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Katharina Schratz Professor at Sorbonne University Laboratoire Jacques-Louis Lions Sorbonne Université 4 place Jussieu, 75005 Paris France office: 15-16 312 email:
katharina.schratz@sorbonne-universite.fr
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ERC Starting Grant LAHACODE
Low-regularity and high oscillations: numerical analysis and computation of dispersive evolution equations
2020 - 2025 (financed by the European Research Council)
https://cordis.europa.eu/project/id/850941
Plenary talks
Editorial boards (associated editor)
SIAM Journal on Numerical Analysis (SINUM) (since 2023)
https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum
IMA Journal of Numerical Analysis (since 2021)
https://academic.oup.com/imajna
Acta Applicandae Mathematicae (since 2021)
https://www.springer.com/journal/10440
Organsiation of workshops
Modern methods for differential equations of quantum mechanics
Banff International Research Station, Banff (Canada) 2024
Women in nonlinear dispersive PDEs
Banff International Research Station, Banff (Canada) 2023
Normal forms and splitting methods
13-17 June 2022, Pornichet (France)
Computational Mathematics for Quantum Technologies
1-5 August 2022, Bath (UK)
Recorded talks
Institute for Advanced Study: Analysis and Mathematical Physics seminar
Resonances as a computational tool
Séminaire du LJLL 2020
Resonances as a computational tool
MSRI Introductory Workshop: Mathematical problems in fluid dynamics 2021
Introduction to time discretisation of some nonlinear PDEs (at low regularity)
One World Numerical Analysis: ICMS 2022
Resonances as a computational tool
Publications
Y. A. Bronsard, Y. Bruned, G. Maierhofer, K. Schratz,
Symmetric resonance based integrators and forest formulae
http://arxiv.org/abs/2305.16737
(preprint 2023)
Y. Feng, G. Maierhofer, K. Schratz,
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
https://arxiv.org/abs/2302.00383
(preprint 2023)
L. Ji, A. Ostermann, F. Rousset, K. Schratz,
Low regularity error estimates for the time integration of 2D NLS
https://arxiv.org/abs/2301.10639
(preprint 2023)
Y. Feng, K. Schratz,
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time
dynamics of sine-Gordon equation
https://arxiv.org/abs/2211.09402
(preprint 2022)
V. Banica, G. Maierhofer, K. Schratz,
Numerical integration of Schrödinger maps via the Hasimoto transform
https://arxiv.org/abs/2211.01282
(preprint 2022)
G. Maierhofer, K. Schratz,
Bridging the gap: symplecticity and low regularity on the example of the KdV equation
https://arxiv.org/abs/2205.05024
(preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz,
Low regularity integrators via decorated trees
https://arxiv.org/abs/2202.01171
(preprint 2022)
K. Kropielnicka, K. Lademann, K. Schratz
Effective high order integrators for
low to highly oscillatory Klein-Gordon equations (preprint 2021)
A. Iserles, K. Kropielnicka, K. Schratz, M. Webb. Solving the linear Schrödinger equation on the real line
http://arxiv.org/abs/2102.00413
(preprint 2021)
Y. A. Bronsard, Y. Bruned, K. Schratz,
Approximations of dispersive PDEs in the presence of low-regularity randomness
Found. Comput. Math. (to appear)
https://arxiv.org/abs/2205.02156
C.-K. Doan, T.-T.-P. Hoang, K. Schratz,
Low regularity integrators for semilinear parabolic equations
with maximum bound principles
BIT Numer Math (to appear) https://link.springer.com/article/10.1007/s10543-023-00946-2
B. Li, K. Schratz, F. Zivcovich,
A second-order low-regularity correction of Lie splitting for the
semilinear Klein-Gordon equation
M2AN (to appear) http://arxiv.org/abs/2203.15539
B. Li, S. Ma, K. Schratz,
A semi-implicit low-regularity integrator for Navier-Stokes equations
SIAM J. Numer. Anal. 60:2273-2292 (2022) http://arxiv.org/abs/2107.13427
M. Cabrera Calvo, K. Schratz. Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony
equation with dispersive parameter
BIT Numer Math 60:888-912 (2022)
http://arxiv.org/abs/2105.03732
M. Cabrera Calvo, F. Rousset, K. Schratz. Time integrators for dispersive equations in the long wave regime
Math. Comp. Math. Comp. 91:2197-2214 (2021) \url{http://arxiv.org/abs/2105.03731} http://arxiv.org/abs/2105.03731
M. Cabrera Calvo, K. Schratz. Uniformly accurate low regularity integrators for the Klein-Gordon equation
from the classical to non-relativistic limit regime
SIAM J. Numer. Anal. (to appear)
http://arxiv.org/abs/2104.11672
F. Rousset, K. Schratz. Convergence error estimates at low regularity for time discretizations of KdV
Pure and Applied Analysis (to appear) https://arxiv.org/abs/2102.11125
Y. Bruned, K. Schratz. Resonance based schemes for dispersive equations via decorated trees
Forum of Mathematics, Pi 10:e2 1-76 (2022) doi:10.1017/fmp.2021.13
A. Poulain, K. Schratz. Convergence, error analysis and longtime behavior of the Scalar Auxiliary
Variable method for the nonlinear Schrödinger equation
IMA J. Numer. Anal. (to appear) https://arxiv.org/abs/2012.13943
A. Ostermann, F. Rousset, K. Schratz. Error estimates at low regularity of splitting schemes for NLS
Math. Comp. (to appear)
https://arxiv.org/abs/2012.14146
F. Rousset, K. Schratz. A general framework of low regularity integrators
SIAM J. Numer. Anal. 59:1735-1768 (2021) http://arxiv.org/abs/2010.01640
A. Ostermann, F. Rousset, K. Schratz. Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
J. Eur. Math. Soc. (JEMS) 25:3913-3952 (2022) http://arxiv.org/abs/2006.12785
K. Schratz, Y. Wang, X. Zhao. Low-regularity integrators for nonlinear Dirac equations.
Math. Comp. 90:189-214 (2021) 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.
Found. Comput. Math. 21:725-765 (2021) doi 10.1007/s10208-020-09468-7
M. Hofmanová, M. Knöller, K. Schratz. Randomized exponential integrators for modulated non-linear Schrödinger equations.
IMA J. Numer. Anal. 40:2143-2162 (2020)
https://doi.org/10.1093/imanum/drz050
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. Comp. 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. Comput. 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. Comp. 87:1227-1254 (2018)
doi:10.1090/mcom/3263
M. Hofmanová, K. Schratz. An exponential-type integrator for the KdV equation.
Numer. Math. 136:1117-1137 (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 equa- tions.
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
| 2022- : | Yue Feng, Post-doc, Sorbonne Université, France |
| Sep 2021- : | Georg Maierhofer, Post-doc, Sorbonne Université, France |
| 2021-2022 : | Nikola Stoilov, Post-doc, Sorbonne Université, France |
| 2021-2022 : | Franco Zivcovich, Post-doc, Sorbonne Université, France |
| 2018-2019 : | Simon Baumstark, Post-doc, KIT, Allemagne |
| 2017-2018 : | Patrick Krämer, Post-doc, KIT, Allemagne |
| 2018-2019 : | Xiaofei Zhao, Post-doc, KIT, Allemagne |
| Sep 2021- : | Yvonne Bronsard Alama, Thèse de doctorat, Sorbonne Université, France |
| 2020-2023 : | 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 |
| 2023 : | Qinyan Zhou, Stage, Sorbonne Université, France |
| 2021 : | Yvonne Bronsard Alama, Stage, Sorbonne Université, France |
| 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 |