## Publications

Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation. SIAM J. Math. Anal., 56(1):454–473, February 2024. URL https://doi.org/10.1137/22M1504810. . [preprint]

Approximation of high-frequency wave propagation in dispersive media. SIAM J. Math. Anal., 55(2):1214–1245, April 2023. URL https://doi.org/10.1137/22M1474035. . [preprint]

On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation. BIT, 63:26, 28pp., April 2023. URL https://doi.org/10.1007/s10543-023-00971-1. . [preprint] [files]

Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations. BIT, 63:9, 24pp., January 2023. URL https://doi.org/10.1007/s10543-023-00942-6. Online first. . [preprint] [files]

Dynamical low-rank integrators for second-order matrix differential equations. BIT, 63:4, 21pp., January 2023. URL https://doi.org/10.1007/s10543-023-00941-7. Online first. . [preprint] [files]

A multilevel stochastic collocation method for Schrödinger equations with a random potential. SIAM/ASA J. Uncertain. Quantif., 10(4):1753–1780, December 2022. URL https://doi.org/10.1137/21M1440517. . [preprint] [files]

On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. SN Partial Differ. Equ. Appl., 2(2):23, 27pp., March 2021. URL https://doi.org/10.1007/s42985-020-00045-9. . [preprint] [files]

On the convergence of Lawson methods for semilinear stiff problems. Numer. Math., 145(3):553–580, July 2020. URL https://doi.org/10.1007/s00211-020-01120-4. . [preprint]

A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Numer. Math., 144(4):787–809, April 2020. URL https://doi.org/10.1007/s00211-020-01105-3. . [preprint]

Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Numer. Math., 144(3):699–728, March 2020. URL https://doi.org/10.1007/s00211-019-01093-z. . [preprint]

A conjugate-gradient-type rational Krylov subspace method for ill-posed problems. Inverse Problems, 36(1):015008, January 2020. URL https://doi.org/10.1088/1361-6420/ab5819. . [preprint]

Heterogeneous multiscale method for Maxwell's equations. Multiscale Model. Simul., 17(4):1147–1171, October 2019. URL https://doi.org/10.1137/18M1234072. . [preprint]

Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation. IMA J. Numer. Anal., 39(4):1818–1859, October 2019. URL https://doi.org/10.1093/imanum/dry045. . [preprint]

Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation. Numer. Math., 138(4):975–1009, April 2018. URL https://doi.org/10.1007/s00211-017-0926-2. . [preprint]

Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations. IMA J. Numer. Anal., 38(1):57–74, January 2018. URL https://doi.org/10.1093/imanum/drx007. . [preprint]

Finite element heterogeneous multiscale method for time-dependent Maxwell's equations. In M. L. Bittencourt, N. A. Dumont, and J. S. Hesthaven, editors, Spectral and high order methods for partial differential equations—ICOSAHOM 2016, volume 119 of

*Lect. Notes Comput. Sci. Eng.*, pages 269–281. Springer, Cham, November 2017. . [preprint]On the approximation of electromagnetic fields by edge finite elements. Part 2: A heterogeneous multiscale method for Maxwell's equations. Comput. Math. Appl., 73(9):1900–1919, May 2017. URL https://doi.org/10.1016/j.camwa.2017.02.043. . [preprint]

Long-term analysis of semilinear wave equations with slowly varying wave speed. Comm. Partial Differential Equations, 41(12):1934–1959, September 2016. URL https://doi.org/10.1080/03605302.2016.1235581. . [preprint]

## Preprints

Improved error bounds for approximations of high-frequency wave propagation in nonlinear dispersive media. CRC 1173 Preprint 2024/5, Karlsruhe Institute of Technology, February 2024. . [files]

Variational Gaussian approximation for the magnetic Schrödinger equation. CRC 1173 Preprint 2023/4, Karlsruhe Institute of Technology, January 2023. Revised version from October 2023. .

## Theses

*On dynamical low-rank integrators for matrix differential equations*. PhD thesis, Karlsruhe Institute of Technology (KIT), July 2022. .*High-frequency wave-propagation: error analysis for analytical and numerical approximations*. PhD thesis, Karlsruhe Institute of Technology (KIT), July 2022. .*Error analysis of exponential integrators for nonlinear wave-type equations*. PhD thesis, Karlsruhe Institute of Technology (KIT), February 2021. .*Fehleranalyse von auf trigonometrischen Integratoren basierenden Splittingverfahren für hochoszillatorische, semilineare Probleme*. PhD thesis, Karlsruhe Institute of Technology (KIT), November 2018. .*Time-integration methods for a dispersion-managed nonlinear Schrödinger equation*. PhD thesis, Karlsruhe Institute of Technology (KIT), June 2017. .

## Other references

Large-stepsize integrators for charged-particle dynamics over multiple time scales. Numer. Math., 151(3):659–691, 2022. URL https://doi.org/10.1007/s00211-022-01298-9. .

(Semi-)nonrelativisitic limit of the nonlinear Dirac equations. J. Math. Study, 53(2):125–142, 2020. URL https://doi.org/10.4208/jms.v53n2.20.01. .

Computing quantum dynamics in the semiclassical regime. Acta Numer., 29:229–401, 2020. URL https://doi.org/10.1017/s0962492920000033. .

A projector-splitting integrator for dynamical low-rank approximation. BIT, 54(1):171–188, 2014. URL https://doi.org/10.1007/s10543-013-0454-0. .

Dispersion-managed solitons in fibre systems and lasers. Phys. Rep., 521(4):135–203, December 2012. URL https://doi.org/10.1016/j.physrep.2012.09.004. .

Short pulses approximations in dispersive media. SIAM J. Math. Anal., 41(2):708–732, 2009. URL https://doi.org/10.1137/070711724. .

A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems. J. Comput. Phys., 227(16):7701–7719, 2008. URL https://doi.org/10.1016/j.jcp.2008.04.024. .

Dynamical low-rank approximation. SIAM J. Matrix Anal. Appl., 29(2):434–454, 2007. URL https://doi.org/10.1137/050639703. .

Error analysis of exponential integrators for oscillatory second-order differential equations. J. Phys. A, 39(19):5495–5507, April 2006. URL https://doi.org/10.1088/0305-4470/39/19/S10. .

*Geometric numerical integration*, volume 31 of*Springer Series in Computational Mathematics*. Springer-Verlag, Berlin, Second edition, 2006. Structure-preserving algorithms for ordinary differential equations. .Numerical solution of nonlinear wave equations in stratified dispersive media. J. Comput. Phys., 216(1):138–152, 2006. URL https://doi.org/10.1016/j.jcp.2005.11.024. .

Long-time-step integrators for almost-adiabatic quantum dynamics. SIAM J. Sci. Comput., 25(6):2145–2164, July 2004. URL https://doi.org/10.1137/S1064827502411316. .

Numerical integrators for quantum dynamics close to the adiabatic limit. Numer. Math., 94(2):289–314, April 2003. URL https://doi.org/10.1007/s00211-002-0421-1. .