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Numerical Analysis Group

Office
Kollegiengebäude Mathematik (20.30)
Room 3.002 (3rd floor)

Address
Karlsruhe Institute of Technology
Institute for Applied and Numerical Mathematics 1
Englerstr. 2
76131 Karlsruhe
Germany

Office hours:

Mon. - Fri.

9 - 12 o'clock

Mon. - Thu.

13 - 16 o'clock

Contact:

Phone: +49 721 608-42061
Fax: +49 721 608-43767
Email:na-sek@math.kit.edu

Publications


Ordered by

Preprints

[1] S. Buchholz, B. Dörich and M. Hochbruck
On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
CRC 1173-Preprint, no. 2020/8, Karlsruhe Institute of Technology (2020)
Preprint, Paper, BibTex

[2] M. Hochbruck and J. Leibold
Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions
CRC 1173-Preprint, no. 2019/26, Karlsruhe Institute of Technology (2020)
Preprint, Paper, BibTex

[3] C. Carle, M. Hochbruck and A. Sturm
On leapfrog-Chebyshev schemes
CRC 1173-Preprint, no. 2019/19, Karlsruhe Institute of Technology (2019)
Preprint, Paper, BibTex

[4] M. Hochbruck and J. Köhler
Error analysis of discontinuous Galerkin discretizations of a class of linear wave-type problems
CRC 1173-Preprint, no. 2019/14, Karlsruhe Institute of Technology (2019)
Preprint, Paper, BibTex

[5] M. Hochbruck and M. E. Hochstenbach
Subspace extraction for matrix functions
preprint (2005)
Preprint, Paper, BibTex

Papers

[1] M. Hochbruck, J. Leibold and A. Ostermann
On the convergence of Lawson methods for semilinear stiff problems
Numer. Math., pp. 1—28, online first (2020)
Preprint, Paper, BibTex

[2] M. Hochbruck, B. Maier and C. Stohrer
Heterogeneous Multiscale Method for Maxwell's Equations
Multiscale Model. Sim., vol. 17, no. 4, pp. 1147—1171 (2019)
Preprint, Paper, BibTex

[3] M. Hochbruck and A. Sturm
Upwind discontinuous Galerkin space discretization and locally implicit time integration for linear Maxwell's equations
Math. Comp., vol. 88, no. 317, pp. 1121—1153 (2019)
Preprint, Paper, BibTex

[4] M. M. Müller, B. Maier, M. Hochbruck and C. Rockstuhl
Analytical and numerical analysis of linear and nonlinear properties of an rf-SQUID based metasurface
Phys. Rev. B, vol. 99, no. 7, pp. 075401 (2019)
Preprint, Paper, BibTex

[5] M. Hochbruck, and J. Köhler
On the efficiency of the Peaceman—Rachford ADI-dG method for wave-type problems
in Numerical Mathematics and Advanced Applications ENUMATH 2017 , edited by Radu, F.A., Kumar, K., Berre, I., Nordbotten, J.M. and Pop and I.S. , Lecture Notes in Computational Science and Engineering , Springer International Publishing , vol. 126 pp. 135—144 (2019)
Preprint, Paper, BibTex

[6] S. Buchholz, L. Gauckler, V. Grimm, M. Hochbruck and T. Jahnke
Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations
IMA J. Numer. Anal., vol. 38, no. 1, pp. 57—74 (2018)
Preprint, Paper, BibTex

[7] D. Hipp, M. Hochbruck and C. Stohrer
Unified error analysis for non-conforming space discretizations of wave-type equations
IMA Journal of Numerical Analysis, pp. 1—40, online first (2018)
Preprint, Paper, BibTex

[8] M. Hochbruck, T. Pažur and R. Schnaubelt
Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations
Numerische Mathematik, vol. 138, no. 3, pp. 557—579 (2018)
Preprint, Paper, BibTex

[9] L. Fath, M. Hochbruck and C.V. Singh
A fast mollified impulse method for biomolecular atomistic simulations
J. Comp. Phys., vol. 333, pp. 180—198 (2017)
Preprint, Paper, BibTex

[10] M. Hochbruck and T. Pažur
Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations
Numerische Mathematik, vol. 135, no. 2, pp. 547—569 (2017)
Preprint, Paper, BibTex

[11] J. Deppler, B. Braun, A. Fidlin and M. Hochbruck
Convergence of viscoelastic constraints to nonholonomic idealization
European Journal of Mechanics - A/Solids, vol. 58, pp. 140—147 (2016)
Preprint, Paper, BibTex

[12] M. Hochbruck and C. Stohrer
Finite element heterogeneous multiscale method for time-dependent Maxwell's equations
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 (978-3-319-65870-4), pp. 269-281, online first (2016)
Preprint, Paper, BibTex

[13] M. Hochbruck and A. Sturm
Error analysis of a second-order locally implicit method for linear Maxwell's equations
SIAM J. Numer. Anal., vol. 54, no. 5, pp. 3167-3191 (2016)
Preprint, Paper, BibTex

[14] A. Demirel, J. Niegemann, K. Busch and M. Hochbruck
Efficient Multiple Time-Stepping Algorithms of Higher Order
J. Comp. Phys., vol. 285, pp. 133—148 (2015)
Preprint, Paper, BibTex

[15] M. Hochbruck, T. Jahnke and R. Schnaubelt
Convergence of an ADI splitting for Maxwell's equations
Numerische Mathematik, vol. 129, pp. 535—561 (2015)
Preprint, Paper, BibTex

[16] M. Hochbruck and T. Pažur
Implicit Runge—Kutta methods and discontinuous Galerkin discretizations for linear Maxwell's equations
SIAM J. Numer. Anal., vol. 53, no. 1, pp. 485—507 (2015)
Preprint, Paper, BibTex

[17] M. Hochbruck, T. Pažur, A. Schulz, E. Thawinan and C. Wieners
Efficient time integration for discontinuous Galerkin approximations of linear wave equations
ZAMM, vol. 95, no. 3, pp. 237—259 (2015)
Preprint, Paper, BibTex

[18] D. Hipp and M. Hochbruck
A preconditioned Krylov method for an exponential integrator for non-autonomous parabolic systems
Oberwolfach Reports, vol. 11, no. 1, pp. 822—824 (2014)
Preprint, Paper, BibTex

[19] D. Hipp, M. Hochbruck and A. Ostermann
An exponential integrator for non-autonomous parabolic problems
ETNA, vol. 41, pp. 497—511 (2014)
Preprint, Paper, BibTex

[20] M. A. Botchev, V. Grimm and M. Hochbruck
Residual, restarting and Richardson iteration for the matrix exponential
SIAM J. Sci. Comput., vol. 35, no. 3, pp. A1376-A1397 (2013)
Preprint, Paper, BibTex

[21] D. Hipp, M. Hochbruck and A. Ostermann
Exponential integrators for parabolic problems with time dependent coefficients
Oberwolfach Reports, vol. 9, no. 4, pp. 3602—3606 (2012)
Preprint, Paper, BibTex

[22] M. Hochbruck and A. Ostermann
Exponential multistep methods of Adams-type
BIT, vol. 51, pp. 889-908 (2011)
Preprint, Paper, BibTex

[23] M. Hochbruck and D. Löchel
A multilevel Jacobi-Davidson method for polynomial PDE eigenvalue problems arising in plasma physics
SIAM Journal on Scientific Computing, vol. 32, no. 6, pp. 3151—3169 (2010)
Preprint, Paper, BibTex

[24] M. Hochbruck and A. Ostermann
Exponential integrators
Acta Numerica, vol. 19, pp. 209-286 (2010)
Preprint (© Cambridge University Press), Paper, BibTex

[25] M. Hochbruck and M. Hönig
On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems
Numerische Mathematik, vol. 115, no. 1, pp. 71—79 (2010)
Preprint, Paper, BibTex

[26] T. Tückmantel, A. Pukhov, J. Liljo and M. Hochbruck
Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator
IEEE Transactions on Plasma Science, vol. 38, no. 9, pp. 2383-2389 (2010)
Preprint, Paper, BibTex

[27] D. Löchel, M. Tokar, M. Hochbruck and D. Reiser
Effect of poloidal inhomogeneity in plasma parameters on edge anomalous transport
IOP, Physics of Plasmas, vol. 16, no. 4 (April 2009)
Preprint, Paper, BibTex

[28] M. Hochbruck, M. Hönig and A. Ostermann
A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems
Inverse Problems, vol. 25 (2009)
Preprint, Paper, BibTex

[29] M. Hochbruck, M. Hönig and A. Ostermann
Regularization of nonlinear ill-posed problems by exponential integrators
M2NA, vol. 43, pp. 709-720 (2009)
Preprint, Paper, BibTex

[30] M. Hochbruck, A. Ostermann and J. Schweitzer
Exponential Rosenbrock-type methods
SIAM J. Numer. Anal., vol. 47, no. 1, pp. 786—803 (2009)
Preprint, Paper, BibTex

[31] V. Grimm and M. Hochbruck
Rational approximation to trigonometric operators
BIT, vol. 48, no. 2, pp. 215—229 (2008)
Preprint, Paper, BibTex

[32] M. Hochbruck and J. Niehoff
Approximation of matrix operators applied to multiple vectors
Math. Comput. Simul., vol. 79, no. 4, pp. 1270—1283 (2008)
Preprint, Paper, BibTex

[33] C. Karle, J. Schweitzer, M. Hochbruck and K. H. Spatschek
A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems
J. Comp. Phys., vol. 227, pp. 7701—7719 (2008)
Preprint, Paper, BibTex

[34] J. Liljo, A. Karmakar, A. Pukhov and M. Hochbruck
One dimensional electromagnetic relativistic PIC-hydrodynamic hybrid simulation code H-VLPL (Hybrid Virtual Laser Plasma Lab)
Computer Physics Communication, vol. 179, no. 6, pp. 371—379 (2008)
Preprint, Paper, BibTex

[35] V. Grimm (joint work with M. Hochbruck)
Exponential integrators for highly oscillatory differential equations
Oberwolfach Reports, vol. 3, no. 1, pp. 868—869 (2006)
Preprint, Paper, BibTex

[36] V. Grimm and M. Hochbruck
Error analysis of exponential integrators for oscillatory second-order differential equations
J. Phys. A: Math. Gen., vol. 39, pp. 5495—5507 (2006)
Preprint, Paper, BibTex

[37] C. Karle, J. Schweitzer, M. Hochbruck, E. W. Laedke and K. H. Spatschek
Numerical solution of nonlinear wave equations in stratified dispersive media
J. Comp. Phys., vol. 216, pp. 138—152 (2006)
Preprint, Paper, BibTex

[38] Marlis Hochbruck and Alexander Ostermann
Explicit integrators of Rosenbrock-type
Oberwolfach Reports, vol. 3, no. 2, pp. 1107—1110 (2006)
Preprint, Paper, BibTex

[39] J. van den Eshof and M. Hochbruck
Preconditioning Lanczos approximations to the matrix exponential
SIAM J. Sci. Comp., vol. 27, no. 4, pp. 1438—1457 (2006)
Preprint, Paper, BibTex

[40] Marlis Hochbruck and Alexander Ostermann
Explicit exponential Runge-Kutta methods for semilinear parabolic problems
SIAM J. Numer. Anal., vol. 43, no. 3, pp. 1069—1090 (2005)
Preprint, Paper, BibTex

[41] Marlis Hochbruck and Alexander Ostermann
Exponential Runge-Kutta methods for parabolic problems
Appl. Numer. Math., vol. 53, no. 2—4, pp. 323—339 (2005)
Preprint, Paper, BibTex

[42] Marlis Hochbruck and Christian Lubich
On Magnus integrators for time-dependent Schrödinger equations
SIAM J. Numer. Anal., vol. 41, no. 3, pp. 945—963 (2003)
Preprint, Paper, BibTex

[43] Marlis Hochbruck and Jörg-M. Sautter
Mathematik fürs Leben am Beispiel der Computertomographie
Mathematische Semesterberichte, vol. 49, no. 1, pp. 95—113 (2002)
Preprint, Paper, BibTex

[44] Marlis Hochbruck and Christian Lubich
A Gautschi-type method for oscillatory second-order differential equations
Numer. Math., vol. 83, no. 3, pp. 403—426 (1999)
Preprint, Paper, BibTex

[45] Marlis Hochbruck and Christian Lubich
Exponential integrators for quantum-classical molecular dynamics
BIT, vol. 39, no. 4, pp. 620—645 (1999)
Preprint, Paper, BibTex

[46] M. Hochbruck and Ch. Lubich
A bunch of time integrators for quantum/classical molecular dynamics
pp. 421—432 in Algorithms for Macromolecular Modelling , edited by P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich and R.D. Skeel , Lecture Notes in Computational Science and Engineering , Springer (1999)
Preprint, Paper, BibTex

[47] Marlis Hochbruck
A numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems
in Special issue on "High Performance Algorithms for Structured Linear Systems". Volume II in the series "Advances in the Theory of Computation and Computational Mathematics" edited by P. Arbenz, M. Paprzycki, and A. Sameh., vol. 2 (1998)
Preprint, Paper, BibTex

[48] Marlis Hochbruck and Christian Lubich
Error analysis of Krylov methods in a nutshell
SIAM J. Sci. Comput., vol. 19, no. 2, pp. 695—701 (1998)
Preprint, Paper, BibTex

[49] Marlis Hochbruck, Christian Lubich and Hubert Selhofer
Exponential integrators for large systems of differential equations
SIAM J. Sci. Comp., vol. 19, no. 5, pp. 1552—1574 (1998)
Preprint, Paper, BibTex

[50] Marlis Hochbruck
Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
J. Comp. Appl. Math., vol. 86, no. 1, pp. 219—236 (1997)
Preprint, Paper, BibTex

[51] Marlis Hochbruck and Christian Lubich
On Krylov subspace approximations to the matrix exponential operator
SIAM J. Numer. Anal., vol. 34, no. 5, pp. 1911—1925 (1997)
Preprint, Paper, BibTex

[52] Martin H. Gutknecht and Marlis Hochbruck
Optimized look-ahead recurrences for adjacent rows in the Padé table
BIT, vol. 36, no. 2, pp. 264—286 (1996)
Preprint, Paper, BibTex