Publications

Numerical Mathematics
Publications

Publications in peer-reviewed journals (Published/In Press)
Preprints (Submitted)
Refereed publications in conference proceedings (Published/In Press):
Habilitation thesis
Chapters in books and survey articles
Monographs

Publications in peer-reviewed journals (Published/In Press)

J. Kraus, P. Lederer, M. Lymbery, K. Osthues, J. Schöberl (2023). Hybridized discontinuous Galerkin/hybrid mixed methods for a multiple network poroelasticity model with applications in biomechanics. To appear in SIAM J. Sci. Comput.
Q. Hong, J. Kraus, M. Lymbery, F. Philo (2023). A new practical framework for the stability analysis of perturbed saddle-point problems and applications. Math. Comp. 92(340), pp. 607–634.
Q. Hong, J. Kraus, M. Kuchta, M. Lymbery, K.-A. Mardal, M. Rognes (2022). Robust approximation of generalized Biot-Brinkman problems. J. Sci. Comput. 93(3), Paper No. 77, 28 pp.
J. Kraus, M. Lymbery, P. Lederer, J. Schöberl (2021). Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model. Comput. Methods Appl. Mech. Engrg. 384, Paper No. 113991, 23 pp.
S. Nakov, E. Sobakinskaya, T. Renger, J. Kraus (2021). ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson–Boltzmann equation. J. Comput. Chem. 42(26), 1832–1860.
Q. Hong, J. Kraus, M. Lymbery, F. Philo (2020). Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot's consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555.
J. Kraus, S. Nakov, S. Repin (2020). Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation. Comput. Meth. Appl. Math. 20(4), 643–676.
Q. Hong, J. Kraus, M. Lymbery, M.F. Wheeler (2020). Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Sim. 18(2), 916–941.
J. Kraus, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, B. Stiftner (2019). Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. J. Comput. Phys. 398, https://doi.org/10.1016/j.jcp.2019.108866.
J. Kraus, S. Nakov, S. Repin (2019). Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation. Comput. Methods Appl. Math. 20(2), https://doi.org/10.1515/cmam-2018-0252.
Q. Hong, J. Kraus, M. Lymbery, F. Philo (2019). Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models. Numer. Linear Alg. Appl. 2019;e2242, https://doi.org/10.1002/nla.2242.
Q. Hong, J. Kraus (2018). Parameter-robust stability of classical three-field formulation of Biot's consolidation model. Electron. Trans. Numer. Anal. 48, pp. 202–226.
J. Kraus, M. Lymbery (2018). Incomplete factorization by local exact factorization (ILUE). Math. Comput. Simul. 145, pp. 50–61.
N. R. Bayramov, J. Kraus (2017). Multigrid methods for convection–diffusion problems discretized by a monotone scheme. Comput. Methods Appl. Mech. Engrg. 317, pp. 723–745.
Q. Hong, J. Kraus (2016). Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem. SIAM J. Numer. Anal. 54(5), pp. 2750–2774.
J. Kraus, R. Lazarov, M. Lymbery, S. Margenov, L. Zikatanov (2016). Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications. SIAM J. Sci. Comput. 38(2), pp. A875–A898.
Q. Hong, J. Kraus, J. Xu, L. Zikatanov (2016). A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Numer. Math. 132(1), pp. 23–49.
N. R. Bayramov, J.K. Kraus (2015). On the stable solution of transient convection–diffusion equations. J. Comput. Appl. Math. 280, pp. 275–293.
J. Kraus, M. Lymbery, S. Margenov (2015). Auxiliary space multigrid method based on additive Schur complement approximation. Numer. Linear Alg. Appl. 22(6), pp. 965–986.
J. Kraus, M. Lymbery, S. Margenov (2014). Robust multilevel methods for quadratic finite element anisotropic elliptic problems. Numer. Linear Alg. Appl. 21(3), pp. 375–398.
J. Kraus, M. Wolfmayr (2013). On the robustness and optimality of algebraic multilevel methods for reaction-diffusion type problems. Computing and Visualization in Science 16(1), pp. 15–32.
B. Ayuso, I. Georgiev, J. Kraus, L. Zikatanov (2013). A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. ESAIM: Math. Model. Numer. Anal. (M2AN) 47(05), pp. 1315–1333.
J. Brannick, Y. Chen, J. Kraus, L. Zikatanov (2013). Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. SIAM J. Numer. Anal. 51(03), pp. 1805–1827.
K. Gahalaut, J. Kraus, S. Tomar (2013). Multigrid methods for isogeometric discretization. Computer Methods in Applied Mechanics and Engineering 253, pp. 413–425.
K. Gahalaut, S. Tomar, J. Kraus (2013). Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies. Computer Methods in Applied Mechanics and Engineering 266, pp. 40–56.
J. Kraus, P. Vassilevski, L. Zikatanov (2012). Polynomial of best uniform approximation to 1/x and smoothing in two-level methods. Computational Methods in Applied Mathematics 12, pp. 448–468. Special issue devoted to Sergey Nepomnyaschikh.
J. Kraus (2012). Additive Schur complement approximation and application to multilevel preconditioning. SIAM J. Sci. Comput. 34, pp. A2872–A2895.
J. Kraus, S. Tomar (2011). Algebraic multilevel iteration method for lowest-order Raviart-Thomas space and applications. Int. J. Numer. Meth. Engng. 86, pp. 1175–1196.
E. Karer, J. Kraus (2010). Algebraic multigrid for finite element elasticity equations: Determination of nodal dependence via edge matrices and two-level convergence. Int. J. Numer. Meth. Engng. 83, pp. 642–670.
I. Georgiev, J. Kraus, S. Margenov, J. Schicho (2009). Locally optimized MIC(0) preconditioning of Rannacher-Turek FEM systems. Appl. Numer. Math. 59, pp. 2402–2415.
J. Kraus (2008). Algebraic multigrid based on computational molecules, 2: Linear elasticity problems. SIAM J. Sci. Comput. 30(1), pp. 505–524.
J. Kraus, S. Tomar (2008). A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problems. Numer. Linear Alg. Appl. 15, pp. 417–438.
J. Kraus, S. Tomar (2008). Multilevel preconditioning of two-dimensional elliptic problems discretized by a class of discontinuous Galerkin methods. SIAM J. Sci. Comput. 30, pp. 684–706.
J. Kraus, J. Synka, S. Margenov (2008). On the multilevel preconditioning of Crouzeix-Raviart elliptic problems. Numer. Linear Alg. Appl. 15, pp. 395–416.
I. Georgiev, J. Kraus, S. Margenov (2008). Multilevel preconditioning of rotated bilinear non-conforming FEM problems. Computers and Mathematics with Applications 55, pp. 2280–2294.
I. Georgiev, J. Kraus, S. Margenov (2008). Multilevel algorithms for Rannacher-Turek finite element approximation of 3D elliptic problems. Computing 82, pp. 217–239.
J. Kraus, J. Schicho (2006). Algebraic multigrid based on computational molecules, 1: Scalar elliptic problems. Computing 77, pp. 57–75.
J. Kraus (2006). Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Numer. Linear Alg. Appl. 13, pp. 49–70.
J. Kraus (2005). Computing interpolation weights in AMG based on multilevel Schur complements. Computing 74, pp. 319–335.
J. Kraus (2002). An algebraic preconditioning method for M-matrices: Linear versus nonlinear multilevel iteration. Numer. Linear Alg. Appl. 9, pp. 599–618.
J. Kraus, C. Brand (2000). Condition numbers of approximate Schur complements in two- and three-dimensional discretizations on hierarchically ordered grids. Computing 65, pp. 135–154.

Preprints (Submitted)

J. Kraus, S. Repin: A posteriori error estimates for domain decomposition methods. arXiv:2111.07706v1 [math.NA], November, 2021.

Refereed publications in conference proceedings (Published/In Press):

J. Kraus, M. Lymbery: Auxiliary space multigrid method for elliptic problems with highly varying coefficients. In Domain Decomposition Methods in Science and Engineering XXII, Volume 104 of the series Lecture Notes in Computational Science and Engineering, pp. 29-40, 2016.
J. Brannick, Y. Chen, J. Kraus, L. Zikatanov: An algebraic multigrid method based on matching in graphs. In Domain Decomposition Methods in Science and Engineering XX, R. Bank et al., eds., Lecture Notes in Computational Science and Engineering 91, pp. 143–150, Springer, Berlin Heidelberg, 2013.
E. Karer, J. Kraus, L. Zikatanov: A subspace correction method for nearly singular linear elasticity problems. In Domain Decomposition Methods in Science and Engineering XX, R. Bank et al., eds., Lecture Notes in Computational Science and Engineering 91, pp. 159–166, Springer, Berlin Heidelberg, 2013.
I. Georgiev, J. Kraus: Preconditioning of elasticity problems with discontinuous material parameters. In Numerical Mathematics and Advanced Applications (ENUMATH 2011), A. Cangiani et al., eds., Springer, pp. 761-769 , Springer, Berlin Heidelberg, 2013.
J. Kraus, M. Lymbery, S. Margenov: Semi-coarsening AMLI preconditioning of higher order elliptic problems. AIP Conf. Proc. 1487, pp. 30–41, American Institute of Physics, Melville, 2012.
J. Kraus: Additive Schur complement approximation for elliptic problems with oscillatory coefficients. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, and J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 7116, pp. 52–59, Springer, Berlin Heidelberg, 2012.
J. Kraus, M. Lymbery, S. Margenov: On the robustness of two-level preconditioners for quadratic FE orthotropic elliptic problems. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, and J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 7116, pp. 582–589, Springer, Berlin Heidelberg, 2012.
I. Georgiev, J. Kraus, S. Margenov: Two-level preconditioning for DG discretizations of scalar elliptic problems with discontinuous coeffcients. In Applications of Mathematics in Technical and Natural Sciences, AMiTaNS 2011, C. Christov, M. Todorov, eds. AIP Conference Proceedings, 1404, pp. 389–396, American Institute of Physics, Melville, 2012.
B. Ayuso, I. Georgiev, J. Kraus, L. Zikatanov: A simple preconditioner for the SIPG discretization of linear elasticity equations. In Numerical Methods and Applications, I. Dimov, S. Dimova, and N. Kolkovska, eds., Lecture Notes in Computer Science, vol. 6046, pp. 353–360, Springer, Berlin Heidelberg, 2011.
I. Georgiev, J. Kraus, S. Margenov: Multilevel preconditioning of Crouzeix-Raviart 3D pure displacement elasticity problems. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 5910, pp. 100–107, Springer, Berlin Heidelberg 2010.
D. Lukas and J. Kraus: A fixed-grid finite element algebraic multigrid approach for interface shape optimization governed by 2-dimensional magnetostatics. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 4818, pp. 96–104, Springer, Berlin Heidelberg 2008.
I. Georgiev, J. Kraus, S. Margenov: Multilevel preconditioning of rotated trilinear non-conforming finite element problems. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 4818, pp. 86–95, Springer, Berlin Heidelberg 2008.
J. Kraus and S. Tomar: A multilevel method for discontinuous Galerkin approximation of three-dimensional elliptic problems. In Domain Decomposition Methods in Science and Engineering XVII, Langer et al. eds., Lecture Notes in Computational Science and Engineering, vol. 60, pp. 155–164, Springer, Heidelberg, 2008.
I. Georgiev, J. Kraus, S. Margenov: Multilevel preconditioning of 2D Rannacher-Turek FE problems; Additive and multiplicative methods. In Numerical Methods and Applications, T. Boyanov, S. Dimova, K. Georgiev, G. Nikolov, eds., Lecture Notes in Computer Science, vol. 4310, pp. 56–64, Springer, Berlin Heidelberg 2007.
J. Kraus: On the utilization of edge matrices in algebraic multigrid. In Large-Scale Scientific Computing, I. Lirkov, S. Margenov, J. Wasniewski, eds., Lecture Notes in Computer Science, vol. 3743, pp. 86–95, Springer, Berlin Heidelberg 2006.

Habilitation thesis

Johannes Kraus: Algebraic multilevel methods for solving elliptic finite element equations.

Chapters in books and survey articles

J. Kraus, S. Repin: A Posteriori Error Estimates for Domain Decomposition Methods. In Impact of Scientific Computing on Science and Society, Springer International Publishing, P. Neittaanmäki and M.-L. Rantalainen eds., pp. 127–151, 2023
J. Kraus, M. Lymbery, S. Margenov: Robust algebraic multilevel preconditioners for anisotropic problems. In Numerical Solution of Partial Differential Equations: Theory, Algorithms and their Applications, Springer Proceedings in Mathematics and Statistics 45, O.P. Iliev et al. eds., pp. 217–245, 2013.
J. Kraus, S. Margenov: Multilevel methods for anisotropic elliptic problems. In Lectures on Advanced Computational Methods in Mechanics, Radon Series Comp. Appl. Math., vol. 1, J. Kraus and U. Langer eds., pp. 47–88, 2007.

Monographs

J. Kraus, S. Margenov: Robust Algebraic Multilevel Methods and Algorithms. Radon Series Comp. Appl. Math., vol. 5, Walter de Gruyter, Berlin-NewYork, 2009.