Mechthild Thalhammer

Publications

Please respect copyright restrictions

◊ Paper 1
A. Ostermann, M. Thalhammer
Non-smooth data error estimates for linearly implicit Runge-Kutta methods.
IMA J. Numer. Anal. 20 (2000) 167–184.

◊ Paper 2
C. González, A. Ostermann, C. Palencia, M. Thalhammer
Backward Euler discretization of fully nonlinear parabolic problems.
Math. Comp. 71 (2001) 125–145.

◊ Paper 3
A. Ostermann, M. Thalhammer
Convergence of Runge-Kutta methods for nonlinear parabolic equations.
Applied Numerical Math. 42 (2002) 367–380.

◊ Paper 4
A. Ostermann, M. Thalhammer, G. Kirlinger
Stability of linear multistep methods and applications to nonlinear parabolic problems.
Applied Numerical Math. 48 (2004) 389–407.

◊ Paper 5
M. Thalhammer
On the convergence behaviour of variable stepsize multistep methods for singularly perturbed problems.
BIT Numer. Math. 44/2 (2004) 343–361.

◊ Paper 6
C. González, A. Ostermann, M. Thalhammer
A second-order Magnus-type integrator for non-autonomous parabolic problems.
J. Comp. Appl. Math. 189 (2006) 142–156.

◊ Paper 7
C. González, M. Thalhammer
A second-order Magnus-type integrator for quasi-linear parabolic problems.
Math. Comp. 76/257 (2007) 205–231.

◊ Paper 8
A. Ostermann, M. Thalhammer, W. Wright
A class of explicit exponential general linear methods.
BIT 46/2 (2006) 409–431.

◊ Paper 9
M. Thalhammer
A fourth-order commutator-free exponential integrator for non-autonomous differential equations.
SIAM J. Numer. Anal. 44/2 (2006) 851–864.

◊ Paper 10
M. Thalhammer
High-order exponential operator splitting methods for time-dependent Schrödinger equations.
SIAM J. Numer. Anal. 46/4 (2008) 2022–2038.

◊ Paper 11
M. Caliari, Ch. Neuhauser, M. Thalhammer
High-order time-splitting Hermite and Fourier spectral methods for the Gross–Pitaevskii equation.
J. Comput. Phys. 228 (2009) 822–832.

◊ Paper 12
M. Caliari, A. Ostermann, S. Rainer, M. Thalhammer
A minimisation approach for computing the ground state of Gross–Pitaevskii systems.
J. Comput. Phys. 228 (2009) 349–360.

◊ Paper 13
Ch. Neuhauser, M. Thalhammer
On the convergence of splitting methods for linear evolutionary Schrödinger equations involving an unbounded potential.
BIT Numer. Math. 49 (2009) 199–215.

◊ Paper 14 (Author's personal copy)
S. Descombes, M. Thalhammer
An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime.
BIT Numer Math 50 (2010) 729–749.

◊ Paper 15 (Author's personal copy)
E. Emmrich, M. Thalhammer
Stiffly accurate Runge–Kutta methods for nonlinear evolution problems governed by a monotone operator.
Math. Comp. 79/270 (2010) 785–806.

◊ Paper 16
E. Emmrich, M. Thalhammer
Convergence of a time discretisation for doubly nonlinear evolution equations of second order.
Found. Comput. Math. 10 (2010) 171–190.

◊ Paper 17
E. Emmrich, M. Thalhammer
Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation.
J. Diff. Equ. 251 (2011) 82–118.

◊ Paper 18
E. Emmrich, M. Thalhammer
A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: Existence via time discretisation.
Nonlinearity 24 (2011) 2523–2546.

◊ Paper 19 (Author's personal copy)
W. Auzinger, O. Koch, M. Thalhammer
Defect-based local error estimators for splitting methoids, with application to Schrödinger equations, Part I. The linear case.
J. Comput. Appl. Math. 236 (2012) 2643–2659.

◊ Paper 20 (Author's personal copy)
M. Thalhammer, J. Abhau
A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations.
J. Comput. Phys. 231 (2012) 6665–6681.

◊ Paper 21
M. Thalhammer
Convergence analysis of high-order time-splitting pseudo-spectral methods for nonlinear Schrödinger equations.
SIAM J. Numer. Anal. 50/6 (2012) 3231–3258.

◊ Paper 22
S. Descombes, M. Thalhammer
The Lie–Trotter splitting method for nonlinear evolutionary problems with critical parameters. A compact local error representation and application to nonlinear Schrödinger equations in the semi-classical regime.
IMA J. Numer. Anal. 33/2 (2013) 722–745.

◊ Paper 23 (Author's personal copy)
O. Koch, Ch. Neuhauser, M. Thalhammer
Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations.
Appl. Numer. Math. 63 (2013) 14–24.

◊ Paper 24
O. Koch, Ch. Neuhauser, M. Thalhammer
Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics.
M2AN 47/5 (2013) 1265–1286.

◊ Paper 25 (Author's personal copy)
W. Auzinger, O. Koch, M. Thalhammer
Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part II. Higher-order methods for linear problems.
J. Comput. Appl. Math. 255 (2014) 384–403.

◊ Paper 26 (Open access)
J. Gwinner, M. Thalhammer
Full discretisations for nonlinear evolutionary inequalities based on stiffly accurate Runge-Kutta and hp-finite element methods.
Found. Comput. Math. 14 (2014) 913–949.

◊ Paper 27
H. Hofstätter, O. Koch, M. Thalhammer
Convergence analysis of high-order time-splitting pseudo-spectral methods for Gross–Pitaevskii equations with rotation term.
Numer. Math. 127/2 (2014) 315–364.

◊ Paper 28
B. Kaltenbacher, V. Nikolic, M. Thalhammer
Efficient time integration methods based on operator splitting and application to the Westervelt equation.
IMA J. Numer. Anal. 35/3 (2015) 1092–1124.
Preliminary version including appendix

◊ Paper 29
W. Auzinger, H. Hofstätter, O. Koch, M. Thalhammer
Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part III. The nonlinear case.
J. Comput. Appl. Math. 273 (2015) 182–204.

◊ Paper 30 (Author's personal copy)
W. Auzinger, O. Koch, M. Thalhammer
Defect-based local error estimators for high-order splitting methods involving three linear operators.
Numer. Algor. 70/1 (2015) 61–91.

◊ Paper 31 (Author's personal copy)
E. Emmrich, D. Šiška, M. Thalhammer
On a full discretisation for nonlinear second-order evolution equations with monotone damping: construction, convergence, and error estimates.
Found. Comput. Math. 15 (2015) 1653–1701.

◊ Paper 32
C. González, M. Thalhammer
Higher-order exponential integrators for quasi-linear parabolic problems. Part I. Stability.
SIAM J. Numer. Anal. 53/2 (2015) 701–719.

◊ Paper 33
Ph. Chartier, F. Mehats, M. Thalhammer, Y. Zhang
Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations.
Math. Comp. 85/302 (2016) 2863–2885.

◊ Paper 34
W. Auzinger, Th. Kassebacher, O. Koch, M. Thalhammer
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime.
Numer Algor. 72 (2016) 1–35.

◊ Paper 35
C. González, M. Thalhammer
Higher-order exponential integrators for quasi-linear parabolic problems. Part II. Convergence.
SIAM J. Numer. Anal. 54/5 (2016) 2868–2888.

◊ Paper 36
W. Auzinger, Th. Kassebacher, O. Koch, M. Thalhammer
Convergence of a full discretization for the Schrödinger-Poisson equation.
ESAIM: M2AN 51 (2017) 1245–1278.

◊ Paper 37
S. Blanes, F. Casas, M. Thalhammer
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type.
IMA J. Numer. Anal. 38/2 (2018) 743-778 (published May 2017).

◊ Paper 38
Ph. Chartier, F. Mehats, M. Thalhammer, Y. Zhang
Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type.
ESAIM: M2AN 51 (2017) 1859–1882.

◊ Paper 39
S. Blanes, F. Casas, M. Thalhammer
High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations.
Comp. Phys. Commun. 220 (2017) 243-262.

◊ Paper 40 (paper, preliminary version)
B. Kaltenbacher, M. Thalhammer
Fundamental models in nonlinear acoustics: Part I. Analytical comparison.
M3AS 28/12 (2018) doi.org/10.1142/S0218202518500525.

◊ Paper 41
W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer
A posteriori error estimation for Magnus-type integrators.
ESAIM: M2AN 53 (2019) 197-218.

◊ Paper 42
E. Hausenblas, T. Randrianasolo, M. Thalhammer
Theoretical study and numerical simulation of pattern formation in the deterministic and stochastic Gray-Scott equations.
Journal of Computational and Applied Mathematics 364 (2020) 112335.

◊ Paper 43
S. Blanes, F. Casas, M. Thalhammer
Splitting and composition methods with embedded error estimators.
Journal of Applied Numerical Mathematics 146 (2019) 400–415.

◊ Paper 44
Ph. Bader, S. Blanes, F. Casas, M. Thalhammer
Efficient time integration methods for Gross-Pitaevskii equations with rotation term.
Journal of Computational Dynamics 6/2 (2019) 147–169.

◊ Paper 45
S. Blanes, F. Casas, C. González, M. Thalhammer
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear Schrödinger equations.
IMA J. Numer. Anal. 41/1 (2021) 594–617.

◊ Paper 46
B. Kaltenbacher, M. Thalhammer
Convergence of implicit Runge-Kutta time discretisation methods for fundamental models in nonlinear acoustics.
J. Appl. Numer. Optim. 3/2 (2021) 361-401.

◊ Paper 47 (Preliminary version)
T. Böhle, Ch. Kühn, M. Thalhammer
On the reliable and efficient numerical integration of the Kuramoto model and related dynamical systems on graphs.
International Journal of Computer Mathematics, ahead-of-print (2021) 1-17, https://doi.org/10.1080/00207160.2021.1952997.
Open access

◊ Paper 48
T. Böhle, Ch. Kühn, M. Thalhammer
Community integration algorithms (CIAs) for dynamical systems on networks.
J. Comput. Phys. 469 (2022) 111524.

◊ Paper 49
S. Blanes, F. Casas, C. González, M. Thalhammer
Efficient splitting methods based on modified potentials: numerical integration of linear parabolic problems and imaginary time propagation of the Schrödinger equation.
Commun. Comput. Phys. 33 (2023) 937-961.

◊ Paper 50
S. Blanes, F. Casas, C. González, M. Thalhammer
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type.
Computer Physics Communications 295 (2024) 109007.

◊ Paper 51
S. Blanes, F. Casas, C. González, M. Thalhammer
Symmetric-conjugate splitting methods for evolution equations of parabolic type.
Journal of Computational Dynamics 11/1 (2024) 108-134.

Preprints

◊ Preprint
J.A. Carrillo, M. Thalhammer
Novel approaches for the reliable and efficient numerical evaluation of the Landau operator.
Software

◊ Preprint
S. Blanes, F. Casas, C. González, M. Thalhammer
Splitting methods with complex coefficients for linear and nonlinear evolution equations.

◊ Preprint (in didactics)
J. Hafele, M. Thalhammer
Darstellung und Analyse der Ergebnisse einer Umfrage zu elementaren mathematischen Themen. Welche Erkenntnisse können daraus für unseren eigenen Schulunterricht folgen?
Depiction and analysis of the results drawn from a survey on elementary mathematical subjects. Which findings might follow for our own school teaching?

Publications (Proceedings)

◊ Proceeding 1
A. Ostermann, M. Thalhammer
Positivity of exponential multistep methods.
In: A. Bermudez et al., Numerical Mathematics and Advanced Applications. ENUMATH 2005. Springer, Berlin, 2006.

◊ Proceeding 2
W. Fellin, M. Mergili, A. Ostermann, K. Schratz, M. Thalhammer
An Open Source model for the simulation of granular flows: First results with GRASS GIS and needs for further investigations.
Academic Proceedings of the 2008 Free and Open Source Software for Geospatial (FOSS4G) Conference, Sept. 29 – Oct. 3, Cape Town, South Africa, 231–238.

◊ Proceeding 3
W. Auzinger, O. Koch, M. Thalhammer
Representation of the local error for higher-order exponential splitting schemes involving two or three sub-operators.
AIP Conf. Proc. 1648, 150003 (2015), http://dx.doi.org/10.1063/1.4912433.

◊ Proceeding 4 (preliminary version)
W. Auzinger, W. Herfort, O. Koch, M. Thalhammer
The BCH-formula and order conditions for splitting methods.
In: Lie Groups, Differential Equations, and Geometry, G. Falcone (editor), Springer 2017, p. 71–83.

Theses

◊ Habilitation thesis (2006)
Time Integration of Differential Equations.
Kolloquium

◊ Doctoral thesis (2000)
Runge-Kutta Time Discretization of Fully Nonlinear Parabolic Problems.