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, 2024, in press
    Online Full Text, DOI (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
    DOI, Online Full Text (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
    DOI
  • 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
    DOI, Online Full Text (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
    DOI (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
    DOI, Online Full Text (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
    DOI, Online Full Text (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
    DOI, Online Full Text (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
    DOI, Online Full Text (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
    DOI, Online Full Text (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
    DOI
  • 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
    DOI, Online Full Text (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
    DOI
  • 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
    DOI (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
    DOI
  • 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
    DOI, 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
    DOI
  • 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
    DOI
  • 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
    DOI, 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI
  • 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
    DOI

    • 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, DOI (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, DOI (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.). Cham: Springer Nature, 2024, pp. 259 – 292
    DOI
  • 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.). Cham: Springer, 2023, pp. 127 – 151
    DOI
  • 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.). Cham: Springer International Publishing, 2016, pp. 29 – 40
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 159 – 166
    DOI
  • 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.). Berlin [u.a.]: Springer Berlin Heidelberg, 2013, pp. 143 – 150
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 761 – 769
    DOI
  • 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.). New York, NY: Springer New York, 2013, pp. 217 – 245
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2012, pp. 52 – 59
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2012, pp. 582 – 589
    DOI
  • 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.). Woodbury, NY: AIP Press, 2012, pp. 30 – 41
    DOI
  • 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.). Woodbury, NY: AIP Press, 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2011, pp. 353 – 360
    DOI
  • 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.). Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2010, pp. 100 – 107
    DOI
  • 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. Berlin, Germany: Springer Berlin Heidelberg, 2008, pp. 96 – 104
    DOI
  • 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.). Berlin [u.a.]: Springer, 2008, pp. 155 – 164
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp. 86 – 95
    DOI
  • 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 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.). Berlin, Heidelberg: Springer Berlin Heidelberg, 2006, pp. 121 – 129
    DOI

    • Books, Collections, Proceedings

  • Kraus, Johannes; Margenov, Svetozar
    Robust Algebraic Multilevel Methods and Algorithms
    Berlin [u.a.]: de Gruyter, 2009
    (Radon series on computational and applied mathematics ; 5)

    • 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. Amsterdam: Elsevier, Vol. 189, 2021, pp. 1 – 2
    DOI