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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: Kollegiengebäude Mathematik (20.30)
Email:

Englerstr. 2
D-76131 Karlsruhe

Hello, I moved to Heriot-Watt University (k.schratz@hw.ac.uk - my kit email is no longer active)

https://researchportal.hw.ac.uk/en/persons/katharina-schratz

================

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

Invited plenary talks

Dynamics Days 2020, 40th European Dynamic Days Conference

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