Professional Interests

• Mathematical Methods in Biology and Medicine
• High-Performance Scientific Computing
• Numerical Solution of Partial Differential Equations
• Finite Element Methods
• Numerical Linear Algebra
• Subspace Correction Methods (Domain Decomposition and Multigrid Methods)

• Journal articles:

  • Kraus, Johannes; Kumar, Kundan; Lymbery, Maria; Adrian Radu, Florin

    A fixed-stress type splitting method for nonlinear poroelasticity

    In: Engineering with Computers (2023) in press

    Online Full Text: dx.doi.org/ (Open Access)
  • Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Philo, Fadi

    A new practical framework for the stability analysis of perturbed saddle-point problems and applications

    In: Mathematics of Computation (MCOM) Vol. 92 (2023) Nr. 340, pp. 607 - 634

    Online Full Text: dx.doi.org/ (Open Access)
  • Kraus, Johannes; Lederer, Philip L.; Lymbery, Maria; Osthues, Kevin; Schoberl, Joachim

    Hybridized Discontinuous Galerkin/Hybrid Mixed Methods for a Multiple Network Poroelasticity Model with Application in Biomechanics

    In: SIAM Journal on Scientific Computing Vol. 45 (2023) Nr. 6, pp. B802 - B827

    Online Full Text: dx.doi.org/
  • Hong, Qingguo; Kraus, Johannes; Kuchta, Miroslav; Lymbery, Maria; Mardal, Kent-André; Rognes, Marie E.

    Robust Approximation of Generalized Biot-Brinkman Problems

    In: Journal of Scientific Computing Vol. 93 (2022) Nr. 3, 77

    Online Full Text: dx.doi.org/ (Open Access)
  • Bause, Markus; Lymbery, Maria; Osthues, Kevin
    C¹-conforming variational discretization of the biharmonic wave equation
    In: Computers & Mathematics with Applications Vol. 119 (2022) Pages 208-219
    Online Full Text: dx.doi.org/ (Open Access)
  • Kraus, Johannes; Lederer, Philip L.; Lymbery, Maria; Schöberl, Joachim

    Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model

    In: Computer Methods in Applied Mechanics and Engineering Vol. 384 (2021) 113991

    Online Full Text: dx.doi.org/ (Open Access)
  • Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Wheeler, Mary F.

    Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity Systems

    In: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Vol. 18 (2020) Nr. 2, pp. 916 - 941

    Online Full Text: dx.doi.org/ (Open Access)
  • Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Philo, Fadi

    Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot's consolidation and multiple-network poroelasticity models

    In: Mathematical Models and Methods in Applied Sciences Vol. 30 (2020) Nr. 13, pp. 2523 - 2555

    Online Full Text: dx.doi.org/ (Open Access)
  • Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Philo, Fadi

    Conservative discretizations and parameter-robust preconditioners for Biot and multiple-network flux-based poroelasticity models

    In: Numerical Linear Algebra with Applications Vol. 26 (2019) Nr. 4, pp. e2242

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria

    Incomplete factorization by local exact factorization (ILUE)

    In: Mathematics and Computers in Simulation Vol. 145 (2018) pp. 50 - 61

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria; Margenov, Svetozar; Zikatanov, Ludmil

    Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications

    In: SIAM Journal on Numerical Analysis Vol. 38 (2016) Nr. 2, pp. A875 - A898

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria; Margenov, S.

    Auxiliary space multigrid method based on additive Schur complement approximation

    In: Numerical Linear Algebra with Applications Vol. 22 (2015) Nr. 6, pp. 965 - 986

    Online Full Text: dx.doi.org/ Online Full Text (Open Access)
  • Kraus, Johannes; Lymbery, Maria; Margenov, Svetozar

    Robust multilevel methods for quadratic finite element anisotropic elliptic problems

    In: Numerical Linear Algebra with Applications Vol. 21 (2014) Nr. 3, pp. 375 - 398

    Online Full Text: dx.doi.org/
  • Lymbery, Maria; Margenov, Svetozar
    Robust semi-coarsening multilevel preconditioning of biquadratic FEM systems
    Central European Journal of Mathematics Vol. 10 (2012), pages 357–369
    Online Full Text: dx.doi.org/

• Preprints

  • Kraus, Johannes; Lymbery, Maria; Osthues, Kevin; Philo, Fadi

    Analysis of a family of time-continuous strongly conservative space-time finite element methods for the dynamic Biot model

    (2024)

    Online Full Text: dx.doi.org/

• Book articles / Proceedings papers

  • Jonske, Frederic; Osthues, Kevin; Dada, Amin; Nasca, Enrico; Fragemann, Jana; Alff, Julian; Bakumenko, Oleh; Birnbach, Marcel; Kondratenko, Maxim; Reinike, Lars; Schulz, Benjamin; Siethoff, Fabian; Simon, Tobias; Wang, Joey; Zhang, Nils; Bahnsen, Fin H.; Egger, Jan; Kim, Moon-Sung; Lymbery, Maria; Kleesiek, Jens; Kraus, Johannes

    Designing and Implementing an Interactive Cloud Platform for Teaching Machine Learning with Medical Data

    In: Artificial Intelligence for Security: Enhancing Protection in a Changing World / Sipola, Tuomo; Alatalo, Janne; Wolfmayr, Monika; Kokkonen, Tero (Eds.) 2024, pp. 259 - 292

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria

    Auxiliary Space Multigrid Method for Elliptic Problems with Highly Varying Coefficients

    In: Domain Decomposition Methods in Science and Engineering XXII / Dickopf, Thomas; Gander, Martin J. (Eds.) 2016, pp. 29 - 40

    Online Full Text: dx.doi.org/
  • Lymbery, Maria

    Robust Balanced Semi-coarsening Multilevel Preconditioning of Bicubic FEM Systems

    In: In: Large-Scale Scientific Computing: Revised Selected Papers / 9th International Conference, LSSC 2013, Sozopol, Bulgaria, June 3-7, 2013 / Lirkov, Ivan; Mergenov, Svetozar; Waśniewski, Jerzy (Eds.) 2014,

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria; Margenov, Svetozar

    Robust Algebraic Multilevel Preconditioners for Anisotropic Problems

    In: Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications / Iliev, Oleg; Margenov, Svetozar; Minev, Peter (Eds.) 2013, pp. 217 - 245

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria; Margenov, Svetozar

    On the Robustness of Two-Level Preconditioners for Quadratic FE Orthotropic Elliptic Problems

    In: Large-Scale Scientific Computing: Revised Selected Papers / 8th International Conference, LSSC 2011, Sozopol, Bulgaria, June 6-10, 2011 / Lirkov, Ivan; Mergenov, Svetozar; Waśniewski, Jerzy (Eds.) 2012, pp. 582 - 589

    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Lymbery, Maria; Margenov, Svetozar
    Semi-coarsening AMLI preconditioning of higher order elliptic problems
    In: Numerical Analysis and Applied Mathematics ICNAAM 2012 / International Conference of Numerical Analysis and Applied Mathematics, 19–25 September 2012, Kos, Greece / Simos, Theodore E.; Psihoyios, George (Eds.) 2012, pp. 30 - 41
    Online Full Text: dx.doi.org/
  •  Lymbery, Maria; Margenov, Svetozar
    Robust Balanced Semi-Coarsening AMLI Preconditioning of Biquadratic FEM Systems.
    In: Application Of Mathematics In Technical And Natural Sciences / 3rd International Conference - AMiTaNS'11 / Todorov, Michail D.; Christov, Christo I. (Eds.) 2012, pp. 438–447
    Online Full Text: dx.doi.org/

Dr. habil. Maria Lymbery

Private Lecturer

University of Duisburg-Essen
Faculty of Mathematics
Thea-Leymann-Str. 9
45127 Essen