Publications

    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)
  • Nakov, Svetoslav; Sobakinskaya, Ekaterina; Renger, Thomas; Kraus, Johannes
    ARGOS: An adaptive refinement goal‐oriented solver for the linearized Poisson–Boltzmann equation
    In: Journal of Computational Chemistry Vol. 42 (2021) Nr. 26, pp. 1832 - 1860
    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)
  • Kraus, Johannes; Nakov, Svetoslav; Repin, Sergey
    Reliable Computer Simulation Methods for electrostatic Biomolecular Models Based on the Poisson-Boltzmann Equation
    In: Computational Methods in Applied Mathematics Vol. 20 (2020) Nr. 4, pp. 643 - 676
    Online Full Text: dx.doi.org/ (Open Access)
  • Kraus, Johannes; Nakov, Svetoslav; Repin, Sergey I.
    Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson-Boltzmann Equation
    In: Computational Methods in Applied Mathematics Vol. 20 (2020) Nr. 2, pp. 293 - 319
    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; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
    Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
    In: Journal of Computational Physics Vol. 398 (2019) pp. 108866
    Online Full Text: dx.doi.org/ (Open Access)
  • 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/
  • Hong, Qingguo; Kraus, Johannes
    Parameter-robust stability of classical three-field formulation of Biot's consolidation model
    In: Electronic Transactions on Numerical Analysis (ETNA) Vol. 48 (2018) pp. 202 - 226
    Online Full Text: dx.doi.org/ (Open Access)
  • Bayramov; Kraus, Johannes
    Multigrid methods for convection–diffusion problems discretized by a monotone scheme
    In: Computer Methods in Applied Mechanics and Engineering Vol. 317 (2017) pp. 723 - 745
    Online Full Text: dx.doi.org/
  • Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil
    A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
    In: Numerische Mathematik Vol. 132 (2016) Nr. 1, pp. 23 - 49
    Online Full Text: dx.doi.org/ Online Full Text (Open Access)
  • 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/
  • Hong, Qingguo; Kraus, Johannes
    Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem
    In: SIAM Journal on Numerical Analysis Vol. 54 (2016) Nr. 5, pp. 2750 - 2774
    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)
  • Bayramov, N.R.; Kraus, Johannes
    On the stable solution of transient convection–diffusion equations
    In: Journal of Computational and Applied Mathematics Vol. 280 (2015) Nr. 1, pp. 275 - 293
    Online Full Text: dx.doi.org/
  • 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/
  • Ayuso de Dios, Blanca; Georgiev, Ivan; Kraus, Johannes; Zikatanov, Ludmil
    A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
    In: Mathematical Modelling and Numerical Analysis (ESAIM-M2AN) Vol. 47 (2013) Nr. 5, pp. 1315 - 1333
    Online Full Text: dx.doi.org/
  • Brannick, J.; Zikatanov, Ludmil; Kraus, Johannes; Chen, Y.
    Algebraic Multilevel Preconditioners for the Graph Laplacian Based on Matching in Graphs
    In: SIAM Journal on Numerical Analysis Vol. 51 (2013) Nr. 3, pp. 1805 - 1827
    Online Full Text: dx.doi.org/
  • Gahalaut, K.P.S.; Kraus, Johannes; Tomar, S.K.
    Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies
    In: Computer Methods in Applied Mechanics and Engineering Vol. 266 (2013) pp. 40 - 56
    Online Full Text: dx.doi.org/
  • Gahalaut, K.P.S.; Kraus, Johannes; Tomar, S.K.
    Multigrid methods for isogeometric discretization
    In: Computer Methods in Applied Mechanics and Engineering Vol. 253 (2013) pp. 413 - 425
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Wolfmayr, Monika
    On the robustness and optimality of algebraic multilevel methods for reaction–diffusion type problems
    In: Computing and Visualization in Science Vol. 16 (2013) Nr. 1, pp. 15 - 32
    Online Full Text: dx.doi.org/
  • Kraus, Johannes
    Additive Schur Complement Approximation and Application to Multilevel Preconditioning
    In: SIAM journal on scientific computing Vol. 34 (2012) Nr. 6, pp. A2872 - A2895
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Vassilevski, Panayot; Zikatanov, Ludmill
    Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-level Methods
    In: Computational Methods in Applied Mathematics Vol. 12 (2012) Nr. 4, pp. 448 - 468
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Tomar, S.K.
    Algebraic multilevel iteration method for lowest order Raviart–Thomas space and applications
    In: International journal for numerical methods in engineering Vol. 86 (2011) Nr. 10, pp. 1175 - 1196
    Online Full Text: dx.doi.org/
  • Karer, E.; Kraus, Johannes
    Algebraic multigrid for finite element elasticity equations : Determination of nodal dependence via edge-matrices and two-level convergence
    In: International Journal for Numerical Methods in Engineering Vol. 83 (2010) Nr. 5, pp. 642 - 670
    Online Full Text: dx.doi.org/
  • Georgiev, I.; Schicho, J.; Kraus, Johannes; Margenov, S.
    Locally optimized MIC(0) preconditioning of Rannacher–Turek FEM systems
    In: Applied numerical mathematics Vol. 59 (2009) Nr. 10, pp. 2402 - 2415
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Tomar, S.K.
    A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problems
    In: Numerical linear algebra with applications Vol. 15 (2008) Nr. 5, pp. 417 - 438
    Online Full Text: dx.doi.org/
  • Kraus, Johannes
    Algebraic Multigrid Based on Computational Molecules, 2 : Linear Elasticity Problems
    In: SIAM journal on scientific computing Vol. 30 (2008) Nr. 1, pp. 505 - 524
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Tomar, S.K.
    Multilevel Preconditioning of Two-dimensional Elliptic Problems Discretized by a Class of Discontinuous Galerkin Methods
    In: SIAM journal on scientific computing Vol. 30 (2008) Nr. 2, pp. 684 - 706
    Online Full Text: dx.doi.org/
  • Georgiev, I.; Kraus, Johannes; Margenov, S.
    Multilevel algorithms for Rannacher–Turek finite element approximation of 3D elliptic problems
    In: Computing : archives for informatics and numerical computation Vol. 82 (2008) Nr. 4, pp. 217 - 239
    Online Full Text: dx.doi.org/
  • Georgiev, I.; Kraus, Johannes; Margenov, S.
    Multilevel preconditioning of rotated bilinear non-conforming FEM problems
    In: Computers & Mathematics with Applications Vol. 55 (2008) Nr. 10, pp. 2280 - 2294
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Margenov, S.; Synka, J.
    On the multilevel preconditioning of Crouzeix–Raviart elliptic problems
    In: Numerical linear algebra with applications Vol. 15 (2008) Nr. 5, pp. 395 - 416
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Schicho, J.
    Algebraic Multigrid Based on Computational Molecules, 1 : Scalar Elliptic Problems
    In: Computing : archives for informatics and numerical computation Vol. 77 (2006) Nr. 1, pp. 57 - 75
    Online Full Text: dx.doi.org/
  • Kraus, Johannes
    Algebraic multilevel preconditioning of finite element matrices using local Schur complements
    In: Numerical linear algebra with applications Vol. 13 (2006) Nr. 1, pp. 49 - 70
    Online Full Text: dx.doi.org/
  • Kraus, Johannes
    Computing Interpolation Weights in AMG Based on Multilevel Schur Complements
    In: Computing : archives for informatics and numerical computation Vol. 74 (2005) Nr. 4, pp. 319 - 335
    Online Full Text: dx.doi.org/
  • Kraus, Johannes
    An algebraic preconditioning method for M-matrices : linear versus non-linear multilevel iteration
    In: Numerical linear algebra with applications Vol. 9 (2002) Nr. 8, pp. 599 - 618
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Brand, C.W.
    Condition Numbers of Approximate Schur Complements in Two- and Three-Dimensional Discretizations on Hierarchically Ordered Grids
    In: Computing : archives for informatics and numerical computation Vol. 65 (2000) Nr. 2, pp. 135 - 154
    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/ (Open Access)
  • Meggendorfer, Stefan; Kanschat, Guido; Kraus, Johannes
    Monolithic two-level Schwarz preconditioner for Biot's consolidation model in two space dimensions
    (2024)
    Online Full Text: dx.doi.org/ (Open Access)

    • 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; Repin, Sergey
    A Posteriori Error Estimates for Domain Decomposition Methods
    In: Impact of Scientific Computing on Science and Society / Neittaanmäki, Pekka; Rantalainen, Marja-Leena (Eds.) 2023, pp. 127 - 151
    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/
  • Karer, E.; Kraus, Johannes; Zikatanov, Ludmill
    A Subspace Correction Method for Nearly Singular Linear Elasticity Problems
    In: Domain Decomposition Methods in Science and Engineering XX / Bank, Randolph; Holst, Michael; Widlund, Olof (Eds.) 2013, pp. 159 - 166
    Online Full Text: dx.doi.org/
  • Brannick, James; Zikatanov, Ludmil; Chen, Yao; Kraus, Johannes
    An Algebraic Multigrid Method Based on Matching in Graphs
    In: Domain Decomposition Methods in Science and Engineering XX / Bank, Randolph; Holst, Michael; Widlund, Olof (Eds.) 2013, pp. 143 - 150
    Online Full Text: dx.doi.org/
  • Georgiev, I.; Kraus, Johannes
    Preconditioning of Elasticity Problems with Discontinuous Material Parameters
    In: Numerical Mathematics and Advanced Applications 2011: Proceedings of ENUMATH 2011 / 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 / Cangiani, Andrea; Davidchack, Ruslan; Georgoulis, Emmanuil (Eds.) 2013, pp. 761 - 769
    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
    Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients
    In: Large-Scale Scientific Computing: Revised Selected Papers / 8th International Conference, LSSC 2011, Sozopol, Bulgaria, June 6-10, 2011 / Lirkov, Ivan; Margenov, Svetozar; Waśniewski, Jerzy (Eds.) 2012, pp. 52 - 59
    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, S.
    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/
  • Georgiev, I.; Kraus, Johannes; Margenov, Svetozar
    Two‐level Preconditioning for DG discretizations of Scalar Elliptic Problems with Discontinuous Coefficients
    In: Application Of Mathematics In Technical And Natural Sciences / 3rd International Conference - AMiTaNS'11 / Todorov, Michail D.; Christov, Christo I. (Eds.) 2012
    Online Full Text
  • Ayuso, B.; Georgiev, I.; Kraus, Johannes; Zikatanov, Ludmil
    A Simple Preconditioner for the SIPG Discretization of Linear Elasticity Equations
    In: Numerical Methods and Applications: Revised Papers / 7th International Conference, NMA 2010, Borovets, Bulgaria, August 20-24, 2010 / Dimov, Ivan; Dimova, Stefka; Kolkovska, Natalia (Eds.) 2011, pp. 353 - 360
    Online Full Text: dx.doi.org/
  • Georgiev, Ivan; Kraus, Johannes; Margenov, Svetozar
    Multilevel Preconditioning of Crouzeix-Raviart 3D Pure Displacement Elasticity Problems
    In: Large-Scale Scientific Computing: Revised Papers / 7th International Conference, LSSC 2009, Sozopol, Bulgaria, June 4-8, 2009 / Lirkov, Ivan; Waśniewski, Jerzy; Margenov, Svetozar (Eds.) 2010, pp. 100 - 107
    Online Full Text: dx.doi.org/
  • Lukáš, Dalibor; Kraus, Johannes
    A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics
    In: Large-Scale Scientific Computing: Revised Papers / 6th International Conference, LSSC 2007, Sozopol, Bulgaria, June 5-9, 2007 2008, pp. 96 - 104
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Tomar, Satyendra K.
    A Multilevel Method for Discontinuous Galerkin Approximation of Three-dimensional Elliptic Problems
    In: Domain decomposition methods in science and engineering XVII: with 110 tables / Langer, Ulrich (Eds.) 2008, pp. 155 - 164
    Online Full Text: dx.doi.org/
  • Georgiev, Ivan; Kraus, Johannes; Margenov, Svetozar
    Multilevel Preconditioning of Rotated Trilinear Non-conforming Finite Element Problems
    In: Large-Scale Scientific Computing: Revised Papers / 6th International Conference, LSSC 2007, Sozopol, Bulgaria, June 5-9, 2007 / Hutchison, David; Kanade, Takeo; Kittler, Josef (Eds.) 2008, pp. 86 - 95
    Online Full Text: dx.doi.org/
  • Kraus, Johannes; Georgiev, Ivan; Margenov, Svetozar
    Multilevel Preconditioning of 2D Rannacher-Turek FE Problems; Additive and Multiplicative Methods
    In: Numerical Methods and Applications: Revised Papers / 6th International Conference, NMA 2006, Borovets, Bulgaria, August 20-24, 2006 / Boyanov, Todor; Dimova, Stefka; Georgiev, Krassimir (Eds.) 2007, pp. 56 - 64
  • Kraus, Johannes
    On the Utilization of Edge Matrices in Algebraic Multigrid
    In: Large-Scale Scientific Computing: Revised Papers / 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6-10, 2005 / Margenov, Svetozar; Wasniewski, Jerzy; Lirkov, Ivan (Eds.) 2006, pp. 121 - 129
    Online Full Text: dx.doi.org/

    • Books, Collections, Proceedings

  • Kraus, Johannes; Margenov, Svetozar
    Robust Algebraic Multilevel Methods and Algorithms
    In: Radon series on computational and applied mathematics Berlin [u.a.] Vol. 5 (2009) X, 246 S. : graph. Darst.

    • Prefaces/Postfaces

  • Blaheta, Radim; Haslinger, Jaroslav; Sysala, Stanislav; Arbenz, Peter; Kraus, Johannes;
    MATCOM special issue modelling 2019 : International Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering
    Modelling 2019: The 6th International Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering, 16.-20.09.2019, Olomouc,
    In: Mathematics and Computers in Simulation Vol. 189 (2021) pp. 1 - 2
    Online Full Text: dx.doi.org/