Prof. Dr. Johannes Kraus

< back

Peer Reviewed Journal Publication
  • Q., Hong; J., Kraus; J., Xu; L., Zikatanov (2016) A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Numerische Mathematik, Bd. 132 (1), S. 23-49.
  • Bayramov, Nadir and Kraus, Johannes (2015, online: 2014) On the stable solution of transient convection-diffusion equations. Journal of Computational and Applied Mathematics, Bd. 280, S. 275-293 . (link)
  • Kraus, Johannes and Lymbery, Maria and Margenov, Svetozar (2014, online: 2014) Auxiliary space multigrid method based on additive Schur complement approximation. Numer. Linear Algebra Appl., Bd. Published online in Wiley Online Library, S. wileyonlinelibrary.com . (link)
  • Kraus, Johannes and Lymbery, Maria and Margenov, Svetozar (2014, online: 2013) Robust multilevel methods for quadratic finite element anisotropic elliptic problems. Numer. Linear Algebra Appl., Bd. 21 (3), S. 375-398 . (link)
  • K.P.S. Gahalaut, S.K. Tomar and J.K. Kraus (2013, online: 2013) Algebraic Multilevel Preconditioning in Isogeometric Analysis: Construction and Numerical Studies. Computer Methods in Applied Mechanics and Engineering, Bd. 266, S. 40-56. (link)
  • B. Ayuso de Dios, I. Georgiev, J. Kraus, L. Zikatanov (2013) A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. ESAIM: Mathematical Modelling and Numerical Analysis, Bd. 47 (05), S. 1315-1333.
  • J. Brannick, Y. Chen, J. Kraus, L. Zikatanov (2013) Algebraic multilevel preconditioners for the graph {L}aplacian based on matching in graphs. SIAM Journal on Numerical Analysis, Bd. 51 (3), S. 1805-1827.
  • J. Kraus, M. Lymbery, S. Margenov (2013, online: 2013) Robust multilevel methods for quadratic finite element anisotropic elliptic problems. Numerical Linear Algebra with Applications, Bd. In Press., S. -.
  • Gahalaut, K.; Kraus, J.; Tomar, S.K. (2012) Multigrid methods for isogeometric discretization. Computer Methods in Applied Mechanics and Engineering, Bd. 253 (413-425), S. 13.
  • Kraus, J. (2012, online: 2012) Additive Schur complement approximation and application to multilevel preconditioning. SIAM Journal on Scientific Computing, Bd. 34 (6), S. A2872–A2895 .
  • J.K. Kraus, S.K. Tomar (2011) Algebraic multilevel iteration method for lowest-order Raviart-Thomas space and applications. International Journal of Numerical Methods in Engineering, Bd. 86, S. 1175–1196 . (link)
  • Karer, E.; Kraus, J. (2010) Algebraic multigrid for finite element elasticity equations: Determination of nodal dependence via edge matrices and two-level convergence. International Journal for Numerical Methods in Engineering.
  • Ivan Georgiev, Johannes Kraus, Svetozar Margenov, Josef Schicho (2009) Locally Optimized MIC(0) Preconditioning of Rannacher-Turek FEM Systems. APPLIED NUMERICAL MATHEMATICS, Bd. 59, S. 2402-2415.
  • I. Georgiev, J. Kraus, S. Margenov (2008) Multilevel algorithms for Rannacher–Turek finite element approximation of 3D elliptic problems. Computing, Bd. 82, S. 217-239 . (link)
  • J.K. Kraus, S.K. Tomar (2008) A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problems. Numer. Linear Algebra Appl., Bd. 15, S. 417-438. (link)
  • J.K. Kraus, S.K. Tomar (2008) Multilevel preconditioning of two-dimensional elliptic problems discretized by a class of discontinuous Galerkin methods. SIAM J. Sci. Comput., Bd. 30 (2), S. 684-706. (link)
  • Kraus, J.K. (2008) Algebraic multigrid based on computational molecules, II: Linear elasticity problems. SIAM J. Sci. Comput., Bd. 30 (1), S. 505-524 .
  • J.K. Kraus, S.D. Margenov, J. Synka (2008) On the multilevel preconditioning ofCrouzeix-Raviart elliptic problems. Numer. Linear Algebra Appl., Bd. 15, S. 395-416.
  • I. Georgiev, J.K. Kraus, S. Margenov (2008) Multilevel preconditioning of rotated bilinear non-conforming FEM problems. Computers & Mathematics with Applications, Bd. 55, S. 2280-2294.
  • Kraus, J.K. (2006) Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Num. Lin. Alg. Appl., Bd. 13(1), S. 49-70. (link)
  • J.K. Kraus, J. Schicho (2006) Algebraic multigrid based on computational molecules, I: Scalar elliptic problems. Computing, Bd. 77, S. 57-75. (link)
  • Kraus, J.K. (2005) Computing interpolation weights in AMG based on multilevel Schur complements. Computing, Bd. 74(4), S. 319-335. (link)
  • Kraus, J.; Vassilevski, P.; Zikatanov, L. (online: 2012 Polynomial of best uniform approximation to 1/x and smoothing in two-level methods. Computational Methods in Applied Mathematics, Bd. 12 (4), S. 448–468. (link)
  • J. Kraus, M. Wolfmayr On the robustness and optimality of algebraic multilevel methods for reaction-diffusion type problems. Computing and Visualization in Science, Bd. 16 (1), S. 15-32.
  • Qingguo, Hong; Johannes, Kraus (online: 2016 Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem. SIAM Journal on Numerical Analysis, Bd. 54 (5), S. 2750-2774.
  • J., Kraus; R., Lazarov; M., Lymbery; S., Margenov; L., Zikatanov (online: 2016 Preconditioning Heterogeneous H(div) Problems by Additive Schur Complement Approximation and Applications. SIAM Journal on Scientific Computing, Bd. 38 (2), S. A875-A898.
  • N., Bayramov; J., Kraus (online: 2017 Multigrid methods for convection–diffusion problems discretized by a monotone scheme. Computer Methods in Applied Mechanics and Engineering, Bd. 317, S. 723-745.

Book/Monograph
  • Kraus, J.; Margenov, S. (2009) Robust Algebraic Multilevel Methods and Algorithms. In Reihe: Radon Series Comp. Appl. Math., hrsg. v. Engl, H., 1. Aufl.; Berlin, New York: Walter de Gruyter .

Conference Contribution: Publication in Proceedings
  • Georgiev, I.; Kraus, J. (2013) Preconditioning of Elasticity Problems with Discontinuous Material Parameters. In: Cangiani, A.; Davidchack, R.L.; Georgoulis, E.; Gorban, A.N.; Levesley, J.; Tretyakov, M.V. (Hrsg.), Numerical Mathematics and Advanced Applications 2011 (9th European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2011)); Berlin Heidelberg: Springer-Verlag.
  • Kraus, J. (2012) Additive Schur complement approximation for elliptic problems with oscillatory coefficients. In: Ivan Lirkov, Svetozar Margenov, Jerzy Wasniewski (Hrsg.), Large-Scale Scientific Computing (8th International Conference, LSSC 2011, Sozopol, Bulgaria, June 6-10th, 2011) In Reihe: Lecture Notes in Computer Science, Vol. 7116; Berlin, Heidelberg: Springer, S. 52-59. (link)
  • Kraus, J.; Lymbery, M.; S.Margenov (2012) On the robustness of two-level preconditioners for quadratic FE orthotropic elliptic problems. In: Ivan Lirkov, Svetozar Margenov, Jerzy Wasniewski (Hrsg.), Large-Scale Scientific Computing (8th International Conference, LSSC 2011, Sozopol, Bulgaria, June 6-10th, 2011) In Reihe: Lecture Notes in Computer Science, Vol. 7116; Berlin Heidelberg: Springer, S. 582-589. (link)
  • Karer, E.; Kraus, J.; Zikatanov, L. (2012) A subspace correction method for nearly singular linear elasticity problems., Lecture Notes in Computational Science and Engineering (20th International Conference on Domain Decomposition Methods); Berlin, Heidelberg: Springer.
  • Georgiev, I.; Kraus, J.; Margenov, S. (2011, online: 2011) Two-level Preconditioning for DG discretizations of Scalar Elliptic Problems with Discontinuous Coefficients. In: Michail D. Todorov, Christo I. Christov (Hrsg.), APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (3rd International Conference—AMiTaNS'11) In Reihe: AIP Conference Proceedings, Volume 1404; Melville, New York: American Institute of Physics, S. 389-396. (link)
  • Kraus, J. (2011) Additive Schur complement approximation for elliptic problems with oscillatory coefficients. In: I. Lirkov, S. Margenov, J. Wasniewski (Hrsg.), Large-Scale Scientific Computing (8th International Conference on "Large-Scale Scientific Computations") In Reihe: Lecture Notes in Computer Science; Berlin, Heidelberg: Springer, S. 8.
  • J. Kraus, M. Lymbery, S. Margenov (2011) On the robustness of two-level preconditioners for quadratic FE orthotropic elliptic problems. In: I. Lirkov, S. Margenov, J. Wasniewski (Hrsg.), Large Scale Scientific Computing (8th International Conference on "Large-Scale Scientific Computations") In Reihe: Lecture Notes in Computer Science; Berlin, Heidelberg: Springer, S. 8.
  • I. Georgiev, J. Kraus, M. Limbery, and S. Margenov (2011) On two-level splittings for quadratic FEM anisotropic elliptic problems., BGSIAM’10 Proceedings (Fifth Annual Meeting of the Bulgarian Section of SIAM); Sofia: Demetra, S. 35-40.
  • B. Ayuso, I. Georgiev, J.K. Kraus, L. Zikatanov (2011) A simple preconditioner for the SIPG discretization of linear elasticity equations. In: Dimov, Ivan; Dimova, Stefka; Kolkovska, Natalia (Hrsg.), Numerical Methods and Applications (7th International Conference, NMA 2010) In Reihe: Lecture Notes in Computer Science, 6046; Berlin, Heidelberg: Springer, S. 353-360. (link)
  • I. Georgiev, J.K. Kraus, S.D. Margenov (2010) Multilevel Preconditioning of Crouzeix-Raviart 3D Pure DisplacementElasticity Problems., Large-Scale Scientific Computing (LSSC 2009) In Reihe: Lecture Notes in Computer Science, 5910; Berlin, Heidelberg: Springer.
  • J.K. Kraus, D. Lucas (2008) A fixed-grid finite element algebraic multigrid approach for interface shape optimization governed by 2-dimensional magnetostatics., Large Scale Scientific Computing (LSSC 2007) In Reihe: Lecture Notes in Computer Science (LNCS) 4818, hrsg. v. Ivan Lirkov, Svetozar Margenov, Jerzy Wasniewski; Berlin, Heidelberg: Springer.
  • I. Georgiev, J.K. Kraus, S.D. Margenov (2008) Multilevel preconditioning of rotated trilinearnon-conforming finite element problems., Large Scale Scientific Computing (LSSC 2007) In Reihe: Lecture Notes in Computer Science (LNCS); Berlin, Heidelberg: Springer.
  • Kraus, J.; Tomar, S. (2008) A multilevel method for discontinuous Galerkin approximation of three-dimensional elliptic problems. In: Langer, U.; Discacciati, M.; Keyes, D.; Widlund, O.; Zulehner, W. (Hrsg.), Domain Decomposition Methods in Science and Engineering XVII (17th International Conference on Domain Decomposition Methods, St. Wolfgang/Strobl, Austria) In Reihe: Lecture Notes in Computational Science and Engineering, vol. 60; Heidelberg: Springer, S. 155-164.
  • I. Georgiev, J.K. Kraus, S. Margenov (2007) Multilevel preconditioning of 2D Rannacher-Turek FE problems; Additive and multiplicative methods. In: T. Boyanov, S. Dimova, K. Georgiev, G. Nikolov (Hrsg.), Numerical Methods and Applications (NMA 2006) In Reihe: Lecture Notes in Computer Science (LNCS) 4310, hrsg. v. D. Hutchison, et al.; Berlin, Heidelberg: Springer, S. 56-64.
  • Kraus, J.K. (2006) On the utilization of edge matrices in algebraic multigrid. In: Lirkov, I.; Margenov, S.; Wasniewski, J. (Hrsg.), Large-Scale Scientific Computations In Reihe: Lecture Notes in Computer Science (LNCS) 3743: Springer, S. LSSC 2005.
  • J. Brannick, Y. Chen, J. Kraus, L. Zikatanov An algebraic multigrid method based on matching of graphs., Lecture Notes in Computational Science and Engineering (20th International Conference on Domain Decomposition Methods); Berlin, Heidelberg: Springer.

Contribution in Collection
  • Kraus, Johannes; Lymbery, Maria (2015) Auxiliary space multigrid method for elliptic problems with highly varying coefficients., Domain Decomposition methods in Science and Engineering 22; Berlin Heidelberg: Springer.
  • J.K. Kraus, S.D. Margenov (2007) Multilevel methods for anisotropic elliptic problems. In: J.K. Kraus, U. Langer (Hrsg.), Lectures on Advanced Computational Methods in Mechanics; Berlin, New York: Walter de Gruyter, S. 47-88.

Research Report
  • Kraus, Johannes and Lazarov, Raytcho and Lymbery, Maria and Margenov, Svetozar and Zikatanov, Ludmil (2014, online: 2014) Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneaous media. Bericht-Nr. arXiv:1406.4455; . (link)
  • Hong, Qingguo and Kraus, Johannes (2014) Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem. Bericht-Nr. 2014-36; Johann Radon Institute for Computational and Applied Mathematics: Linz . (link)
  • Qingguo, Hong; Johannes, Kraus; Jinchao, Xu; Ludmil, Zikatanov (2013, online: 2013) A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Bericht-Nr. 2013-19; Johann Radon Institute for Computational and Applied Mathematics: Linz . (link)
  • Gahalaut, K.; Kraus, J.; Tomar, S. (2012, online: 2012) Multigrid Methods for Isogeometric Discretization. Bericht-Nr. RICAM Report 2012-08; Linz. (link)
  • Dios, B. Ayuso de; Georgiev, I.; Kraus, J.; Zikatanov, L. (2011) A Subspace Correction Method for Discontinuous Galerkin Discretizations of Linear Elasticity Equations. Bericht-Nr. 2011-29; RICAM: Linz. (link)
  • Kraus, J. (2011, online: 2011) Additive Schur complement approximation and application to multilevel preconditioning. Bericht-Nr. 2011-22; RICAM, Austrian Academy of Sciences: Linz .
  • Kraus, J.; Pillwein, V.; Zikatanov, L. (2009) Algebraic multilevel iteration methods and the best approximation to 1/x in the uniform norm. Bericht-Nr. 2009-17; RICAM: Linz. (link)
  • J. Kraus, S. Margenov (2008) Generalized hierarchical bases for discontinuous Galerkin discretizationsof elliptic problems with highly varying coefficients. Bericht-Nr. 2008-32; RICAM: Linz. (link)
  • J.K. Kraus, S.K. Tomar (2008) Multilevel preconditioning in H(div) and applications to a posteriori error estimates for discontinuous Galerkin approximations. Linz. (link)
  • Ivan Georgiev, Johannes Kraus, Svetozar Margenov (2008) On the robustness of hierarchical multilevel splittings for discontinuous Galerkin rotated bilinear FE problems.
  • I. Georgiev, J. Kraus, S. Margenov, J. Schicho (2007) Locally optimized MIC(0) preconditioning of Rannacher-Turek FEM systems. Bericht-Nr. 2007-32; RICAM: Linz. (link)
  • I. Georgiev, J.K. Kraus, S.D. Margenov (2007) Multilevel algorithms for Rannacher-Turek finite element approximation of 3D elliptic problems. Bericht-Nr. 2007-21; RICAM: Linz. (link)
  • J.K. Kraus, S.K. Tomar (2006) Multilevel preconditioning of elliptic problems discretized by a class of discontinuous Galerkin methods. Bericht-Nr. 2006-36; RICAM: Linz. (link)
  • J.K. Kraus, S.K. Tomar (2006) A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problems. Bericht-Nr. 39; RICAM, Austrian Academy of Sciences:. (link)
  • I. Georgiev, J.K. Kraus, S. Margenov (2006) Multilevel preconditioning of rotated bilinear non-conforming FEM problems. RICAM:. (link)
  • Kraus, J.K. (2005) Algebraic multigrid based on computational molecules, 2: Systems of elliptic partial differential equations. RICAM:. (link)