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Research Group 3: Scientific Computing

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.039

Address
Hausadresse:
Zimmer 3.039
Englerstr. 2
Kollegiengebäude Mathematik (20.30)
76131 Karlsruhe

Postadresse:
Karlsruher Institut für Technologie (KIT)
Fakultät für Mathematik
Institut für Angewandte und Numerische Mathematik
Arbeitsgruppe 3: Wissenschaftliches Rechnen
Englerstr. 2
Kollegiengebäude Mathematik (20.30)
D-76131 Karlsruhe

Office hours:
Mon-Thu 9-12 Uhr

Tel.: +49 721 608 42062

Fax.: +49 721 608 43197

Publications

Preprints






Reviewed articles in journals


Tobias Jahnke and Marcel Mikl.
Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation.
Accepted for publication in Numerische Mathematik.
Paper (DOI 10.1007/s00211-017-0926-2), Preprint


Tobias Jahnke, Marcel Mikl and Roland Schnaubelt.
Strang splitting for a semilinear Schrödinger equation with damping and forcing.
J. Math. Anal. Appl. 455 (2), 1051-1071.
Paper (DOI 10.1016/j.jmaa.2017.06.004), Preprint


Simone Buchholz, Ludwig Gauckler, Volker Grimm, Marlis Hochbruck and Tobias Jahnke.
Closing the gap between trigonometric integrators and splitting for highly oscillatory differential equations.
IMA J Numer Anal 2017.
Paper (DOI 10.1093/imanum/drx007), Preprint


Marlis Hochbruck, Tobias Jahnke and Roland Schnaubelt.
Convergence of an ADI splitting for Maxwell's equations.
Numerische Mathematik: Volume 129, Issue 3 (2015), pages 535-561.
Paper (DOI 10.1007/s00211-014-0642-0), Preprint


Andreas Arnold and Tobias Jahnke.
On the approximation of high-dimensional differential equations in the hierarchical Tucker format.
BIT Numer. Math. (2014) 54:305–341
Paper (DOI 10.1007/s10543-013-0444-2), Preprint


Tobias Jahnke and Michael Kreim.
Error bound for piecewise deterministic processes modeling stochastic reaction systems.
SIAM Multiscale Model. Simul., 10(4), 1119–1147, 2012.


Tobias Jahnke.
On reduced models for the chemical master equation.
SIAM Multiscale Model. Simul. 9(4), pp. 1646-1676, 2011


Tobias Jahnke and Derya Altintan.
Efficient simulation of discrete stochastic reaction systems with a splitting method.
BIT, 50(4):797–822, 2010.


Tobias Jahnke and Tudor Udrescu.
Solving chemical master equations by adaptive wavelet compression.
J. Comput. Phys. 229 (16), 5724-5741, 2010.


Tobias Jahnke.
An adaptive wavelet method for the chemical master equation.
SIAM J. Sci. Comput. 31 (6), pp. 4373-4394, 2010.


Christof Schütte and Tobias Jahnke.
Towards effective dynamics in complex systems by Markov kernel approximation.
ESAIM, Math. Model. Numer. Anal. 43, No. 4, 721 (2009).


Tobias Jahnke and Wilhelm Huisinga.
A dynamical low-rank approach to the chemical master equation.
Bulletin of Mathematical Biology, 70(8):2283-2302, 2008.


Wilhelm Huisinga, Peter Deuflhard, Tobias Jahnke, and Michael Wulkow.
Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation.
SIAM J. Sci. Comput. 30 (6), pp. 2990-3011, 2008.


Philipp Metzner, Evelyn Dittmer, Tobias Jahnke, and Christof Schütte.
Generator estimation methods for discretely observed Markov jump processes.
J. Comp. Phys. 227 (1), pp. 353-375, 2007.


Tobias Jahnke and Wilhelm Huisinga.
Solving the chemical master equation for monomolecular reaction systems analytically.
Journal of Mathematical Biology, 54(1):1--26, 2007.


Katina Lorenz, Tobias Jahnke, and Christian Lubich.
Adiabatic integrators for highly oscillatory second-order linear differential equations with time-
varying eigendecomposition.

BIT, 45(1):91--115, 2005.


Tobias Jahnke.
Long-time-step integrators for almost-adiabatic quantum dynamics.
SIAM J. Sci. Comput., 25(6):2145--2164, 2004.


Tobias Jahnke and Christian Lubich.
Numerical integrators for quantum dynamics close to the adiabatic limit.
Numer. Math., 94(2):289--314, 2003.


Tobias Jahnke and Christian Lubich.
Error bounds for exponential operator splittings.
BIT, 40(4):735--744, 2000.





Reviewed articles in conference proceedings


Tobias Jahnke.
Convergence of piecewise deterministic processes modeling two-scale reaction networks.
To appear in the proceedings of the International conference on numerical analysis and applied mathematics (ICNAAM) 2012.


Tudor Udrescu and Tobias Jahnke.
An adaptive method for solving Chemical Master Equations using a sparse wavelet basis.
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18--22, 2009. Vol. 1. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1168, 489-492 (2009).


Tobias Jahnke.
On hybrid models in stochastic reaction kinetics.
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18--22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1168, 1540–1543 (2009).


Tobias Jahnke and Steffen Galan.
Solving chemical master equations by an adaptive wavelet method.
In T. E. Simos, G. Psihoyios, and C. Tsitouras, editors, Numerical Analysis and applied mathematics: International Conference on Numerical Analysis and Applied Mathematics 2008. Psalidi, Kos, Greece, 16-20 September 2008, volume 1048 of AIP Conference Proceedings, pages 290–293, 2008.





Miscellaneous


Tobias Jahnke and Vikram Sunkara.
Error bound for hybrid models of two-scaled stochastic reaction systems.
In: Stephan Dahlke et al., editors, Extraction of quantifiable Information from complex systems. Lecture notes in computational science and engineering 102. Springer (Berlin), 2014. Pages 303-319.


David Cohen, Tobias Jahnke, Katina Lorenz, and Christian Lubich.
Numerical integrators for highly oscillatory Hamiltonian systems: a review.
In: Alexander Mielke, editor, Analysis, Modeling and Simulation of Multiscale Problems. Springer (Berlin), 2006. Pages 553--576.