Katharina-Schratz

logoljll LOGO_ERC photo

Katharina Schratz
Professeure à Sorbonne Université
Laboratoire Jacques-Louis Lions
Bureau : 16-26-315, 4 place Jussieu, Paris 5ème
courriel: katharina.schratz@ljll.math.upmc.fr

Adresse postale :
Laboratoire Jacques-Louis Lions
Boite courrier 187
Sorbonne Université
4 place Jussieu
75252 Paris cedex 05

Projets subventionnés

ERC Starting Grant : LAHACODE
Low-regularity and high oscillations: numerical analysis and computation of dispersive evolution equations
Période de financement : 2020 - 2025 (financée par l'European Research Council)
https://cordis.europa.eu/project/id/850941

LMS Joint Research Group : Computational Mathematics for Quantum Mechanics (LMS award holder)
Groupe : Arieh Iserles (Cambridge), Karolina Kropielnicka (Gdansk), Caroline Lasser (TU Munich), Sheehan Olver (Imperial College), Christof Ortner (Warwick), Pranav Singh (Bath), Marcus Webb (Manchester),
Période de financement : 2020 - 2021 (financée par la London Mathematical Society)
https://www.pranavsingh.co.uk/cmqm

DAAD : Subject-Related Partnerships with Institutions of Higher Education in Developing Countries
Peruvian Competence Center of Scientific Computing - Enforcing scientific computing in teaching in Peru
Période de financement: 2019 - 2022 (financée par le DAAD)
https://www.pec3.org

DFG Collaborative Research Centre 1173 Wave phenomena: analysis and numerics (ancien membre)
Projet B1: Klein-Gordon-Zakharov systems in high-frequency regimes (collaborateur Guido Schneider)
Période de financement : 2015 - 2019 (financée par la DFG)
http://www.waves.kit.edu

Tiroler Wissenschaftsfonds (projet terminé)
Splitting methods on arbitrary domains
Période de financement : 2010 - 2011 (financée par le Tiroler Wissenschaftsfonds)

Conférences plénières

Conférence plénière à la NUMDIFF-16 (2021)

Conférence plénière à la 40th European Dynamic Days Conference (2021)

Conférence plénière au congrès 30 Years of Acta Numerica (2021)

Conférence plénière au congrès SciCADE (2019)

Exposés (vidéo)

Séminaire du LJLL 2020

Resonances as a computational tool

Comité éditorial

IMA Journal of Numerical Analysis (associate editor)

https://academic.oup.com/imajna

Publications

F. Rousset, K. Schratz. A general framework of low regularity integrators
http://arxiv.org/abs/2010.01640 (preprint 2020)
Y. Bruned, K. Schratz. Resonance based schemes for dispersive equations via decorated trees http://arxiv.org/abs/2005.01649 (preprint 2020)
A. Ostermann, F. Rousset, K. Schratz. Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces http://arxiv.org/abs/2006.12785 (preprint 2020)
K. Schratz, Y. Wang, X. Zhao. Low-regularity integrators for nonlinear Dirac equations. to appear in Math. Comput. https://arxiv.org/abs/1906.09413
A. Ostermann, F. Rousset, K. Schratz. Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. to appear in Found. Comput. Math. https: //arxiv.org/abs/1902.06779
M. Hofmanová, M. Knöller, K. Schratz. Randomized exponential integrators for modulated non- linear Schrödinger equations. to appear in IMA J. Numer. Anal. https://arxiv.org/abs/1711.01091
S. Baumstark, K. Schratz. Asymptotic preserving integrators for the quantum Zakharov system. BIT Numer Math (2020) doi:10.1007/s10543-020-00815-2
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) doi/10.1137/18M1198375
S. Baumstark, K. Schratz. Oscillatory integrators for Klein-Gordon-Zakharov systems 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. Comput. 88:717-749 (2019) doi/10.1090/mcom/3339
P. Krämer, K. Schratz, X. Zhao. Splitting Methods for Nonlinear Dirac Equations with Thirring type Interaction in the Nonrelativistic Limit Regime. J. Computat. Appl. Math. 112494, 2019. Online first doi:10.1016/j.cam.2019.112494
K. Schratz, X. Zhao. On the comparison of the asymptotic expansion techniques for the nonlinear Klein-Gordon equation in the non relativistic limit regime. DCDS-B 2019. Online first doi:10.3934/dcdsb.2020043
S. Baumstark, G. Schneider, K. Schratz, D. Zimmermann. Effective slow dynamics models for a class of dispersive systems. J. Dyn. Diff. Equat. 2019. Online first doi:10.1007/s10884- 019-09791-w
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. Comput. 87:1227-1254 (2018) doi:10.1090/mcom/3263
M. Hofmanová, K. Schratz. An exponential-type integrator for the KdV equation. Numer. Math. 136:1117-1137 (2017) doi:10.1007/s00211-016-0859-1
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. 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 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
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. 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. Anal. 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. 3:367-373 (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

Encadrement

2018-2019 : Simon Baumstark, Post-doc, KIT, Allemagne
2017-2018 : Patrick Krämer, Post-doc, KIT, Allemagne
2018-2019 : Xiaofei Zhao, Post-doc, KIT, Allemagne
Nov 2020- : María Cabrera Calvo, Thèse de doctorat, Sorbonne Université, France
2015-2018 : Simon Baumstark, Thèse de doctorat, KIT, Allemagne
2014-2017 : Patrick Krämer, Thèse de doctorat, KIT, Allemagne
2017-2018 : Jelena Stjepanovic, Master, KIT, Allemagne
2017-2018 : Irina Wetteborn, Master, KIT, Allemagne
2017-2018 : Jan Bohn, Master, KIT, Allemagne
2016-2017 : Georgia Kokkala, Master, KIT, Allemagne
2014-2015 : Simon Baumstark, Master, KIT, Allemagne
2013-2014 : Patrick Krämer, Master (co-advisor), KIT, Allemagne
2011-2012 : Tobias Hell, Master (co-advisor), Université d'Innsbruck, Autriche
2011-2012 : Georg Spielberger, Master (co-advisor), Université d'Innsbruck, Autriche