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Arbeitsgruppe 3: Wissenschaftliches Rechnen

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 3.039

Adresse
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

Öffnungszeiten:
Mo-Do 9-12 Uhr

Tel.: 0721 608 42062

Fax.: 0721 608 43197

Foto von Katharina Schratz JProf. Dr. Katharina Schratz

Sprechstunde: By Appointment
Zimmer: 3.024 Kollegiengebäude Mathematik (20.30)
Tel.: 0721 608 47651
Fax.: 0721 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

Computational Science & Engineering (CSE) Workshop 2019

New Publications

S. Baumstark, K. Schratz:
Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes
To appear in SIAM Journal on Numerical Analysis

L. Gauckler, J. Lu, J. Marzuola, F. Rousset, K. Schratz:
Trigonometric integrators for quasilinear wave equations.
To appear in Math. Comp. (2018)
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

Members:

Katharina Schratz (head)
Patrick Krämer (post-doc)
Simon Baumstark (post-doc)

Former members:
Post-docs:
Xiaofei Zhao (now in Rennes, France)
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)





Aktuelles Lehrangebot
Semester Titel Typ
Wintersemester 2018/19 Vorlesung
Seminar
Seminar
Sommersemester 2018 Vorlesung
Seminar
Wintersemester 2017/18 Seminar
Sommersemester 2017 Vorlesung
Wintersemester 2016/17 Vorlesung
Sommersemester 2016 Vorlesung
Wintersemester 2015/16 Vorlesung
Sommersemester 2015 Vorlesung
Wintersemester 2014/15 Vorlesung
Vorlesung
Sommersemester 2014 Vorlesung
Wintersemester 2013/14 Vorlesung
Seminar


Current Projects

Principal investigator within the Collaborative Research Centre 1173 Wave phenomena: analysis and numerics (07/15 - 06/19), funded by DFG (Germany)

Project B1: "Klein-Gordon-Zakharov systems in high-frequency regimes"
PIs: Prof. Dr. Guido Schneider, JProf. Dr. Katharina Schratz
Links: CRC 1173 Wave phenomena, Project B1

Preprints

M. Knöller, A. Ostermann, K. Schratz:
A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data
(preprint 2018)

M. Hofmanová, M. Knöller, K. Schratz:
Randomized exponential integrator for modulated nonlinear Schrödinger equations
(preprint 2017)

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 2017)

S. Baumstark, G. Schneider, K. Schratz, D. Zimmermann:
Normal form transformations and singular limits
(preprint 2017)

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

Publications

S. Baumstark, K. Schratz:
Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes
To appear in SIAM Journal on Numerical Analysis


L. Gauckler, J. Lu, J. Marzuola, F. Rousset, K. Schratz:
Trigonometric integrators for quasilinear wave equations.
To appear in Math. Comp. (2018)
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 PhD students / Post-doc