Home |  deutsch | Legals |  Mathematics | KIT
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:
Monday to Friday 10-11 o'clock

Contact:

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

Publications

Ordered by , author (No german umlauts required.)

[1] 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., pp. 1—18 (online first) (2017)
Preprint, Paper, BibTex

[2] P. Ciarlet, S. Fliss and C. Stohrer
On the approximation of electromagnetic fields by edge finite elements. Part 2: A heterogeneous multiscale method for Maxwell's equations
Comput. Math. Appl., vol. 73, no. 9, pp. 1900—1919 (2017)
Preprint, Paper, BibTex

[3] 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

[4] T. Göckler and V. Grimm
Acceleration of contour integration techniques by rational Krylov subspace methods
J. Comp. Appl. Math., vol. 316, pp. 133—142 (2017)
Preprint, Paper, BibTex

[5] V. Grimm
Implementation of digcrete gradient methods for dissipative PDEs in image processing on GPUs
Proceedings of Geometric Numerical Integration and its Applications, MI Lecture Note Series, Kyushu University, Japan, vol. 74, pp. 69—71 (2017)
Preprint, Paper, BibTex

[6] V. Grimm and T. Göckler
Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $C_0$-semigroups
SIAM Journal on Numerical Analysis, vol. 55, no. 3, pp. 1483—1504 (2017)
Preprint, Paper, BibTex

[7] 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

[8] V. Grimm, R. I. McLachlan, D. I. McLaren, G. R. W. Quispel and C.-B. Schönlieb
Discrete gradient methods for solving variational image regularisation models
Journal of Physics. A. Mathematical and Theoretical, vol. 50, no. 29, pp. 0—21 (online first) (2017)
Preprint, Paper, BibTex

[9] M. Hochbruck, T. Pažur and R. Schnaubelt
Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations
Numerische Mathematik, pp. 1—23 (online first) (2017)
Preprint, Paper, BibTex

[10] D. Arjmand and C. Stohrer
A Finite Element Heterogeneous Multiscale Method with Improved Control over the Modeling Error
Commun. Math. Sci., vol. 14, no. 2, pp. 463—487 (2016)
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 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

[13] N. Nedialkoav, K. Jackson and M. Neher
On the Blunting Method in Verified Integration of ODEs
Rel. Comp., vol. 23, pp. 15—34 (2016)
Preprint, Paper, BibTex

[14] D. Cohen and J. Schweitzer
High order numerical methods for highly oscillatory problems
M2NA, vol. 49, no. 3, pp. 695—711 (2015)
Preprint, Paper, BibTex

[15] 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

[16] 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

[17] 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

[18] 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

[19] P. Ciarlet Jr., S. Fliss and C. Stohrer
Finite Element Heterogeneous Multiscale Method for Maxwell's Equations in Frequency Domain
in Proceedings of the 12th International Conference on the Mathematical and Numerical Aspects of Waves (2015)
Preprint, Paper, BibTex

[20] A. Abdulle, M. J. Grote and C. Stohrer
Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long Time Effects
Multiscale Model. Simul., vol. 12, no. 3, pp. 1230—1257 (2014)
Preprint, Paper, BibTex

[21] R. Andreev and J. Schweitzer
Conditional Space-Time Stability of Collocation Runge-Kutta for Parabolic Evolution Equations
ETNA, no. 41, pp. 62—80 (2014)
Preprint, Paper, BibTex

[22] P. Ciarlet Jr. and C. Stohrer
Finite Element Heterogeneous Multiscale Method for the classical Helmholtz Equation
C. R. Acad. Sci., vol. 352, pp. 755—760 (2014)
Preprint, Paper, BibTex

[23] 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

[24] 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

[25] T. Göckler
Rational Krylov subspace methods for phi-functions in exponential integrators
Karlsruhe Institute of Technology (KIT), Germany (July 2014)
Preprint, Paper, BibTex

[26] T. Göckler and V. Grimm
Uniform approximation of $\varphi$-functions in exponential integrators by a rational Krylov subspace method with simple poles
SIAM J. Matrix Anal. Appl., vol. 35, no. 4, pp. 1467—1489 (2014)
Preprint, Paper, BibTex

[27] A. Abdulle, M. J. Grote and C. Stohrer
FE Heterogeneous Multiscale Method for Long-Time Wave Propagation
C. R. Acad. Sci., vol. Ser I., no. 351, pp. 495—499 (2013)
Preprint, Paper, BibTex

[28] 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

[29] T. Göckler and V. Grimm
Convergence analysis of an extended Krylov subspace method for the approximation of operator functions in exponential integrators
SIAM Journal on Numerical Analysis, vol. 51, no. 4, pp. 2189—2213 (2013)
Preprint, Paper, BibTex

[30] A. Abdulle, M. J. Grote and C. Stohrer
Finite Element Heterogeneous Multiscale Method for the Wave Equ ation: Long-Time Effects
in Proceedings of the 11th International Conference on the Mathematical and Numerical Aspects of Waves pp. 233—234 (2013)
Preprint, Paper, BibTex

[31] M. J. Grote, A. Abdulle and C. Stohrer
Finite Element Heterogeneous Multiscale Method for the Wave Equation: Long Time Effects
in Computational Electromagnetism and Acoustics , Oberwolfach Reports , vol. 10, no. 1 pp. 185—189 (2013)
Preprint, Paper, BibTex

[32] C. Stohrer
Finite Element Heterogeneous Multiscale Methods for the Wave Equation
University of Basel (2013)
Preprint, Paper, BibTex

[33] A. Wortmann
Positivity Preservation in the Simulation of Relativistic Laser-Plasma Interaction
Karlsruhe Institute of Technology (KIT), Germany (July 2013)
Preprint, Paper, BibTex

[34] E. Celledoni, V. Grimm, R. I. McLachlan, D. I. McLaren, D. O'Neale, B. Owren and G. R. W. Quispel
Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field'' method
J. Comput. Phys., vol. 231, pp. 6670—6789 (2012)
Preprint, Paper, BibTex

[35] V. Grimm
Resolvent Krylov subspace approximation to operator functions
BIT Numerical Mathematics, vol. 52, pp. 639—659 (2012)
Preprint, Paper, BibTex

[36] 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

[37] M. Gugat and V. Grimm
Optimal boundary control of the wave equation with pointwise control constraints
Comput. Optim. Appl., no. 1, pp. 123—147 (2011)
Preprint, Paper, BibTex

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

[39] A. Abdulle, M. J. Grote and C. Stohrer
Finite Element Heterogeneous Multiscale Method for Transient Wave Propagation
in Proceedings of the 10th International Conference on the Mathematical and Numerical Aspects of Waves pp. 45—48 (2011)
Preprint, Paper, BibTex

[40] V. Grimm and M. Gugat
Approximation of semigroups and related operator functions by resolvent series
SIAM Journal on Numerical Analysis, vol. 48, no. 5, pp. 1826—1845 (2010)
Preprint, Paper, BibTex

[41] 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

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

[43] 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

[44] 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

Please find additional papers on the personal website of our group members.