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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

Photo of Katharina Schratz JProf. Dr. Katharina Schratz

Office hour for students: By Appointment
Room: 3.024 Kollegiengebäude Mathematik (20.30)
Tel.: +49 721 608 47651
Fax.: +49 721 608 43197
Email: Katharina.Schratz@kit.edu

Englerstr. 2
D-76131 Karlsruhe

HEAD OF JUNIOR RESEARCH GROUP: NUMERICS OF TIME-DEPENDENT PDES

Invited plenary talks

SciCADE, the International Conference on Scientific Computation and Differential Equations 2019

New Preprints

A. Ostermann, F. Rousset, K. Schratz
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
(preprint 2019)

New Publications

M. Knöller, A. Ostermann, K. Schratz:
A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data
SIAM J. Numer. Anal. 57, 1967-1986 (2019)
https://doi.org/10.1137/18M1198375

S. Baumstark, K. Schratz:
Uniformly Accurate Oscillatory Integrators for the Klein-Gordon-Zakharov System
from Low- to High-Plasma Frequency Regimes.
SIAM J. Numer. Anal. 57, 429-457 (2019)
doi:10.1137/18M1177184

L. Gauckler, J. Lu, J. Marzuola, F. Rousset, K. Schratz:
Trigonometric integrators for quasilinear wave equations.
Math. Comp. 88, 717-749 (2019)
doi:10.1090/mcom/3339

A. Ostermann, K. Schratz:
Low regularity exponential-type integrators for semilinear Schrödinger equations.
Found. Comput. Math. 18, 731-755 (2018)
doi:10.1007/s10208-017-9352-1

S. Baumstark, E. Faou, K. Schratz:
Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting.
Math. Comp. 87, 1227-1254 (2018)
doi:10.1090/mcom/3263

M. Hofmanová, K. Schratz:
An exponential-type integrator for the KdV equation.
Numer. Math. 136(4), 1117-1137 (2017)
doi:10.1007/s00211-016-0859-1

(full list of publications and preprints below)

JUNIOR RESEARCH GROUP: NUMERICS OF TIME-DEPENDENT PDES

Dateibezeichnung
Group photo December 2017 (left to right): Patrick, Simon, Katharina, Irina, Xiaofei, Jan, Marvin


Katharina Schratz (head)

Former members:
Post-docs:
Simon Baumstark
Xiaofei Zhao
Patrick Krämer
PhD students:
Patrick Krämer (PhD defense 29.08.2017)
Simon Baumstark (PhD defense 12.07.2018)
Master students:
Jelena Stjepanovic (2018)
Irina Wetteborn (2018)
Jan Bohn (2018)
Georgia Kokkala (2017)
Simon Baumstark (2015)





Current List of Courses
Semester Titel Typ
Summer Semester 2019 Lecture
Winter Semester 2018/19 Lecture
Seminar
Seminar
Summer Semester 2018 Lecture
Seminar
Winter Semester 2017/18 Seminar
Summer Semester 2017 Lecture
Winter Semester 2016/17 Lecture
Summer Semester 2016 Lecture
Winter Semester 2015/16 Lecture
Summer Semester 2015 Lecture
Winter Semester 2014/15 Lecture
Lecture
Summer Semester 2014 Lecture
Winter Semester 2013/14 Lecture
Seminar


Preprints

K. Schratz, Y. Wang, X. Zhao
Low-regularity integrators for nonlinear Dirac equations
(preprint 2019)

A. Ostermann, F. Rousset, K. Schratz
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
(preprint 2019)

M. Hofmanová, M. Knöller, K. Schratz:
Randomized exponential integrator for modulated nonlinear Schrödinger equations
(preprint 2018)

K. Schratz, X. Zhao:
On the comparison of the asymptotic expansion techniques for the nonlinear Klein-Gordon equation in the non relativistic limit regime
(preprint 2018)

S. Baumstark, G. Schneider, K. Schratz, D. Zimmermann:
Effective slow dynamics models for a class of dispersive systems
(preprint 2018)

P. Krämer, K. Schratz, X. Zhao:
Splitting Methods for Nonlinear Dirac Equations with Thirring type Interaction in the Nonrelativistic Limit Regime
(preprint 2018)

S. Baumstark, K. Schratz:
Asymptotic preserving integrators for the quantum Zakharov system
(preprint 2019)

S. Baumstark, G. Schneider, K. Schratz:
Effective numerical simulation of the Klein-Gordon-Zakharov system in the Zakharov limit
(preprint 2019)

Publications

M. Knöller, A. Ostermann, K. Schratz:
A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data
SIAM J. Numer. Anal. 57, 1967-1986 (2019)
https://doi.org/10.1137/18M1198375


S. Baumstark, K. Schratz:
Uniformly Accurate Oscillatory Integrators for the Klein-Gordon-Zakharov System
from Low- to High-Plasma Frequency Regimes.
SIAM J. Numer. Anal. 57, 429-457 (2019)
doi:10.1137/18M1177184


L. Gauckler, J. Lu, J. Marzuola, F. Rousset, K. Schratz:
Trigonometric integrators for quasilinear wave equations.
Math. Comp. 88, 717-749 (2019)
doi:10.1090/mcom/3339


A. Ostermann, K. Schratz:
Low regularity exponential-type integrators for semilinear Schrödinger equations.
Found. Comput. Math. 18, 731-755 (2018)
doi:10.1007/s10208-017-9352-1


S. Baumstark, G. Kokkala, K. Schratz :
Asymptotic consistent exponential-type integrators for Klein-Gordon-Schrödinger systems from relativistic to non-relativistic regimes.
ETNA 48, 63-80 (2018)
doi:10.1553/etna_vol48s63


S. Baumstark, E. Faou, K. Schratz:
Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting.
Math. Comp. 87, 1227-1254 (2018)
doi:10.1090/mcom/3263


M. Hofmanová, K. Schratz:
An exponential-type integrator for the KdV equation.
Numer. Math. 136(4), 1117-1137 (2017)
doi:10.1007/s00211-016-0859-1


S. Herr, K. Schratz:
Trigonometric time integrators for the Zakharov system.
IMA J. Numer. Anal. 37, 2042–2066 (2017)
doi:10.1093/imanum/drw059


P. Krämer, K. Schratz:
Efficient time integration of the Maxwell-Klein-Gordon system in the non-relativistic limit regime.
J. Comput. Appl. Math. 316, 247-259 (2017)
doi:10.1016/j.cam.2016.07.007


M. Daub, G. Schneider, K. Schratz:
From the Klein-Gordon-Zakharov system to the Klein-Gordon equation.
Math. Meth. Appl. Sci. 39, 5371-5380 (2016)
doi:10.1002/mma.3922


A. Ostermann, K. Schratz:
Derivation of a low regularity exponential-type integrator for semilinear Schrödinger equations with polynomial nonlinearities.
Oberwolfach Reports 18, 928-931 (2016)
doi:0.4171/OWR/2016/18


J. Eilinghoff, R. Schnaubelt, K. Schratz:
Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation.
J. Math. Anal. Appl. 442, 740-760 (2016)
doi:10.1016/j.jmaa.2016.05.014


E. Hansen, A. Ostermann, K. Schratz:
The error structure of the Douglas-Rachford splitting method for stiff linear problems.
J. Comput. Appl. Math. 303, 140-145 (2016)
doi:10.1016/j.cam.2016.02.037


E. Faou, A. Ostermann, K. Schratz:
Analysis of exponential splitting methods for inhomogeneous parabolic equations.
IMA J. Numer. Anal. 35, 161-178 (2015)
doi:doi.org/10.1093/imanum/dru002


E. Faou, K. Schratz:
Efficient time integration of Klein-Gordon-type equations in high-frequency limit regimes.
Oberwolfach Reports 14, 852-853 (2014)
doi:10.4171/OWR/2014/14


E. Faou, K. Schratz:
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime.
Numer. Math. 126, 441-469 (2014)
doi:10.1007/s00211-013-0567-z


A. Ostermann, K. Schratz:
Stability of exponential operator splitting methods for non-contractive semigroups.
SIAM J. Numer. 51, 191-203 (2013)
doi:10.1137/110846580


M. Mergili, K. Schratz, A. Ostermann, W. Fellin:
A GRASS GIS implementation of the Savage-Hutter avalanche model and its application to the 1987 Val Pola event.
Landslide Science and Practice, vol. 3: Spatial Analysis and Modelling (C. Margottini, P. Canuti, K. Sassa, eds.), Springer, Berlin Heidelberg, 367-373 (2013)
doi:10.1007/978-3-642-31310-3_50


A. Ostermann, K. Schratz:
Error analysis of splitting methods for inhomogeneous evolution equations.
Appl. Numer. Math. 62, 1436-1446 (2012)
doi:10.1016/j.apnum.2012.06.002


M. Mergili, K. Schratz, A. Ostermann, W. Fellin:
Physically-based modelling of granular flows with Open Source GIS.
Nat. Hazards Earth Syst. Sci. 12, 187-200 (2012)
doi:10.5194/nhess-12-187-2012


A. Ostermann, K. Schratz, G. Spielberger:
Lie splitting on polygonal domains.
Proc. Appl. Math. Mech. 11, 787-788 (2011)
doi:10.1002/pamm.201110382


Theses

PhD thesis: Splitting methods for parabolic evolution equations (2012)

Diploma thesis: Modeling of landslides and avalanches – mathematical and numerical analysis (2009)


Short CV

2012: Dr., University of Innsbruck, Austria

2012 - 2013: Post-Doc at the ENS Cachan Bretagne & INRIA, Rennes, France

September 2013 - current: Junior professor at the Karlsruhe Institute of Technology, Karlsruhe, Germany

Links to my former PhD students / Post-doc