Doctoral AbstractThesis
Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition
- Supervisor
- Professor Dr. Mario Ohlberger
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
Publications
- Singh, A, Thale, S, Leibner, T, Lamparter, L, Ricker, A, Nüsse, H, Klingauf, J, Galic, M, Ohlberger, M, and Matis, M. . “Dynamic interplay of microtubule and actomyosin forces drive tissue extension.” Nature Communications 15 (1): 3198–3198. doi: 10.1038/s41467-024-47596-8.
- Leibner, Tobias. . “Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition.” Dissertation thesis, Universität Münster.
- Singh, A, Thale, S, Leibner, T, Ricker, A, Nüsse, H, Klingauf, J, Ohlberger, M, and Matis, M. . “Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.” eLife 2022. doi: 10.1101/2022.06.21.496930.
- Leibner, T, and Ohlberger, M. . “A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations.” ESAIM: Mathematical Modelling and Numerical Analysis 55: 2567–2608.. doi: 10.1051/m2an/2021065.
- Leibner, T, Matis, M, Ohlberger, M, and Rave, S. . “Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.” arXiv [math.NA] 2111.00129.
- Schneider, Florian Leibner Tobias. . “First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory.” Journal of Computational Physics 416: 109547.. doi: 10.1016/j.jcp.2020.109547.
- Schneider, Florian Leibner Tobias. . “First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis.” arXiv 2019.
- Himpe, C, Leibner, T, and Rave, S. . “Hierarchical Approximate Proper Orthogonal Decomposition.” SIAM Journal on Scientific Computing 40 (5): A3267–A3292.
- Himpe, C, Leibner, T, and Rave, S. . “HAPOD - Fast, Simple and Reliable Distributed POD Computation.” in Vol. 55 of ARGESIM Report doi: 10.11128/arep.55.a55283.
- Leibner, T, Milk, R, and Schindler, F. . “Extending DUNE: The dune-xt modules.” Archive of Numerical Software 5 (1): 193–216. doi: 10.11588/ans.2017.1.27720.
- Himpe, C, Leibner, T, Rave, S, and Saak, J. . “Fast Low-Rank Empirical Cross Gramians.” PAMM 17 (1): 841–842. doi: 10.1002/pamm.201710388.
- Brunken, Julia, Leibner, Tobias, Ohlberger, Mario, and Smetana, Kathrin. . “Problem adapted hierachical model reduction for the Fokker-Planck equation.” in ALGORITMY 2016 Proceedings of contributed papers and posters, edited by Angela Handlovicova and Daniel Sevcovic. Bratislava: Publishing House of Slovak University of Technology.
- Leibner, Tobias. . Numerical methods for kinetic equations (Master's thesis)