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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
katharina.schratz@sorbonne-universite.fr
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 (Malika, Franco, María, Katharina, Yvonne, Georg) |
LAHACODE (ERC Starting Grant)
Low-regularity and high oscillations:
numerical analysis and computation of dispersive evolution equations
2020 - 2025 (funded by European Research Council)
https://cordis.europa.eu/project/id/850941
• Editorial boards
Mathematical Foundations of Machine Learning
https://link.springer.com/journal/44439
SIAM Journal on Numerical Analysis (SINUM)
https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum
IMA Journal of Numerical Analysis
https://academic.oup.com/imajna
Acta Applicandae Mathematicae
https://www.springer.com/journal/10440
• Plenary talks
• Organsiation of workshops
Analysis and Computation of dispersive PDE and fluid dynamics (IHP) 2025
with T. Buckmaster and J. Krieger
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
June 2022, Pornichet (France)
Computational Mathematics for Quantum Technologies
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
J. Rowbottom, G. Maierhofer, T. Deveney, K. Schratz, P. Lio, CB Schönlieb, C. Budd,
G-Adaptive mesh refinement -- leveraging graph neural networks and differentiable finite element solvers
https://arxiv.org/abs/2407.04516
(preprint)
T. Jin, G. Maierhofer, K. Schratz, Y. Xiang,
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
https://arxiv.org/abs/2407.03945
(preprint)
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)
Y. A. Bronsard, Y. Bruned, K. Schratz,
Low regularity integrators via decorated trees
https://arxiv.org/abs/2202.01171
(preprint)
A. Iserles, K. Kropielnicka, K. Schratz, M. Webb, Solving the linear Schrödinger equation on the real line
http://arxiv.org/abs/2102.00413
(preprint)
L. Ji, A. Ostermann, F. Rousset, K. Schratz,
Low regularity error estimates for the time integration of 2D NLS
IMA J. Numer. Anal. (to appear) https://arxiv.org/abs/2301.10639
F. Rousset, K. Schratz,
Resonances as a computational tool
Found. Comput. Math. (to appear) https://arxiv.org/abs/2405.10572
Y. Feng, K. Schratz,
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation
Numer. Math. (to appear) https://arxiv.org/abs/2211.09402
Y. Feng, G. Maierhofer, K. Schratz,
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
Math. Comp. (to appear) https://arxiv.org/abs/2302.00383
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
L. Ji, A. Ostermann, F. Rousset, K. Schratz,
Low regularity full error estimates for the cubic nonlinear Schrödinger equation
SIAM J. Numer. Anal. 62:2071-2086
https://arxiv.org/abs/2311.14366
V. Banica, G. Maierhofer, K. Schratz,
Numerical integration of Schrödinger maps via the Hasimoto transform
SIAM J. Numer. Anal. 62:322-352 https://arxiv.org/abs/2211.01282
C.-K. Doan, T.-T.-P. Hoang, L. Ju, 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 57:899-919 (2023) 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) 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. 60:888-912 (2022)
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 4:127-152 (2022) 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. 91:169-182 (2022)
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
| Post-doc | |
| 2022-2023 : | Yue Feng, Post-doc, Sorbonne Université, France |
| 2021-2023 : | 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 |
| PhD | 2024 : | Chengewei Fan, PhD student, Sorbonne Université, France |
| 2021-2024 : | Yvonne Bronsard Alama, PhD student, Sorbonne Université, France |
| 2020-2023 : | María Cabrera Calvo, PhD student, Sorbonne Université, France |
| 2015-2018 : | Simon Baumstark, PhD student, KIT, Allemagne |
| 2014-2017 : | Patrick Krämer, PhD student, KIT, Allemagne |
| Master | |
| 2024 : | Chengewei Fan, Master student, Sorbonne Université, France |
| 2023 : | Qinyan Zhou, Master student, Sorbonne Université, France |
| 2021 : | Yvonne Bronsard Alama, Master student, Sorbonne Université, France |
| 2017-2018 : | Jelena Stjepanovic, Master student, KIT, Allemagne |
| 2017-2018 : | Irina Wetteborn, Master student, KIT, Allemagne |
| 2017-2018 : | Jan Bohn, Master student, KIT, Allemagne |
| 2016-2017 : | Georgia Kokkala, Master student, KIT, Allemagne |
| 2014-2015 : | Simon Baumstark, Master student, KIT, Allemagne |
| 2013-2014 : | Patrick Krämer, Master student (co-advisor), KIT, Allemagne |
| 2011-2012 : | Tobias Hell, Master student (co-advisor), Université d'Innsbruck, Autriche |
| 2011-2012 : | Georg Spielberger,Master student (co-advisor), Université d'Innsbruck, Autriche |