Former Member

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) 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 .
  • 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.
  • 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.
  • 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. (2006) Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Num. Lin. Alg. Appl., Bd. 13(1), S. 49-70. (link)
  • Kraus, J.K. (2005) Computing interpolation weights in AMG based on multilevel Schur complements. Computing, Bd. 74(4), S. 319-335. (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.
  • 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.
  • 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.
  • 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)

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.
  • 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.
  • 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.
  • 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)