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Low-regularity and high oscillations: numerical analysis and
computation of dispersive evolution equations
Funding period: 2020 - 2025
(financed by the European Research Council)
https://cordis.europa.eu/project/id/850941
Members :
Yvonne Bronsard Alama
María Cabrera Calvo
Albert Cohen
Yue Feng
Katharina Schratz
Former Members :
Georg Maierhofer
Nikola Stoilov
Franco Zivcovich
Publications :
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,
Approximations of dispersive PDEs in the presence of low-regularity randomness
https://arxiv.org/abs/2205.02156
(preprint 2022)
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
C.-K. Doan, T.-T.-P. Hoang, K. Schratz,
Low regularity integrators for semilinear parabolic equations
with maximum bound principles (preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz,
Low regularity integrators via decorated trees
https://arxiv.org/abs/2202.01171
(preprint 2022)
M. Caliari, F. Cassini, F. Zivcovich,
A μ-mode BLAS approach for multidimensional tensor-structured problems
https://arxiv.org/abs/2112.11238
(preprint 2021)
M. Caliari, F. Cassini, L. Einkemmer, A. Ostermann, F. Zivcovich,
A μ-mode integrator for solving evolution equations in Kronecker form
https://arxiv.org/abs/2103.01691
(preprint 2021)
Y. Alama Bronsard Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity
https://arxiv.org/abs/2201.13314 J. Comp. App. Math, 114632, July 202
M. Cabrera Calvo Uniformly accurate integrators for Klein-Gordon-Schrödinger systems from the
classical to non-relativistic limit regime
https://arxiv.org/abs/2201.05339
to appear in Journal of Computational and Applied Mathematics
G. Maierhofer, D. Huybrechs, An analysis of least-squares oversampled collocation methods for
compactly perturbed boundary integral equations in two dimensions
https://arxiv.org/abs/2201.11683
(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)
B. Li, S. Ma, K. Schratz,
A semi-implicit low-regularity integrator for Navier-Stokes equations
http://arxiv.org/abs/2107.13427
to appear in SIAM J. Numer. Anal.
M. Cabrera Calvo, K. Schratz. Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony
equation with dispersive parameter
http://arxiv.org/abs/2105.03732
to appear in BIT Numer Math
M. Cabrera Calvo, F. Rousset, K. Schratz. Time integrators for dispersive equations in the long wave regime
http://arxiv.org/abs/2105.03731
to appear in Math. Comp.
M. Cabrera Calvo, K. Schratz. Uniformly accurate low regularity integrators for the classical to non-relativistic limit regime
http://arxiv.org/abs/2104.11672
to appear in SIAM J. Numer. Anal.
F. Rousset, K. Schratz. Convergence error estimates at low regularity for time discretizations of KdV
https://arxiv.org/abs/2102.11125
to appear in Pure and Applied Analysis
Y. Bruned, K. Schratz. Resonance based schemes for dispersive equations via decorated trees
doi:10.1017/fmp.2021.13
Forum of Mathematics, Pi 10:e2 1-76 (2022)
A. Poulain, K. Schratz. Convergence, error analysis and longtime behavior of the Scalar Auxiliary
Variable method for the nonlinear Schrödinger equation
https://arxiv.org/abs/2012.13943
to appear in IMA J. Numer. Anal.
A. Ostermann, F. Rousset, K. Schratz. Error estimates at low regularity of splitting schemes for NLS
https://arxiv.org/abs/2012.14146
to appear in Math. Comp.
F. Rousset, K. Schratz. A general framework of low regularity integrators
http://arxiv.org/abs/2010.01640
SIAM J. Numer. Anal. 59:1735-1768 (2021)
A. Ostermann, F. Rousset, K. Schratz. Fourier integrator for periodic NLS:
low regularity estimates via discrete Bourgain spaces
http://arxiv.org/abs/2006.12785
to appear in J. Eur. Math. Soc. (JEMS)
K. Schratz, Y. Wang, X. Zhao. Low-regularity integrators for nonlinear Dirac equations.
https://arxiv.org/abs/1906.09413 Math. Comp. 90:189-214 (2021)
A. Ostermann, F. Rousset, K. Schratz. Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity.
https://arxiv.org/abs/1902.06779 Found. Comput. Math. 21:725-765 (2021)
S. Baumstark, K. Schratz. Asymptotic preserving integrators for the quantum Zakharov system.
doi:10.1007/s10543-020-00815-2
BIT Numer Math (2020)