[{"user_id":"85279","department":[{"_id":"636"}],"_id":"19945","language":[{"iso":"eng"}],"extern":"1","article_type":"original","type":"journal_article","publication":"Journal of Computational Dynamics","status":"public","abstract":[{"text":"Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected to conservation properties and other geometric features of solutions to the PDE and, therefore, of great interest for numerical integration. For the example of Burgers' equations and related PDEs we use Clebsch variables to lift the original system to a collective Hamiltonian system on a symplectic manifold whose structure is related to the original Lie-Poisson structure. On the collective Hamiltonian system a symplectic integrator can be applied. Our numerical examples show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be outweighed by the advantage of symplectic integration.","lang":"eng"}],"author":[{"full_name":"McLachlan, Robert I","last_name":"McLachlan","first_name":"Robert I"},{"orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","id":"85279","full_name":"Offen, Christian","first_name":"Christian"},{"full_name":"Tapley, Benjamin K","last_name":"Tapley","first_name":"Benjamin K"}],"date_created":"2020-10-06T16:44:07Z","volume":6,"publisher":"American Institute of Mathematical Sciences (AIMS)","date_updated":"2022-01-06T06:54:15Z","oa":"1","main_file_link":[{"url":"http://www.aimsciences.org/article/doi/10.3934/jcd.2019005","open_access":"1"}],"doi":"10.3934/jcd.2019005","title":"Symplectic integration of PDEs using Clebsch variables","issue":"1","publication_identifier":{"issn":["2158-2505"]},"citation":{"bibtex":"@article{McLachlan_Offen_Tapley_2019, title={Symplectic integration of PDEs using Clebsch variables}, volume={6}, DOI={<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>}, number={1}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={McLachlan, Robert I and Offen, Christian and Tapley, Benjamin K}, year={2019}, pages={111–130} }","mla":"McLachlan, Robert I., et al. “Symplectic Integration of PDEs Using Clebsch Variables.” <i>Journal of Computational Dynamics</i>, vol. 6, no. 1, American Institute of Mathematical Sciences (AIMS), 2019, pp. 111–30, doi:<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>.","short":"R.I. McLachlan, C. Offen, B.K. Tapley, Journal of Computational Dynamics 6 (2019) 111–130.","apa":"McLachlan, R. I., Offen, C., &#38; Tapley, B. K. (2019). Symplectic integration of PDEs using Clebsch variables. <i>Journal of Computational Dynamics</i>, <i>6</i>(1), 111–130. <a href=\"https://doi.org/10.3934/jcd.2019005\">https://doi.org/10.3934/jcd.2019005</a>","ama":"McLachlan RI, Offen C, Tapley BK. Symplectic integration of PDEs using Clebsch variables. <i>Journal of Computational Dynamics</i>. 2019;6(1):111-130. doi:<a href=\"https://doi.org/10.3934/jcd.2019005\">10.3934/jcd.2019005</a>","ieee":"R. I. McLachlan, C. Offen, and B. K. Tapley, “Symplectic integration of PDEs using Clebsch variables,” <i>Journal of Computational Dynamics</i>, vol. 6, no. 1, pp. 111–130, 2019.","chicago":"McLachlan, Robert I, Christian Offen, and Benjamin K Tapley. “Symplectic Integration of PDEs Using Clebsch Variables.” <i>Journal of Computational Dynamics</i> 6, no. 1 (2019): 111–30. <a href=\"https://doi.org/10.3934/jcd.2019005\">https://doi.org/10.3934/jcd.2019005</a>."},"intvolume":"         6","page":"111-130","year":"2019"},{"publication":"The Journal of Chemical Physics","type":"journal_article","status":"public","department":[{"_id":"101"}],"user_id":"81513","_id":"21944","extern":"1","language":[{"iso":"eng"}],"article_number":"044116","publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","citation":{"bibtex":"@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular systems by spectral matching}, DOI={<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>}, number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }","mla":"Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 044116, 2019, doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>.","short":"F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).","apa":"Nüske, F., Boninsegna, L., &#38; Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>","chicago":"Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 2019. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>.","ieee":"F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” <i>The Journal of Chemical Physics</i>, 2019.","ama":"Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. 2019. doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>"},"year":"2019","date_created":"2021-04-30T17:01:13Z","author":[{"id":"81513","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","first_name":"Feliks"},{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"date_updated":"2022-01-06T06:55:20Z","doi":"10.1063/1.5100131","title":"Coarse-graining molecular systems by spectral matching"},{"status":"public","publication":"Nonlinear Dynamics","type":"journal_article","language":[{"iso":"eng"}],"_id":"16709","department":[{"_id":"101"}],"user_id":"47427","year":"2019","citation":{"apa":"Sahai, T., Ziessler, A., Klus, S., &#38; Dellnitz, M. (2019). Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>","bibtex":"@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations for the traveling salesman problem}, DOI={<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>}, journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}, year={2019} }","short":"T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).","mla":"Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019, doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>.","ieee":"T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for the traveling salesman problem,” <i>Nonlinear Dynamics</i>, 2019.","chicago":"Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>.","ama":"Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. 2019. doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>"},"publication_identifier":{"issn":["0924-090X","1573-269X"]},"publication_status":"published","title":"Continuous relaxations for the traveling salesman problem","doi":"10.1007/s11071-019-05092-5","date_updated":"2022-01-06T06:52:55Z","date_created":"2020-04-16T14:05:04Z","author":[{"first_name":"Tuhin","last_name":"Sahai","full_name":"Sahai, Tuhin"},{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}]},{"type":"journal_article","publication":"Automatica","abstract":[{"lang":"eng","text":"We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy."}],"status":"public","_id":"10593","user_id":"47427","department":[{"_id":"101"}],"article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0005-1098"]},"year":"2019","citation":{"ieee":"S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system control of PDEs,” <i>Automatica</i>, vol. 106, pp. 184–191, 2019.","chicago":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i> 106 (2019): 184–91. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>.","ama":"Peitz S, Klus S. Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>. 2019;106:184-191. doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>","apa":"Peitz, S., &#38; Klus, S. (2019). Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>, <i>106</i>, 184–191. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>","mla":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i>, vol. 106, 2019, pp. 184–91, doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>.","bibtex":"@article{Peitz_Klus_2019, title={Koopman operator-based model reduction for switched-system control of PDEs}, volume={106}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>}, journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019}, pages={184–191} }","short":"S. Peitz, S. Klus, Automatica 106 (2019) 184–191."},"page":"184-191","intvolume":"       106","date_updated":"2022-01-06T06:50:46Z","date_created":"2019-07-10T08:08:16Z","author":[{"last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"full_name":"Klus, Stefan","last_name":"Klus","first_name":"Stefan"}],"volume":106,"title":"Koopman operator-based model reduction for switched-system control of PDEs","doi":"10.1016/j.automatica.2019.05.016"},{"abstract":[{"lang":"eng","text":"In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set."}],"publication":"Journal of Global Optimization","language":[{"iso":"eng"}],"year":"2019","issue":"4","title":"On the hierarchical structure of Pareto critical sets","date_created":"2019-07-10T08:13:31Z","status":"public","type":"journal_article","article_type":"original","_id":"10595","department":[{"_id":"101"}],"user_id":"47427","intvolume":"        73","page":"891-913","citation":{"bibtex":"@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure of Pareto critical sets}, volume={73}, DOI={<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>}, number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }","mla":"Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i>, vol. 73, no. 4, 2019, pp. 891–913, doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>.","short":"B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019) 891–913.","apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2019). On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>, <i>73</i>(4), 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>","ama":"Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>. 2019;73(4):891-913. doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i> 73, no. 4 (2019): 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>.","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto critical sets,” <i>Journal of Global Optimization</i>, vol. 73, no. 4, pp. 891–913, 2019."},"publication_identifier":{"issn":["0925-5001","1573-2916"]},"publication_status":"published","doi":"10.1007/s10898-019-00737-6","date_updated":"2022-01-06T06:50:46Z","volume":73,"author":[{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"full_name":"Peitz, Sebastian","id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}]},{"status":"public","abstract":[{"text":"In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models.","lang":"eng"}],"type":"conference","publication":"2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)","language":[{"iso":"eng"}],"user_id":"47427","department":[{"_id":"101"}],"_id":"10597","citation":{"ama":"Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In: <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. ; 2019. doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>","ieee":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification,” in <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019.","chicago":"Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>.","apa":"Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., &#38; Dellnitz, M. (2019). Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>","bibtex":"@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}, DOI={<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>}, booktitle={2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019} }","mla":"Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019, doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>.","short":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019."},"year":"2019","publication_status":"published","publication_identifier":{"isbn":["9781538694145"]},"doi":"10.1109/precede.2019.8753313","title":"Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification","author":[{"first_name":"Soren","full_name":"Hanke, Soren","last_name":"Hanke"},{"full_name":"Peitz, Sebastian","id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"last_name":"Wallscheid","full_name":"Wallscheid, Oliver","first_name":"Oliver"},{"last_name":"Böcker","full_name":"Böcker, Joachim","first_name":"Joachim"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"date_created":"2019-07-10T08:15:23Z","date_updated":"2022-01-06T06:50:46Z"},{"_id":"29867","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"conference","status":"public","date_updated":"2023-11-08T08:09:01Z","author":[{"first_name":"Tim","full_name":"Faulwasser, Tim","last_name":"Faulwasser"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, K.","first_name":"K."},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"}],"date_created":"2022-02-17T07:23:52Z","volume":"52(16)","title":"Towards velocity turnpikes in optimal control of mechanical systems","year":"2019","citation":{"short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine (Ed.), 2019, pp. 490–495.","bibtex":"@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Towards velocity turnpikes in optimal control of mechanical systems}, volume={52(16)}, author={Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, Karl}, editor={IFAC-PapersOnLine}, year={2019}, pages={490–495} }","mla":"Faulwasser, Tim, et al. <i>Towards Velocity Turnpikes in Optimal Control of Mechanical Systems</i>. Edited by IFAC-PapersOnLine, vol. 52(16), 2019, pp. 490–95.","apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2019). <i>Towards velocity turnpikes in optimal control of mechanical systems: Vol. 52(16)</i> (IFAC-PapersOnLine, Ed.; pp. 490–495).","ieee":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Towards velocity turnpikes in optimal control of mechanical systems,” 2019, vol. 52(16), pp. 490–495.","chicago":"Faulwasser, Tim, K. Flaßkamp, Sina Ober-Blöbaum, and Karl Worthmann. “Towards Velocity Turnpikes in Optimal Control of Mechanical Systems.” edited by IFAC-PapersOnLine, 52(16):490–95, 2019.","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. Towards velocity turnpikes in optimal control of mechanical systems. In: IFAC-PapersOnLine, ed. Vol 52(16). ; 2019:490-495."},"page":"490-495","corporate_editor":["IFAC-PapersOnLine"]},{"main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/18M1204395"}],"doi":"10.1137/18m1204395","title":"The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques","author":[{"last_name":"Ziessler","full_name":"Ziessler, Adrian","first_name":"Adrian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Gerlach","id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael"}],"date_created":"2020-04-16T14:04:20Z","volume":18,"date_updated":"2023-11-17T13:13:09Z","citation":{"ama":"Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>. 2019;18(3):1265-1292. doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>","chicago":"Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i> 18, no. 3 (2019): 1265–92. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>.","ieee":"A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, pp. 1265–1292, 2019, doi: <a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","apa":"Ziessler, A., Dellnitz, M., &#38; Gerlach, R. (2019). The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>18</i>(3), 1265–1292. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>","mla":"Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, 2019, pp. 1265–92, doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","bibtex":"@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}, volume={18}, DOI={<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292} }","short":"A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems 18 (2019) 1265–1292."},"intvolume":"        18","page":"1265-1292","year":"2019","issue":"3","publication_status":"published","publication_identifier":{"issn":["1536-0040"]},"language":[{"iso":"eng"}],"user_id":"32655","department":[{"_id":"101"}],"_id":"16708","status":"public","abstract":[{"text":" In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for\r\nthe computation of such objects of finite dimensional systems with the results obtained in the work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis\r\nof partial differential equations and illustrate its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n","lang":"eng"}],"type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems"},{"user_id":"82258","department":[{"_id":"102"}],"_id":"34917","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"type":"journal_article","publication":"International Journal of Number Theory","status":"public","abstract":[{"text":"We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).","lang":"eng"}],"author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer"},{"first_name":"Gabriele","last_name":"Nebe","full_name":"Nebe, Gabriele"}],"date_created":"2022-12-23T11:05:09Z","volume":15,"publisher":"World Scientific Pub Co Pte Lt","date_updated":"2023-12-06T10:05:59Z","doi":"10.1142/s1793042119500131","title":"Quaternary quadratic lattices over number fields","issue":"02","publication_status":"published","publication_identifier":{"issn":["1793-0421","1793-7310"]},"citation":{"ama":"Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>. 2019;15(02):309-325. doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i> 15, no. 02 (2019): 309–25. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>.","ieee":"M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,” <i>International Journal of Number Theory</i>, vol. 15, no. 02, pp. 309–325, 2019, doi: <a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","bibtex":"@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over number fields}, volume={15}, DOI={<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>}, number={02}, journal={International Journal of Number Theory}, publisher={World Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019}, pages={309–325} }","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.","mla":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i>, vol. 15, no. 02, World Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","apa":"Kirschmer, M., &#38; Nebe, G. (2019). Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>, <i>15</i>(02), 309–325. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>"},"intvolume":"        15","page":"309-325","year":"2019"},{"page":"121-134","intvolume":"       197","citation":{"ama":"Kirschmer M. Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>. 2019;197:121-134. doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>","chicago":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i> 197 (2019): 121–34. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>.","ieee":"M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,” <i>Journal of Number Theory</i>, vol. 197, pp. 121–134, 2019, doi: <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","apa":"Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number fields. <i>Journal of Number Theory</i>, <i>197</i>, 121–134. <a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">https://doi.org/10.1016/j.jnt.2018.08.004</a>","bibtex":"@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices over number fields}, volume={197}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2019}, pages={121–134} }","mla":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” <i>Journal of Number Theory</i>, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:<a href=\"https://doi.org/10.1016/j.jnt.2018.08.004\">10.1016/j.jnt.2018.08.004</a>.","short":"M. Kirschmer, Journal of Number Theory 197 (2019) 121–134."},"year":"2019","publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","doi":"10.1016/j.jnt.2018.08.004","title":"Automorphisms of even unimodular lattices over number fields","volume":197,"author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"}],"date_created":"2022-12-23T11:04:34Z","publisher":"Elsevier BV","date_updated":"2023-12-06T10:07:17Z","status":"public","abstract":[{"text":"We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.","lang":"eng"}],"publication":"Journal of Number Theory","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"user_id":"82258","_id":"34916"},{"publication_identifier":{"issn":["0029-599X","0945-3245"]},"publication_status":"published","issue":"4","year":"2019","page":"797-853","intvolume":"       143","citation":{"mla":"Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 143, no. 4, Springer Science and Business Media LLC, 2019, pp. 797–853, doi:<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>.","bibtex":"@article{Kovács_Li_Lubich_2019, title={A convergent evolving finite element algorithm for mean curvature flow of closed surfaces}, volume={143}, DOI={<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2019}, pages={797–853} }","short":"B. Kovács, B. Li, C. Lubich, Numerische Mathematik 143 (2019) 797–853.","apa":"Kovács, B., Li, B., &#38; Lubich, C. (2019). A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>, <i>143</i>(4), 797–853. <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">https://doi.org/10.1007/s00211-019-01074-2</a>","chicago":"Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” <i>Numerische Mathematik</i> 143, no. 4 (2019): 797–853. <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">https://doi.org/10.1007/s00211-019-01074-2</a>.","ieee":"B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm for mean curvature flow of closed surfaces,” <i>Numerische Mathematik</i>, vol. 143, no. 4, pp. 797–853, 2019, doi: <a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>.","ama":"Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>. 2019;143(4):797-853. doi:<a href=\"https://doi.org/10.1007/s00211-019-01074-2\">10.1007/s00211-019-01074-2</a>"},"date_updated":"2024-04-03T09:21:40Z","publisher":"Springer Science and Business Media LLC","volume":143,"date_created":"2023-07-10T11:40:56Z","author":[{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"},{"last_name":"Li","full_name":"Li, Buyang","first_name":"Buyang"},{"first_name":"Christian","full_name":"Lubich, Christian","last_name":"Lubich"}],"title":"A convergent evolving finite element algorithm for mean curvature flow of closed surfaces","doi":"10.1007/s00211-019-01074-2","publication":"Numerische Mathematik","type":"journal_article","status":"public","_id":"45948","department":[{"_id":"841"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics"],"language":[{"iso":"eng"}]},{"extern":"1","language":[{"iso":"eng"}],"_id":"55284","department":[{"_id":"102"}],"user_id":"106108","status":"public","publication":"Mathematika","type":"journal_article","title":"The maximal order of iterated multiplicative functions","doi":"10.1112/S0025579319000214","date_updated":"2024-07-24T07:25:42Z","volume":64,"author":[{"first_name":"Ch.","full_name":"Elsholtz, Ch.","last_name":"Elsholtz"},{"orcid":"0000-0001-9650-2459","last_name":"Technau","id":"106108","full_name":"Technau, Marc","first_name":"Marc"},{"full_name":"Technau, N.","last_name":"Technau","first_name":"N."}],"date_created":"2024-07-16T11:09:02Z","year":"2019","intvolume":"        64","page":"990–1009","citation":{"apa":"Elsholtz, Ch., Technau, M., &#38; Technau, N. (2019). The maximal order of iterated multiplicative functions. <i>Mathematika</i>, <i>64</i>(4), 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>","mla":"Elsholtz, Ch., et al. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i>, vol. 64, no. 4, 2019, pp. 990–1009, doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","short":"Ch. Elsholtz, M. Technau, N. Technau, Mathematika 64 (2019) 990–1009.","bibtex":"@article{Elsholtz_Technau_Technau_2019, title={The maximal order of iterated multiplicative functions}, volume={64}, DOI={<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>}, number={4}, journal={Mathematika}, author={Elsholtz, Ch. and Technau, Marc and Technau, N.}, year={2019}, pages={990–1009} }","ieee":"Ch. Elsholtz, M. Technau, and N. Technau, “The maximal order of iterated multiplicative functions,” <i>Mathematika</i>, vol. 64, no. 4, pp. 990–1009, 2019, doi: <a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","chicago":"Elsholtz, Ch., Marc Technau, and N. Technau. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i> 64, no. 4 (2019): 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>.","ama":"Elsholtz Ch, Technau M, Technau N. The maximal order of iterated multiplicative functions. <i>Mathematika</i>. 2019;64(4):990–1009. doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>"},"issue":"4"},{"language":[{"iso":"eng"}],"extern":"1","user_id":"106108","department":[{"_id":"102"}],"_id":"55285","status":"public","type":"journal_article","publication":"Notes Number Theory Discrete Math.","doi":"10.7546/nntdm.2019.25.2.127-135","title":"Generalised Beatty sets","date_created":"2024-07-16T11:09:02Z","author":[{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108"}],"volume":25,"date_updated":"2024-07-24T07:25:59Z","citation":{"mla":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, 2019, pp. 127–135, doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>.","bibtex":"@article{Technau_2019, title={Generalised Beatty sets}, volume={25}, DOI={<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>}, number={2}, journal={Notes Number Theory Discrete Math.}, author={Technau, Marc}, year={2019}, pages={127–135} }","short":"M. Technau, Notes Number Theory Discrete Math. 25 (2019) 127–135.","apa":"Technau, M. (2019). Generalised Beatty sets. <i>Notes Number Theory Discrete Math.</i>, <i>25</i>(2), 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>","ama":"Technau M. Generalised Beatty sets. <i>Notes Number Theory Discrete Math</i>. 2019;25(2):127–135. doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>","chicago":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i> 25, no. 2 (2019): 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>.","ieee":"M. Technau, “Generalised Beatty sets,” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, pp. 127–135, 2019, doi: <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>."},"intvolume":"        25","page":"127–135","year":"2019","issue":"2"},{"intvolume":"       113","page":"337-347","citation":{"apa":"Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields. <i>Archiv Der Mathematik</i>, <i>113</i>(4), 337–347. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>","bibtex":"@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices over local fields}, volume={113}, DOI={<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>}, number={4}, journal={Archiv der Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kirschmer, Markus}, year={2019}, pages={337–347} }","short":"M. Kirschmer, Archiv Der Mathematik 113 (2019) 337–347.","mla":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i>, vol. 113, no. 4, Springer Science and Business Media LLC, 2019, pp. 337–47, doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>.","ama":"Kirschmer M. Determinant groups of Hermitian lattices over local fields. <i>Archiv der Mathematik</i>. 2019;113(4):337-347. doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>","chicago":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i> 113, no. 4 (2019): 337–47. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>.","ieee":"M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,” <i>Archiv der Mathematik</i>, vol. 113, no. 4, pp. 337–347, 2019, doi: <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>."},"publication_identifier":{"issn":["0003-889X","1420-8938"]},"publication_status":"published","doi":"10.1007/s00013-019-01348-z","date_updated":"2023-04-04T09:05:04Z","volume":113,"author":[{"last_name":"Kirschmer","id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus"}],"status":"public","type":"journal_article","_id":"34915","department":[{"_id":"102"}],"user_id":"93826","year":"2019","issue":"4","title":"Determinant groups of Hermitian lattices over local fields","publisher":"Springer Science and Business Media LLC","date_created":"2022-12-23T11:03:41Z","abstract":[{"lang":"eng","text":"We describe the determinants of the automorphism groups of Hermitian lattices over local fields. Using a result of G. Shimura, this yields an explicit method to compute the special genera in a given genus of Hermitian lattices over a number field."}],"publication":"Archiv der Mathematik","keyword":["General Mathematics"],"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"external_id":{"arxiv":["1703.02456"]},"abstract":[{"lang":"eng","text":"We address the general mathematical problem of computing the inverse p-th\r\nroot of a given matrix in an efficient way. A new method to construct iteration\r\nfunctions that allow calculating arbitrary p-th roots and their inverses of\r\nsymmetric positive definite matrices is presented. We show that the order of\r\nconvergence is at least quadratic and that adaptively adjusting a parameter q\r\nalways leads to an even faster convergence. In this way, a better performance\r\nthan with previously known iteration schemes is achieved. The efficiency of the\r\niterative functions is demonstrated for various matrices with different\r\ndensities, condition numbers and spectral radii."}],"publication":"Communications in Computational Physics","title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","publisher":"Global Science Press","date_created":"2017-07-25T14:48:26Z","year":"2019","quality_controlled":"1","issue":"2","project":[{"name":"Performance and Efficiency in HPC with Custom Computing","_id":"32","grant_number":"PL 595/2-1 / 320898746"},{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"21","user_id":"15278","department":[{"_id":"27"},{"_id":"518"},{"_id":"304"},{"_id":"104"}],"status":"public","type":"journal_article","doi":"10.4208/cicp.OA-2018-0053","date_updated":"2023-09-26T11:45:02Z","author":[{"full_name":"Richters, Dorothee","last_name":"Richters","first_name":"Dorothee"},{"first_name":"Michael","last_name":"Lass","orcid":"0000-0002-5708-7632","full_name":"Lass, Michael","id":"24135"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"},{"last_name":"Plessl","orcid":"0000-0001-5728-9982","id":"16153","full_name":"Plessl, Christian","first_name":"Christian"},{"first_name":"Thomas","full_name":"Kühne, Thomas","id":"49079","last_name":"Kühne"}],"volume":25,"citation":{"apa":"Richters, D., Lass, M., Walther, A., Plessl, C., &#38; Kühne, T. (2019). A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. <i>Communications in Computational Physics</i>, <i>25</i>(2), 564–585. <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">https://doi.org/10.4208/cicp.OA-2018-0053</a>","mla":"Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” <i>Communications in Computational Physics</i>, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>.","short":"D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics 25 (2019) 564–585.","bibtex":"@article{Richters_Lass_Walther_Plessl_Kühne_2019, title={A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}, volume={25}, DOI={<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>}, number={2}, journal={Communications in Computational Physics}, publisher={Global Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}, year={2019}, pages={564–585} }","ama":"Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. <i>Communications in Computational Physics</i>. 2019;25(2):564-585. doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>","ieee":"D. Richters, M. Lass, A. Walther, C. Plessl, and T. Kühne, “A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices,” <i>Communications in Computational Physics</i>, vol. 25, no. 2, pp. 564–585, 2019, doi: <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>.","chicago":"Richters, Dorothee, Michael Lass, Andrea Walther, Christian Plessl, and Thomas Kühne. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” <i>Communications in Computational Physics</i> 25, no. 2 (2019): 564–85. <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">https://doi.org/10.4208/cicp.OA-2018-0053</a>."},"intvolume":"        25","page":"564-585"},{"date_created":"2020-04-16T14:06:21Z","author":[{"first_name":"Raphael","id":"32655","full_name":"Gerlach, Raphael","last_name":"Gerlach"},{"first_name":"Péter","last_name":"Koltai","full_name":"Koltai, Péter"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"date_updated":"2024-09-24T12:09:27Z","oa":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08824"}],"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems","has_accepted_license":"1","citation":{"apa":"Gerlach, R., Koltai, P., &#38; Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. In <i>arXiv:1902.08824</i>.","short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).","mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","bibtex":"@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems}, journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}, year={2019} }","ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. <i>arXiv:190208824</i>. Published online 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems,” <i>arXiv:1902.08824</i>. 2019.","chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019."},"year":"2019","user_id":"32655","department":[{"_id":"101"}],"external_id":{"arxiv":["1902.08824"]},"_id":"16711","language":[{"iso":"eng"}],"ddc":["510"],"type":"preprint","publication":"arXiv:1902.08824","status":"public","abstract":[{"text":"Embedding techniques allow the approximations of finite dimensional\r\nattractors and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and continuation methods. These approximations give a topological\r\none-to-one image of the original set. In order to additionally reveal their\r\ngeometry we use diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation, as well as for the attractor of the Mackey-Glass delay differential\r\nequation.","lang":"eng"}]},{"title":"Arbitrary sensitivity for inverse problems in piezoelectricity","date_updated":"2026-01-05T07:53:43Z","author":[{"last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin","first_name":"Benjamin"},{"full_name":"Schulze, Veronika","last_name":"Schulze","first_name":"Veronika"},{"first_name":"Nadine","full_name":"Feldmann, Nadine","id":"23082","last_name":"Feldmann"},{"orcid":"0000-0002-4393-268X","last_name":"Claes","id":"11829","full_name":"Claes, Leander","first_name":"Leander"}],"date_created":"2019-03-08T13:20:14Z","place":"GAMM Annual Meeting, Wien","year":"2019","citation":{"apa":"Jurgelucks, B., Schulze, V., Feldmann, N., &#38; Claes, L. (2019). <i>Arbitrary sensitivity for inverse problems in piezoelectricity</i>.","mla":"Jurgelucks, Benjamin, et al. <i>Arbitrary Sensitivity for Inverse Problems in Piezoelectricity</i>. 2019.","short":"B. Jurgelucks, V. Schulze, N. Feldmann, L. Claes, Arbitrary Sensitivity for Inverse Problems in Piezoelectricity, GAMM Annual Meeting, Wien, 2019.","bibtex":"@book{Jurgelucks_Schulze_Feldmann_Claes_2019, place={GAMM Annual Meeting, Wien}, title={Arbitrary sensitivity for inverse problems in piezoelectricity}, author={Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes, Leander}, year={2019} }","chicago":"Jurgelucks, Benjamin, Veronika Schulze, Nadine Feldmann, and Leander Claes. <i>Arbitrary Sensitivity for Inverse Problems in Piezoelectricity</i>. GAMM Annual Meeting, Wien, 2019.","ieee":"B. Jurgelucks, V. Schulze, N. Feldmann, and L. Claes, <i>Arbitrary sensitivity for inverse problems in piezoelectricity</i>. GAMM Annual Meeting, Wien, 2019.","ama":"Jurgelucks B, Schulze V, Feldmann N, Claes L. <i>Arbitrary Sensitivity for Inverse Problems in Piezoelectricity</i>.; 2019."},"language":[{"iso":"eng"}],"_id":"8482","project":[{"name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"department":[{"_id":"104"},{"_id":"49"}],"user_id":"11829","status":"public","type":"misc"},{"status":"public","abstract":[{"lang":"eng","text":"A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples. "}],"publication":"Nonlinearity","type":"journal_article","language":[{"iso":"eng"}],"extern":"1","article_type":"original","department":[{"_id":"636"}],"user_id":"85279","_id":"19935","page":"2895-2927","citation":{"apa":"McLachlan, R. I., &#38; Offen, C. (2018). Bifurcation of solutions to Hamiltonian boundary value problems. <i>Nonlinearity</i>, 2895–2927. <a href=\"https://doi.org/10.1088/1361-6544/aab630\">https://doi.org/10.1088/1361-6544/aab630</a>","mla":"McLachlan, Robert I., and Christian Offen. “Bifurcation of Solutions to Hamiltonian Boundary Value Problems.” <i>Nonlinearity</i>, 2018, pp. 2895–927, doi:<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>.","bibtex":"@article{McLachlan_Offen_2018, title={Bifurcation of solutions to Hamiltonian boundary value problems}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>}, journal={Nonlinearity}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={2895–2927} }","short":"R.I. McLachlan, C. Offen, Nonlinearity (2018) 2895–2927.","ama":"McLachlan RI, Offen C. Bifurcation of solutions to Hamiltonian boundary value problems. <i>Nonlinearity</i>. 2018:2895-2927. doi:<a href=\"https://doi.org/10.1088/1361-6544/aab630\">10.1088/1361-6544/aab630</a>","chicago":"McLachlan, Robert I, and Christian Offen. “Bifurcation of Solutions to Hamiltonian Boundary Value Problems.” <i>Nonlinearity</i>, 2018, 2895–2927. <a href=\"https://doi.org/10.1088/1361-6544/aab630\">https://doi.org/10.1088/1361-6544/aab630</a>.","ieee":"R. I. McLachlan and C. Offen, “Bifurcation of solutions to Hamiltonian boundary value problems,” <i>Nonlinearity</i>, pp. 2895–2927, 2018."},"year":"2018","publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","doi":"10.1088/1361-6544/aab630","main_file_link":[{"url":"https://doi.org/10.1088/1361-6544/aab630"}],"title":"Bifurcation of solutions to Hamiltonian boundary value problems","date_created":"2020-10-06T16:28:36Z","author":[{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","first_name":"Christian"}],"date_updated":"2022-01-06T06:54:14Z"},{"citation":{"bibtex":"@article{McLachlan_Offen_2018, title={Symplectic integration of boundary value problems}, DOI={<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>}, journal={Numerical Algorithms}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={1219–1233} }","short":"R.I. McLachlan, C. Offen, Numerical Algorithms (2018) 1219–1233.","mla":"McLachlan, Robert I., and Christian Offen. “Symplectic Integration of Boundary Value Problems.” <i>Numerical Algorithms</i>, 2018, pp. 1219–33, doi:<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>.","apa":"McLachlan, R. I., &#38; Offen, C. (2018). Symplectic integration of boundary value problems. <i>Numerical Algorithms</i>, 1219–1233. <a href=\"https://doi.org/10.1007/s11075-018-0599-7\">https://doi.org/10.1007/s11075-018-0599-7</a>","ama":"McLachlan RI, Offen C. Symplectic integration of boundary value problems. <i>Numerical Algorithms</i>. 2018:1219-1233. doi:<a href=\"https://doi.org/10.1007/s11075-018-0599-7\">10.1007/s11075-018-0599-7</a>","chicago":"McLachlan, Robert I, and Christian Offen. “Symplectic Integration of Boundary Value Problems.” <i>Numerical Algorithms</i>, 2018, 1219–33. <a href=\"https://doi.org/10.1007/s11075-018-0599-7\">https://doi.org/10.1007/s11075-018-0599-7</a>.","ieee":"R. I. McLachlan and C. Offen, “Symplectic integration of boundary value problems,” <i>Numerical Algorithms</i>, pp. 1219–1233, 2018."},"page":"1219-1233","year":"2018","publication_status":"published","publication_identifier":{"issn":["1017-1398","1572-9265"]},"main_file_link":[{"url":"https://rdcu.be/b79ap"}],"doi":"10.1007/s11075-018-0599-7","title":"Symplectic integration of boundary value problems","date_created":"2020-10-06T16:29:14Z","author":[{"full_name":"McLachlan, Robert I","last_name":"McLachlan","first_name":"Robert I"},{"last_name":"Offen","orcid":"https://orcid.org/0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279","first_name":"Christian"}],"date_updated":"2022-01-06T06:54:14Z","status":"public","abstract":[{"lang":"eng","text":"Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical properties. These all refer to {\\em long-time} behaviour. They are directly connected to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under iteration. Boundary value problems, in contrast, are posed for fixed (and often quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is not iterated. Is there any point, therefore, for a symplectic integrator to be used on a Hamiltonian boundary value problem? In this paper we announce results that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not."}],"type":"journal_article","publication":"Numerical Algorithms","extern":"1","language":[{"iso":"eng"}],"article_type":"original","user_id":"85279","department":[{"_id":"636"}],"_id":"19937"},{"_id":"21634","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:1804.00854","abstract":[{"lang":"eng","text":"Predictive control of power electronic systems always requires a suitable\r\nmodel of the plant. Using typical physics-based white box models, a trade-off\r\nbetween model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This is a challenging task with a lot of constraints, since the model\r\norder is directly linked to the number of system states. Even though white-box\r\nmodels show suitable performance in most cases, parasitic real-world effects\r\noften cannot be modeled satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based model reduction technique is presented which\r\ndirectly links the control action to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear but infinite-dimensional operator\r\ndescribing the dynamics of observables of nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching principle of power\r\nelectronic devices. Following this data-driven approach, the model order and\r\nthe number of system states are decoupled which allows us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility\r\nof the proposed modeling technique in a finite-set model predictive control\r\napplication."}],"status":"public","oa":"1","date_updated":"2022-01-06T06:55:08Z","date_created":"2021-04-19T16:17:30Z","author":[{"full_name":"Hanke, Sören","last_name":"Hanke","first_name":"Sören"},{"id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Wallscheid","full_name":"Wallscheid, Oliver","first_name":"Oliver"},{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"first_name":"Joachim","full_name":"Böcker, Joachim","last_name":"Böcker"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"title":"Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives","main_file_link":[{"url":"https://arxiv.org/pdf/1804.00854.pdf","open_access":"1"}],"year":"2018","citation":{"bibtex":"@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives}, journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018} }","short":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854 (2018).","mla":"Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018.","apa":"Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., &#38; Dellnitz, M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>ArXiv:1804.00854</i>.","ama":"Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>arXiv:180400854</i>. 2018.","chicago":"Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018.","ieee":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives,” <i>arXiv:1804.00854</i>. 2018."}}]