework for fracture-controlled reservoirs, European Geothermal Congress (EGC), October 6 - 10, 2025, Zürich, Switzerland, October 8, 2025.

  • F. Romor, DG-based domain decomposable reduced order models and repartitioning strategies: applications to biomedical models, COUPLED 2025, XI International Conference on Coupled Problems in Science and Engineering, May 25 - 28, 2025, CIMNE, International Centre for Numerical Methods in Engineering, Sardinien, Italy, May 28, 2025.

  • F. Romor, Data assimilation performed with robust shape registration and graph neural networks: Application to aortic coarctation, MESIGA25: Numerical Methods in Applied Mathematics, March 11 - 13, 2025, Institut für Mathematik der Universität Potsdam, March 12, 2025.

  • F. Romor, Registration-based data assimilation from medical images, COLIBRI Focus Workshop on Computational Medicine, January 30 - 31, 2025, Universität Graz, Austria, January 30, 2025.

  • F. Romor, Registration-based data assimilation from medical images, DTE & AICOMAS 2025, 3rd IACM Digital Twins an Engineering Conference (DTE 2025) & 1st ECCOMAS Artificial Intelligence and Computational Methods in Applied Science (AICOMAS 2025), February 17 - 21, 2025, Arts et Métiers - ENSAM (Paris Campus), Paris, France, February 18, 2025.

  • F. Romor, Registration-based data assimilation from medical images, Young Mathematicians in Model Order Reduction, YMMOR2025, May 5 - 9, 2025, Scuola Internazionale Superiore di Studi Avanzati, SISSA, Trieste, Italy, May 5, 2025.

  • F. Romor, Shape-informed data assimilation and graph neural networks: An application to aortic coarctation, 11th GACM Colloquium on Computational Mechanics for Young Scientists, September 21 - 24, 2025, TU Braunschweig, September 22, 2025.

  • H. Stephan, Die Rolle der Zeit in der Mathematik, Tag der Mathematik, Berliner Hochschule für Technik (BFT), May 10, 2025.

  • J.P. Thiele, Easy to use tools for software quality, Leibniz MMS Days 2025, March 26 - 28, 2025, The Leibniz Research Network "Mathematical Modeling and Simulation", Leibniz Institute for Baltic Sea Research Warnemünde (IOW), March 27, 2025.

  • J.P. Thiele, Software Engineering for and with Reserchers: What is required?, deRSE25 - 5th conference for Research Software Engineering in Germany, February 25 - 27, 2025, Karlsruher Institut für Technologie, February 26, 2025.

External Preprints

  • D. Abdel, A. Blaustein, C. Chainais-Hillairet, M. Herda, J. Moatti, Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers, Preprint no. 2511.23250, Cornell University, 2025, DOI 10.48550/arXiv.2511.23250 .
    Abstract
    We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other applications, in the context of semiconductor modeling for perovskite solar cells. Thanks to truncation techniques and iterative energy estimates, we show the existence and uniform upper and lower bounds on the solutions. The dependency of the bounds on the various parameters of the model is investigated numerically on physically relevant test cases.

  • D. Abdel, M. Herda, M. Ziegler, C. Chainais-Hillairet, B. Spetzler, P. Farrell, Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models, Preprint no. 15065, Cornell University, 2024, DOI 10.48550/arXiv.2412.15065 .
    Abstract
    In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential as components for next-generation artificial intelligence (AI) hardware and information technology. Our charge transport model describes the drift-diffusion of electrons, holes, and ionic defects self-consistently in an electric field. We incorporate two types of boundary models: ohmic and Schottky contacts. The coupled drift-diffusion partial differential equations are discretized using a physics-preserving Voronoi finite volume method. It relies on an implicit time-stepping scheme and the excess chemical potential flux approximation. We demonstrate that the fully discrete nonlinear scheme is unconditionally stable, preserving the free-energy structure of the continuous system and ensuring the non-negativity of carrier densities. Novel discrete entropy-dissipation inequalities for both boundary condition types in multiple dimensions allow us to prove the existence of discrete solutions. We perform multi-dimensional simulations to understand the impact of electrode configurations and device geometries, focusing on the hysteresis behavior in lateral 2D memristive devices. Three electrode configurations - side, top, and mixed contacts - are compared numerically for different geometries and boundary conditions. These simulations reveal the conditions under which a simplified one-dimensional electrode geometry can well represent the three electrode configurations. This work lays the foundations for developing accurate, efficient simulation tools for 2D memristive devices and memtransistors, offering tools and guidelines for their design and optimization in future applications.

  • D. Abdel, J. Relle, Th. Kirchartz, P. Jaap, J. Fuhrmann, S. Burger, Ch. Becker, K. Jäger, P. Farrell, Unravelling the mystery of enhanced open-circuit voltages in nanotextured perovskite solar cells, Preprint no. 2506.10691, Cornell University, 2025, DOI 10.48550/arXiv.2506.10691 .
    Abstract
    Perovskite solar cells have reached power conversion efficiencies that rival those of established silicon photovoltaic technologies. Nanotextures in perovskite solar cells optimise light trapping and scattering, thereby improving optical absorption. In addition, nanotextures have been experimentally shown to enhance electronic performance, in particular, by increasing the open- circuit voltage VOC ? a phenomenon that, until now, has remained not fully understood. This study investigates the underlying reasons by combining multi-dimensional optical and charge- transport simulations for a single-junction perovskite solar cell. Our results reveal that the increased open-circuit voltage is not driven by optical effects but by the textured geometry itself. For voltages near VOC, texturing one of the absorber/transport layer interfaces increases the imbalance between electron and hole densities in the absorber, thereby reducing Shockley-Read- Hall (SRH) recombination, which is the dominant loss mechanism in this study. While idealised solar cells benefit unconditionally from increasing texture height, in realistic cells there is an optimal texture height which maximizes the power conversion efficiency. These findings provide new insights into the opto-electronic advantages of texturing and offer guidance for the design of next-generation textured perovskite-based solar cells, light emitting diodes, and photodetectors.

  • S.M. Allen, N. Chue Hong, S. Druskat, T. Hodges, D.S. Katz, J. Linxweiler, F. Löffler, L. Grunske, H. Seibold, J.P. Thiele, S. Wittke, Ten simple rules for PIs to integrate Research Software Engineering into their research group, Preprint no. 2506.20217, Cornell University, 2025, DOI 10.48550/arXiv.2506.20217 .
    Abstract
    Research Software Engineering (RSEng) is a key success factor in producing high-quality research software [1] and thus improves research project outcomes, since better research software leads to better research [2]. However, as a leader of a research group or project you may not know what RSEng is, or how you can maximize its impact on your research. To make matters worse, if you try to read about RSEng or strike up a conversation about how it might be relevant to your research, you might be met with complicated technical details [3]. Surely, it must be possible to learn what RSEng is about without first enrolling in a Computer Science program at your university! Many explanations and tutorials for development aspects like testing, software architecture and version control are very technical. This prevents researchers and other decision makers from making an informed choice about employing these methods. The result may be research software that is less robust [4] and less usable [5], and research that is less reproducible [6]. In contrast, using fundamental RSEng methods can make code good enough, even when programming needs to be quick and dirty [7]. Our aim is to provide comprehensible descriptions of simple rules to improve software-enhanced research.

  • N. Gauger, A. Linke, Ch. Merdon, Refined stability estimates for mixed problems by exploiting semi norm arguments, Preprint no. 2506.11566, Cornell University, 2025, DOI 10.48550/arXiv.2506.11566 .
    Abstract
    Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier?Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.

  • M. Khamlich, F. Romor, G. Rozza, Efficient numerical strategies for entropy-regularized semi-discrete optimal transport, Preprint no. 2507.23602, Cornell University, 2025, DOI 10.48550/arXiv.2507.23602 .
    Abstract
    Semi-discrete optimal transport (SOT), which maps a continuous probability mea- sure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a regularized (RSOT) for- mulation that can be solved efficiently via its convex dual. However, a significant computational challenge emerges when the continuous source measure is discretized via the finite element (FE) method to handle complex geometries or densities, such as those arising from solutions to Par- tial Differential Equations (PDEs). The evaluation of the dual objective function requires dense interactions between the numerous source quadrature points and all target points, creating a se- vere bottleneck for large-scale problems. This paper presents a cohesive framework of numerical strategies to overcome this challenge. We accelerate the dual objective and gradient evaluations by combining distance-based truncation with fast spatial queries using R-trees. For overall con- vergence, we integrate multilevel techniques based on hierarchies of both the FE source mesh and the discrete target measure, alongside a robust scheduling strategy for the regularization parameter. When unified, these methods drastically reduce the computational cost of RSOT, enabling its practical application to complex, large-scale scenarios. We provide an open-source C++ implementation of this framework, built upon the deal.II finite element library, available at https://github.com/SemiDiscreteOT/SemiDiscreteOT.

  • H. Li, C. Cárcamo, H. Rui, V. John, Coupling of conforming and mixed finite element methods for a model of wave propagation in thermo-poroelasticity in the frequency domain, Preprint no. 17984, Cornell University, 2025, DOI 10.48550/arXiv.2511.17984 .
    Abstract
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  • B. Spetzler, E. Spetzler, S. Zamankhani, D. Abdel, P. Farrell, K.-U. Sattler, M. Ziegler, Physics-guided sequence modeling for fast simulation and design Exploration of 2D memristive devices, Preprint no. 2505.13882, Cornell University, 2025, DOI 10.48550/arXiv.2505.13882 .
    Abstract
    Modeling hysteretic switching dynamics in memristive devices is computationally demanding due to coupled ionic and electronic transport processes. This challenge is particularly relevant for emerging two-dimensional (2D) devices, which feature high-dimensional design spaces that remain largely unexplored. We introduce a physics-guided modeling framework that integrates high-fidelity finite-volume (FV) charge transport simulations with a long short-term memory (LSTM) artificial neural network (ANN) to predict dynamic current-voltage behavior. Trained on physically grounded simulation data, the ANN surrogate achieves more than four orders of magnitude speedup compared to the FV model, while maintaining direct access to physically meaningful input parameters and high accuracy with typical normalized errors <1%. This enables iterative tasks that were previously computationally prohibitive, including inverse modeling from experimental data, design space exploration via metric mapping and sensitivity analysis, as well as constrained multi-objective design optimization. Importantly, the framework preserves physical interpretability via access to detailed spatial dynamics, including carrier densities, vacancy distributions, and electrostatic potentials, through a direct link to the underlying FV model. Our approach establishes a scalable framework for efficient exploration, interpretation, and model-driven design of emerging 2D memristive and neuromorphic devices.

  • P. Jaap, O. Sander, How to project onto SL(n), Preprint no. 19310, Cornell University, 2025, DOI 10.48550/arXiv.2501.19310 .
    Abstract
    We consider the closest-point projection with respect to the Frobe- nius norm of a general real square matrix to the set SL (n) of matrices with unit determinant. As it turns out, it is sufficient to consider diagonal matrices only. We investigate the structure of the problem both in Euclidean coordinates and in an n-dimensional generalization of the classical hyperbolic coordinates of the positive quadrant. Using symmetry arguments we show that the global minimizer is contained in a particular cone. Based on different views of the problem, we propose four different iterative algorithms, and we give convergence results for all of them. Numerical tests show that computing the projection costs essentially as much as a singular value decomposition. Finally, we give an explicit formula for the first derivative of the projection.

  • V. John, X. Li, Ch. Merdon, Divergence-free decoupled finite element methods for incompressible flow problems, Preprint no. 2512.05642, Cornell University, 2025, DOI 10.48550/arXiv.2512.05642 .
    Abstract
    Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci. 34(05):919--949, 2024], this paper proposes Hpdivq-conforming finite element methods which decouple the velocity and pressure by constructing divergence-free basis functions. Algorithmic issues like the computation of this basis and the imposition of non-homogeneous Dirichlet boundary conditions are discussed. Numerical studies at two- and three- dimensional Stokes problems compare the efficiency of the proposed methods with methods from the above mentioned paper.

  • F. Romor, F. Galarce, J. Brüning, L. Goubergrits, A. Caiazzo, Data assimilation performed with robust shape registration and graph neural networks: Application to aortic coarctation, Preprint no. 2502.12097, Cornell University, 2025, DOI 10.48550/arXiv.2502.12097 .
    Abstract
    Image-based, patient-specific modelling of hemodynamics can improve diagnostic capabilities and pro- vide complementary insights to better understand the hemodynamic treatment outcomes. However, com- putational fluid dynamics simulations remain relatively costly in a clinical context. Moreover, projection- based reduced-order models and purely data-driven surrogate models struggle due to the high variability of anatomical shapes in a population. A possible solution is shape registration: a reference template geometry is designed from a cohort of available geometries, which can then be diffeomorphically mapped onto it. This provides a natural encoding that can be exploited by machine learning architectures and, at the same time, a reference computational domain in which efficient dimension-reduction strategies can be performed. We compare state-of-the-art graph neural network models with recent data assimilation strategies for the prediction of physical quantities and clinically relevant biomarkers in the context of aortic coarctation.

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