Low-regularity and high oscillations: numerical analysis and computation of dispersive evolution equations

Project Information

LAHACODE

Grant agreement ID: 850941

DOI

10.3030/850941

EC signature date 15 October 2019

Start date 1 May 2020

End date 31 December 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 499 905,00

EU contribution

€ 1 499 905,00

Coordinated by

SORBONNE UNIVERSITE
France

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (31)

Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter

Author(s): Maria Cabrera Calvo, Katharina Schratz
Published in: BIT Numerical Mathematics, Issue 62, 2022, Page(s) 1625-1647, ISSN 0006-3835
Publisher: Lunds Universitet
DOI: 10.1007/s10543-022-00925-z

Resonances as a Computational Tool

Author(s): Frédéric Rousset, Katharina Schratz
Published in: Foundations of Computational Mathematics, Issue 25, 2025, Page(s) 1879-1906, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-024-09665-8

Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation

Author(s): Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 2071-2086, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1619617

A symmetric low-regularity integrator for the nonlinear Schrödinger equation

Author(s): Yvonne Alama Bronsard
Published in: IMA Journal of Numerical Analysis, Issue 44, 2024, Page(s) 3648-3682, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drad093

A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations

Author(s): Buyang Li; Shu Ma; Katharina Schratz
Published in: SIAM Journal of Numerical Analysis, Issue 3, 2022, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1437007

Approximations of Dispersive PDEs in the Presence of Low-Regularity Randomness

Author(s): Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
Published in: Foundations of Computational Mathematics, Issue 24, 2024, Page(s) 1819-1869, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-023-09625-8

Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation

Author(s): Poulain, Alexandre; Schratz, Katharina
Published in: IMA Journal of Numerical Analysis, 2021, Issue 15, 2021, ISSN 1464-3642
Publisher: Oxford University Press
DOI: 10.1093/imanum/drab082

Uniformly accurate integrators for Klein–Gordon–Schrödinger systems from the classical to non-relativistic limit regime

Author(s): Maria Cabrera Calvo
Published in: Journal of Computational and Applied Mathematics, Issue 10, 2023, ISSN 1879-1778
Publisher: Elsevier
DOI: 10.1016/j.cam.2022.114756

A μ-mode BLAS approach for multidimensional tensor-structured problems

Author(s): Franco Zivcovich; Marco Caliari; Fabio Cassini
Published in: Numerical Algorithms, Issue 8, 2022, ISSN 1017-1398
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-022-01399-4

Resonance based schemes for dispersive equations via decorated trees

Author(s): Bruned, Yvain; Schratz, Katharina
Published in: Forum of Mathematics, Pi, Issue 1, 2022, ISSN 2050-5086
Publisher: Cambridge University Press
DOI: 10.48550/arxiv.2005.01649

Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces

Author(s): Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina
Published in: Journal of the European Mathematical Society, Issue 6, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.48550/arxiv.2006.12785

Error estimates at low regularity of splitting schemes for NLS

Author(s): Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: Mathematics of Computation, 2021, Page(s) 1, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3676

Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation

Author(s): Yue Feng, Katharina Schratz
Published in: Numerische Mathematik, Issue 156, 2024, Page(s) 1455-1477, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-024-01423-w

Low-regularity integrators for nonlinear Dirac equations

Author(s): Katharina Schratz, Yan Wang and Xiaofei Zhao
Published in: Mathematics of Computation, 2020, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3557

Uniformly accurate low regularity integrators for the Klein--Gordon equation from the classical to non-relativistic limit regime

Author(s): María Cabrera Calvo; Katharina Schratz
Published in: SIAM Journal of Numerical Analysis, Issue 4, 2022, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/arxiv.2104.11672

An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions

Author(s): Georg Maierhofer, Daan Huybrechs
Published in: Journal of Computational and Applied Mathematics, Issue 416, 2025, Page(s) 114500, ISSN 0377-0427
Publisher: Elsevier BV
DOI: 10.1016/j.cam.2022.114500

Low regularity error estimates for the time integration of 2D NLS

Author(s): Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: IMA Journal of Numerical Analysis, Issue 45, 2025, Page(s) 2023-2059, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drae054

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation

Author(s): Buyang Li; Katharina Schratz; Franco Zivcovich
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 7, 2023, ISSN 2822-7840
Publisher: EDP sciences
DOI: 10.1051/m2an/2022096

Asymptotic preserving trigonometric integrators for the quantum Zakharov system

Author(s): Simon Baumstark, Katharina Schratz
Published in: BIT Numerical Mathematics, Issue 61/1, 2021, Page(s) 61-81, ISSN 0006-3835
Publisher: Lunds Universitet
DOI: 10.1007/s10543-020-00815-2

Computing rough solutions of the stochastic nonlinear wave equation

Author(s): Jiachuan Cao, Buyang Li, Katharina Schratz
Published in: Mathematics of Computation, 2026, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/4163

Numerical Integration of Schrödinger Maps via the Hasimoto Transform

Author(s): Valeria Banica, Georg Maierhofer, Katharina Schratz
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 322-352, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1531555

Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity

Author(s): Alexander Ostermann, Frédéric Rousset, Katharina Schratz
Published in: Foundations of Computational Mathematics, Issue 21/3, 2021, Page(s) 725-765, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09468-7

Low regularity integrators for semilinear parabolic equations with maximum bound principles

Author(s): Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz
Published in: BIT Numerical Mathematics, 2023, ISSN 0006-3835
Publisher: Lunds Universitet

A μ-mode integrator for solving evolution equations in Kronecker form

Author(s): Marco Caliari; Fabio Cassini; Lukas Einkemmer; Alexander Ostermann; Franco Zivcovich
Published in: Journal of Computational Physics, Issue 14, 2022, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2022.110989

Bridging the gap: Symplecticity and low regularity in Runge–Kutta resonance-based schemes

Author(s): Georg Maierhofer, Katharina Schratz
Published in: Mathematics of Computation, 2025, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/4105

Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions

Author(s): G Maierhofer, A Iserles, N Peake
Published in: IMA Journal of Numerical Analysis, Issue 43, 2023, Page(s) 3169-3211, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drac067

A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics

Author(s): Tianyu Jin, Georg Maierhofer, Katharina Schratz, Yang Xiang
Published in: Journal of Computational Physics, Issue 529, 2025, Page(s) 113869, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2025.113869

A General Framework of Low Regularity Integrators

Author(s): Frédéric Rousset and Katharina Schratz
Published in: SIAM Journal on Numerical Analysis, 2021, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1371506

Time integrators for dispersive equations in the long wave regime

Author(s): Calvo, María Cabrera; Rousset, Frédéric; Schratz, Katharina
Published in: Mathematics of Computation, Issue 9, 2021, ISSN 1088-6842
Publisher: AMS
DOI: 10.1090/mcom/3745

Convergence error estimates at low regularity for time discretizations of KdV

Author(s): Frédéric Rousset; Katharina Schratz
Published in: Pure and applied analysis, Issue 12, 2022, ISSN 2578-5885
Publisher: msp
DOI: 10.2140/paa.2022.4.127

"BAMPHI: Matrix-free and transpose-free action of linear combinations of <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" display=""inline"" id=""d1e360"" altimg=""si2.svg""><mml:mi>φ</mml:mi></mml:math>-functions from exponential integrators"

Author(s): Marco Caliari; Fabio Cassini; Franco Zivcovich
Published in: Journal of Computational and Applied Mathematics, Issue 5, 2023, ISSN 0377-0427
Publisher: Elsevier BV
DOI: 10.1016/j.cam.2022.114973