Involved researchers:

Othmar Koch (PI, University of Vienna)

Karsten Held (Co-PI, Vienna University of Technology)

Karolina Kropielnicka (International collaborator, University of Gdansk)

Christian Lubich (International collaborator, University of Tübingen)

Winfried Auzinger (National collaborator, Vienna University of Technology)

Mechthild Thalhammer (National collaborator, University of Innsbruck).

So far, the project yielded the following articles and preprints and conference presentations.

- H. Hofstätter and O. Koch,
*Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four*, Numer. Math.141(2019), pp. 681-691.

You can download a preprint of this paper from https://arxiv.org/abs/1709.08473

- W. Auzinger,
H. Hofstätter, O. Koch, M. Quell, and M. Thalhammer,
*A posteriori error estimation for Magnus-type integrators*, M2AN - Math. Model. Numer. Anal. 53(2019), pp. 197-218. DOI=https://doi.org/10.1051/m2an/2018050

You can download a reprint of this paper as a .pdf file. The original publication is available at www.esaim-m2an.org, the copyright is owned by EDP Sciences. You can download an extended preprint of this paper as a .pdf file.

- W. Auzinger and O. Koch,
*An improved local error estimator for symmetric time-stepping schemes*, Appl. Math. Lett. 82(2018), pp.106-110.

Archived at https://uscholar.univie.ac.at/.

- W. Auzinger,
H. Hofstätter, and O. Koch,
*Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations*, J. Comput. Appl. Math. 234(2019), pp. 195-201. Available online from https://doi.org/10.1016/j.cam.2019.02.011.

You can download a preprint of this paper from https://arxiv.org/abs/1806.07771

- W. Auzinger,
T. Jawecki,
and O. Koch,
*Computable upper bounds for Krylov approximations to matrix exponentials and associated φ-functions*, BIT 60(2020), 157-197. DOI=10.1007/s10543-019-00771-6.

You can download a preprint of this paper from https://arxiv.org/abs/1809.03369

- H. Hofstätter,
*Order conditions for exponential integrators*, submitted.

You can download a preprint of this paper from https://arxiv.org/abs/1902.11256

- W. Auzinger,
H. Hofstätter, and O. Koch,
*An algorithm for computing coefficients of words in expressions involving exponentials and its application to the construction of exponential integrators*, Springer Lecture Notes in Computer Science 11661 (2019), pp. 197-214.

You can download a preprint of this paper from https://arxiv.org/abs/1912.01399v1.

- W. Auzinger, J. Dubois,
K. Held,
H. Hofstätter,
T. Jawecki,
A. Kauch,
K. Kropielnicka, O. Koch,
P. Singh, and
C. Watzenböck,
*Efficient Magnus-type integrators for Hubbard models of solar cells*, submitted.

- M. Innerberger, P. Worm, P. Prauhart, and
A. Kauch,
*Electron-light interaction in nonequilibrium - exact diagonaliation for time dependent Hubbard Hamiltonians*, submitted.

You can download a preprint of this paper from https://arxiv.org/abs/2005.13498.

- T. Schäfer, N. Wentzell, F. Simkovic IV, Y.-Y. He, C. Hille, M. Klett, C. J. Eckhardt, B. Arzhang,
V. Harkov, F.-M. Le Regent, A. Kirsch, Y. Wang, A. J. Kim, E. Kozik, E. A. Stepanov,
A. Kauch,
S. Andergassen,
P. Hansmann, D. Rohe, Y. M. Vilk, J. P. F. LeBlanc, S. Zhang, A.-M. S. Tremblay, M. Ferrero, O. Parcollet, and A. Georges,
*Tracking the Footprints of Spin Fluctuations: A Multi-Method, Multi-Messenger Study of the Two-Dimensional Hubbard Model*, submitted.

You can download a preprint of this paper from https://arxiv.org/abs/2006.10769.

- A. Kauch,
P. Worm, P. Prauhart, M. Innerberger, C. Watzenböck, and
K. Held,
*Enhancement of impact ionization in Hubbard clusters by disorder and next-nearest-neighbor hopping*, submitted.

You can download a preprint of this paper from https://arxiv.org/abs/2006.10769.

- W. Auzinger,
H. Hofstätter,
O. Koch, and
M. Quell,
*Adaptive time propagation for time-dependent Schrödinger equations*, to appear in Int. J. Appl. Comput. Math.. DOI: 10.1007/s40819-020-00937-9

**Oral Presentations**

- H. Hofstätter,
*Order conditions for exponential integrators*, 14th Austrian Numerical Analysis Day 2018, Klagenfurt, May 2018. Joint with W. Auzinger and O. Koch.

- T. Jawecki,
*A computable strict upper bound for Krylov subspace approximations to the exponential of skew-Hermitian matrices*, 14th Austrian Numerical Analysis Day 2018, Klagenfurt, May 2018. Joint with W. Auzinger and O. Koch.

- W. Auzinger (invited talk),
*Sharp a posteriori error estimation for symmetric one-step integrators*, International Conference on Modern Problems of Mechanics and Mathematics, Lviv, Ukraine, May 2018. Joint with H. Hofstätter and O. Koch.

- W. Auzinger (invited talk),
*Sharp local error estimation for time-reversible one-step schemes*, Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with H. Hofstätter and O. Koch.

- H. Hofstätter,
*Order conditions for exponential integrators*, poster presentation at the Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with W. Auzinger and O. Koch.

- T. Jawecki,
*A computable strict upper bound for Krylov subspace approximations to the exponential of skew-Hermitian matrices*, poster presentation at the Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with W. Auzinger and O. Koch. Also supported by Doctoral Program TU-D.

You can download this poster as a .pdf file.

- O. Koch,
*Adaptive Magnus-type integrators for the simulation of solar cells*, ICNAAM 2018, Rhodes, Greece. Joint with W. Auzinger, H. Hofstätter, M. Quell, and M. Thalhammer.

You can view the abstract of this talk here.

- O. Koch,
*Adaptive exponential methods*, SciCADE 2019 - Conference on Scientific Computing and Differential Equations, Innsbruck, July 2019. Joint with W. Auzinger, H. Hofstätter, T. Jawecki, K. Kropielnicka, and P. Singh.

You can view the abstract of this talk here.

- T. Jawecki,
*Computable upper error bounds for Krylov subspace approximations to matrix exponentials*, SciCADE 2019, International Conference on Scientific Computation and Differential Equations, Innsbruck, July 2019. Joint with W. Auzinger, and O. Koch.

- H. Hofstätter,
*An algorithm for computing coefficients of words in expressions envolving exponentials and its application to the construction of exponential integrators*, 21st International Workshop on Computer Algebra in Scientific Computing, Moskow, Russia, August 2019. Joint with W. Auzinger, O. Koch.

page written by Othmar Koch.last modification: Fri Nov 27 10:00 MET 2020 |