[{"author":[{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"date_created":"2019-07-10T08:12:22Z","oa":"1","date_updated":"2022-01-06T06:50:46Z","doi":"10.17619/UNIPB/1-176","main_file_link":[{"open_access":"1","url":"https://d-nb.info/1139356542/34"}],"title":" \tExploiting structure in multiobjective optimization and optimal control","has_accepted_license":"1","publication_status":"published","citation":{"chicago":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>, 2017. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>.","ieee":"S. Peitz, <i>  Exploiting structure in multiobjective optimization and optimal control</i>. 2017.","ama":"Peitz S. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>.; 2017. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>","apa":"Peitz, S. (2017). <i>  Exploiting structure in multiobjective optimization and optimal control</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>","mla":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>. 2017, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>.","bibtex":"@book{Peitz_2017, title={  Exploiting structure in multiobjective optimization and optimal control}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>}, author={Peitz, Sebastian}, year={2017} }","short":"S. Peitz,   Exploiting Structure in Multiobjective Optimization and Optimal Control, 2017."},"year":"2017","department":[{"_id":"101"}],"user_id":"47427","_id":"10594","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"language":[{"iso":"eng"}],"file_date_updated":"2020-03-13T12:52:50Z","ddc":["510"],"type":"dissertation","status":"public","file":[{"file_name":"Dissertation_Peitz.pdf","access_level":"closed","file_id":"16298","file_size":16636801,"date_created":"2020-03-13T12:52:50Z","creator":"speitz","date_updated":"2020-03-13T12:52:50Z","relation":"main_file","success":1,"content_type":"application/pdf"}],"abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute\r\nthe set of optimal compromises (the Pareto set) between the conflicting objectives.\r\n\r\nSince – in contrast to the solution of a single objective optimization problem – the\r\nPareto set generally consists of an infinite number of solutions, the computational\r\neffort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives\r\nare costly to evaluate. Consequently, this thesis is devoted to the identification and\r\nexploitation of structure both in the Pareto set and the dynamics of the underlying\r\nmodel as well as to the development of efficient algorithms for solving problems with\r\nadditional parameters, with a high number of objectives or with PDE-constraints.\r\nThese three challenges are addressed in three respective parts.\r\n\r\nIn the first part, predictor-corrector methods are extended to entire Pareto sets.\r\nWhen certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent\r\nspace can be approximated numerically which yields a direction for the predictor\r\nstep. In the corrector step, the predicted set converges to the Pareto set at a new\r\nparameter value. The resulting algorithm is applied to an example from autonomous\r\ndriving.\r\n\r\nIn the second part, the hierarchical structure of Pareto sets is investigated. When\r\nconsidering a subset of the objectives, the resulting solution is a subset of the Pareto\r\nset of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This\r\nway, the “skeleton” of a Pareto set can be computed and due to the exponential\r\nincrease in computing time with the number of objectives, the computations of\r\nthese subsets are significantly faster which is demonstrated using an example from\r\nindustrial laundries.\r\n\r\nIn the third part, PDE-constrained multiobjective optimal control problems are\r\naddressed by reduced order modeling methods. Reduced order models exploit the\r\nstructure in the system dynamics, for example by describing the dynamics of only the\r\nmost energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of\r\nalgorithms. Both scalarization and set-oriented approaches are coupled with reduced\r\norder modeling. Convergence results are presented and the numerical benefit is\r\ninvestigated. The algorithms are applied to semi-linear heat flow problems as well\r\nas to the Navier-Stokes equations.\r\n","lang":"eng"}]},{"article_type":"original","language":[{"iso":"eng"}],"_id":"8756","user_id":"15694","department":[{"_id":"101"}],"abstract":[{"text":"We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)","title":"A multiobjective MPC approach for autonomously driven electric vehicles","doi":"10.1016/j.ifacol.2017.08.1526","conference":{"end_date":"2017-07-14","start_date":"2017-07-09"},"date_updated":"2022-01-21T13:58:41Z","date_created":"2019-03-29T13:32:46Z","author":[{"last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"full_name":"Schäfer, Kai","last_name":"Schäfer","first_name":"Kai"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Julian","full_name":"Eckstein, Julian","last_name":"Eckstein"},{"first_name":"Ulrich","full_name":"Köhler, Ulrich","last_name":"Köhler"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"volume":50,"year":"2017","citation":{"short":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz, Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC) 50 (2017) 8674–8679.","mla":"Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, vol. 50, no. 1, 2017, pp. 8674–79, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>.","bibtex":"@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A multiobjective MPC approach for autonomously driven electric vehicles}, volume={50}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>}, number={1}, journal={Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017}, pages={8674–8679} }","apa":"Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., &#38; Dellnitz, M. (2017). A multiobjective MPC approach for autonomously driven electric vehicles. <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, <i>50</i>(1), 8674–8679. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>","ama":"Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A multiobjective MPC approach for autonomously driven electric vehicles. <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>. 2017;50(1):8674-8679. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>","ieee":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A multiobjective MPC approach for autonomously driven electric vehicles,” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i>, vol. 50, no. 1, pp. 8674–8679, 2017, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>.","chicago":"Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles.” <i>Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)</i> 50, no. 1 (2017): 8674–79. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>."},"intvolume":"        50","page":"8674-8679","publication_status":"published","publication_identifier":{"issn":["2405-8963"]},"issue":"1"},{"_id":"29430","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"conference","publication":"ECCOMAS Thematic Conference on Multibody Dynamics","status":"public","date_updated":"2022-01-21T14:00:25Z","author":[{"full_name":"Gail, T.","last_name":"Gail","first_name":"T."},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Leyendecker","full_name":"Leyendecker, S. ","first_name":"S. "}],"date_created":"2022-01-19T10:06:50Z","title":"Variational multirate integration in discrete mechanics and optimal control","conference":{"end_date":"2017-06-22","start_date":"2017-06-19"},"year":"2017","citation":{"mla":"Gail, T., et al. “Variational Multirate Integration in Discrete Mechanics and Optimal Control.” <i>ECCOMAS Thematic Conference on Multibody Dynamics</i>, 2017.","short":"T. Gail, S. Ober-Blöbaum, S. Leyendecker, in: ECCOMAS Thematic Conference on Multibody Dynamics, 2017.","bibtex":"@inproceedings{Gail_Ober-Blöbaum_Leyendecker_2017, title={Variational multirate integration in discrete mechanics and optimal control}, booktitle={ECCOMAS Thematic Conference on Multibody Dynamics}, author={Gail, T. and Ober-Blöbaum, Sina and Leyendecker, S. }, year={2017} }","apa":"Gail, T., Ober-Blöbaum, S., &#38; Leyendecker, S. (2017). Variational multirate integration in discrete mechanics and optimal control. <i>ECCOMAS Thematic Conference on Multibody Dynamics</i>.","chicago":"Gail, T., Sina Ober-Blöbaum, and S.  Leyendecker. “Variational Multirate Integration in Discrete Mechanics and Optimal Control.” In <i>ECCOMAS Thematic Conference on Multibody Dynamics</i>, 2017.","ieee":"T. Gail, S. Ober-Blöbaum, and S. Leyendecker, “Variational multirate integration in discrete mechanics and optimal control,” 2017.","ama":"Gail T, Ober-Blöbaum S, Leyendecker S. Variational multirate integration in discrete mechanics and optimal control. In: <i>ECCOMAS Thematic Conference on Multibody Dynamics</i>. ; 2017."}},{"type":"journal_article","status":"public","_id":"45941","user_id":"100441","department":[{"_id":"841"}],"publication_status":"published","publication_identifier":{"issn":["0029-599X","0945-3245"]},"citation":{"apa":"Kovács, B., Li, B., Lubich, C., &#38; Power Guerra, C. A. (2017). Convergence of finite elements on an evolving surface driven by diffusion on the surface. <i>Numerische Mathematik</i>, <i>137</i>(3), 643–689. <a href=\"https://doi.org/10.1007/s00211-017-0888-4\">https://doi.org/10.1007/s00211-017-0888-4</a>","short":"B. Kovács, B. Li, C. Lubich, C.A. Power Guerra, Numerische Mathematik 137 (2017) 643–689.","bibtex":"@article{Kovács_Li_Lubich_Power Guerra_2017, title={Convergence of finite elements on an evolving surface driven by diffusion on the surface}, volume={137}, DOI={<a href=\"https://doi.org/10.1007/s00211-017-0888-4\">10.1007/s00211-017-0888-4</a>}, number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian and Power Guerra, Christian A.}, year={2017}, pages={643–689} }","mla":"Kovács, Balázs, et al. “Convergence of Finite Elements on an Evolving Surface Driven by Diffusion on the Surface.” <i>Numerische Mathematik</i>, vol. 137, no. 3, Springer Science and Business Media LLC, 2017, pp. 643–89, doi:<a href=\"https://doi.org/10.1007/s00211-017-0888-4\">10.1007/s00211-017-0888-4</a>.","ama":"Kovács B, Li B, Lubich C, Power Guerra CA. Convergence of finite elements on an evolving surface driven by diffusion on the surface. <i>Numerische Mathematik</i>. 2017;137(3):643-689. doi:<a href=\"https://doi.org/10.1007/s00211-017-0888-4\">10.1007/s00211-017-0888-4</a>","ieee":"B. Kovács, B. Li, C. Lubich, and C. A. Power Guerra, “Convergence of finite elements on an evolving surface driven by diffusion on the surface,” <i>Numerische Mathematik</i>, vol. 137, no. 3, pp. 643–689, 2017, doi: <a href=\"https://doi.org/10.1007/s00211-017-0888-4\">10.1007/s00211-017-0888-4</a>.","chicago":"Kovács, Balázs, Buyang Li, Christian Lubich, and Christian A. Power Guerra. “Convergence of Finite Elements on an Evolving Surface Driven by Diffusion on the Surface.” <i>Numerische Mathematik</i> 137, no. 3 (2017): 643–89. <a href=\"https://doi.org/10.1007/s00211-017-0888-4\">https://doi.org/10.1007/s00211-017-0888-4</a>."},"intvolume":"       137","page":"643-689","date_updated":"2024-04-03T09:22:43Z","author":[{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"},{"first_name":"Buyang","full_name":"Li, Buyang","last_name":"Li"},{"first_name":"Christian","full_name":"Lubich, Christian","last_name":"Lubich"},{"last_name":"Power Guerra","full_name":"Power Guerra, Christian A.","first_name":"Christian A."}],"volume":137,"doi":"10.1007/s00211-017-0888-4","publication":"Numerische Mathematik","keyword":["Applied Mathematics","Computational Mathematics"],"language":[{"iso":"eng"}],"issue":"3","year":"2017","publisher":"Springer Science and Business Media LLC","date_created":"2023-07-10T11:38:48Z","title":"Convergence of finite elements on an evolving surface driven by diffusion on the surface"},{"issue":"2","publication_status":"published","publication_identifier":{"issn":["0029-599X","0945-3245"]},"citation":{"ama":"Kovács B, Lubich C. Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. <i>Numerische Mathematik</i>. 2017;138(2):365-388. doi:<a href=\"https://doi.org/10.1007/s00211-017-0909-3\">10.1007/s00211-017-0909-3</a>","chicago":"Kovács, Balázs, and Christian Lubich. “Stability and Convergence of Time Discretizations of Quasi-Linear Evolution Equations of Kato Type.” <i>Numerische Mathematik</i> 138, no. 2 (2017): 365–88. <a href=\"https://doi.org/10.1007/s00211-017-0909-3\">https://doi.org/10.1007/s00211-017-0909-3</a>.","ieee":"B. Kovács and C. Lubich, “Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type,” <i>Numerische Mathematik</i>, vol. 138, no. 2, pp. 365–388, 2017, doi: <a href=\"https://doi.org/10.1007/s00211-017-0909-3\">10.1007/s00211-017-0909-3</a>.","apa":"Kovács, B., &#38; Lubich, C. (2017). Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. <i>Numerische Mathematik</i>, <i>138</i>(2), 365–388. <a href=\"https://doi.org/10.1007/s00211-017-0909-3\">https://doi.org/10.1007/s00211-017-0909-3</a>","bibtex":"@article{Kovács_Lubich_2017, title={Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type}, volume={138}, DOI={<a href=\"https://doi.org/10.1007/s00211-017-0909-3\">10.1007/s00211-017-0909-3</a>}, number={2}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Lubich, Christian}, year={2017}, pages={365–388} }","short":"B. Kovács, C. Lubich, Numerische Mathematik 138 (2017) 365–388.","mla":"Kovács, Balázs, and Christian Lubich. “Stability and Convergence of Time Discretizations of Quasi-Linear Evolution Equations of Kato Type.” <i>Numerische Mathematik</i>, vol. 138, no. 2, Springer Science and Business Media LLC, 2017, pp. 365–88, doi:<a href=\"https://doi.org/10.1007/s00211-017-0909-3\">10.1007/s00211-017-0909-3</a>."},"intvolume":"       138","page":"365-388","year":"2017","date_created":"2023-07-10T11:39:05Z","author":[{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","id":"100441","full_name":"Kovács, Balázs"},{"first_name":"Christian","last_name":"Lubich","full_name":"Lubich, Christian"}],"volume":138,"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-03T09:22:34Z","doi":"10.1007/s00211-017-0909-3","title":"Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type","type":"journal_article","publication":"Numerische Mathematik","status":"public","user_id":"100441","department":[{"_id":"841"}],"_id":"45942","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics"]},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics"],"publication":"Numerische Mathematik","title":"Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations","date_created":"2023-07-10T11:38:34Z","publisher":"Springer Science and Business Media LLC","year":"2017","issue":"1","department":[{"_id":"841"}],"user_id":"100441","_id":"45940","status":"public","type":"journal_article","doi":"10.1007/s00211-017-0868-8","volume":137,"author":[{"full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"},{"first_name":"Christian","last_name":"Lubich","full_name":"Lubich, Christian"}],"date_updated":"2024-04-03T09:22:51Z","intvolume":"       137","page":"91-117","citation":{"apa":"Kovács, B., &#38; Lubich, C. (2017). Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>, <i>137</i>(1), 91–117. <a href=\"https://doi.org/10.1007/s00211-017-0868-8\">https://doi.org/10.1007/s00211-017-0868-8</a>","short":"B. Kovács, C. Lubich, Numerische Mathematik 137 (2017) 91–117.","mla":"Kovács, Balázs, and Christian Lubich. “Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>, vol. 137, no. 1, Springer Science and Business Media LLC, 2017, pp. 91–117, doi:<a href=\"https://doi.org/10.1007/s00211-017-0868-8\">10.1007/s00211-017-0868-8</a>.","bibtex":"@article{Kovács_Lubich_2017, title={Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}, volume={137}, DOI={<a href=\"https://doi.org/10.1007/s00211-017-0868-8\">10.1007/s00211-017-0868-8</a>}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Lubich, Christian}, year={2017}, pages={91–117} }","ama":"Kovács B, Lubich C. Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>. 2017;137(1):91-117. doi:<a href=\"https://doi.org/10.1007/s00211-017-0868-8\">10.1007/s00211-017-0868-8</a>","ieee":"B. Kovács and C. Lubich, “Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations,” <i>Numerische Mathematik</i>, vol. 137, no. 1, pp. 91–117, 2017, doi: <a href=\"https://doi.org/10.1007/s00211-017-0868-8\">10.1007/s00211-017-0868-8</a>.","chicago":"Kovács, Balázs, and Christian Lubich. “Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i> 137, no. 1 (2017): 91–117. <a href=\"https://doi.org/10.1007/s00211-017-0868-8\">https://doi.org/10.1007/s00211-017-0868-8</a>."},"publication_identifier":{"issn":["0029-599X","0945-3245"]},"publication_status":"published"},{"title":"Maximum norm stability and error estimates for the evolving surface finite element method","doi":"10.1002/num.22212","publisher":"Wiley","date_updated":"2024-04-03T09:22:00Z","date_created":"2023-07-10T11:40:24Z","author":[{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"},{"last_name":"Power Guerra","full_name":"Power Guerra, Christian Andreas","first_name":"Christian Andreas"}],"volume":34,"year":"2017","citation":{"ama":"Kovács B, Power Guerra CA. Maximum norm stability and error estimates for the evolving surface finite element method. <i>Numerical Methods for Partial Differential Equations</i>. 2017;34(2):518-554. doi:<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>","ieee":"B. Kovács and C. A. Power Guerra, “Maximum norm stability and error estimates for the evolving surface finite element method,” <i>Numerical Methods for Partial Differential Equations</i>, vol. 34, no. 2, pp. 518–554, 2017, doi: <a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>.","chicago":"Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical Methods for Partial Differential Equations</i> 34, no. 2 (2017): 518–54. <a href=\"https://doi.org/10.1002/num.22212\">https://doi.org/10.1002/num.22212</a>.","mla":"Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical Methods for Partial Differential Equations</i>, vol. 34, no. 2, Wiley, 2017, pp. 518–54, doi:<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>.","bibtex":"@article{Kovács_Power Guerra_2017, title={Maximum norm stability and error estimates for the evolving surface finite element method}, volume={34}, DOI={<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>}, number={2}, journal={Numerical Methods for Partial Differential Equations}, publisher={Wiley}, author={Kovács, Balázs and Power Guerra, Christian Andreas}, year={2017}, pages={518–554} }","short":"B. Kovács, C.A. Power Guerra, Numerical Methods for Partial Differential Equations 34 (2017) 518–554.","apa":"Kovács, B., &#38; Power Guerra, C. A. (2017). Maximum norm stability and error estimates for the evolving surface finite element method. <i>Numerical Methods for Partial Differential Equations</i>, <i>34</i>(2), 518–554. <a href=\"https://doi.org/10.1002/num.22212\">https://doi.org/10.1002/num.22212</a>"},"intvolume":"        34","page":"518-554","publication_status":"published","publication_identifier":{"issn":["0749-159X"]},"issue":"2","keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis","Analysis"],"language":[{"iso":"eng"}],"_id":"45946","user_id":"100441","department":[{"_id":"841"}],"status":"public","type":"journal_article","publication":"Numerical Methods for Partial Differential Equations"},{"page":"430-459","intvolume":"        38","citation":{"ieee":"B. Kovács, “High-order evolving surface finite element method for parabolic problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, pp. 430–459, 2017, doi: <a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","chicago":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2017): 430–59. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>.","ama":"Kovács B. High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2017;38(1):430-459. doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>","mla":"Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP), 2017, pp. 430–59, doi:<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>.","short":"B. Kovács, IMA Journal of Numerical Analysis 38 (2017) 430–459.","bibtex":"@article{Kovács_2017, title={High-order evolving surface finite element method for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href=\"https://doi.org/10.1093/imanum/drx013\">10.1093/imanum/drx013</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs}, year={2017}, pages={430–459} }","apa":"Kovács, B. (2017). High-order evolving surface finite element method for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1), 430–459. <a href=\"https://doi.org/10.1093/imanum/drx013\">https://doi.org/10.1093/imanum/drx013</a>"},"year":"2017","issue":"1","publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","doi":"10.1093/imanum/drx013","title":"High-order evolving surface finite element method for parabolic problems on evolving surfaces","volume":38,"author":[{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács"}],"date_created":"2023-07-10T11:39:23Z","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:22:26Z","status":"public","publication":"IMA Journal of Numerical Analysis","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}],"user_id":"100441","_id":"45943"},{"user_id":"100441","department":[{"_id":"841"}],"_id":"45945","type":"journal_article","status":"public","author":[{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs"},{"full_name":"Power Guerra, Christian Andreas","last_name":"Power Guerra","first_name":"Christian Andreas"}],"volume":34,"date_updated":"2024-04-03T09:22:09Z","doi":"10.1002/num.22212","publication_status":"published","publication_identifier":{"issn":["0749-159X"]},"citation":{"bibtex":"@article{Kovács_Power Guerra_2017, title={Maximum norm stability and error estimates for the evolving surface finite element method}, volume={34}, DOI={<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>}, number={2}, journal={Numerical Methods for Partial Differential Equations}, publisher={Wiley}, author={Kovács, Balázs and Power Guerra, Christian Andreas}, year={2017}, pages={518–554} }","short":"B. Kovács, C.A. Power Guerra, Numerical Methods for Partial Differential Equations 34 (2017) 518–554.","mla":"Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical Methods for Partial Differential Equations</i>, vol. 34, no. 2, Wiley, 2017, pp. 518–54, doi:<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>.","apa":"Kovács, B., &#38; Power Guerra, C. A. (2017). Maximum norm stability and error estimates for the evolving surface finite element method. <i>Numerical Methods for Partial Differential Equations</i>, <i>34</i>(2), 518–554. <a href=\"https://doi.org/10.1002/num.22212\">https://doi.org/10.1002/num.22212</a>","ieee":"B. Kovács and C. A. Power Guerra, “Maximum norm stability and error estimates for the evolving surface finite element method,” <i>Numerical Methods for Partial Differential Equations</i>, vol. 34, no. 2, pp. 518–554, 2017, doi: <a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>.","chicago":"Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical Methods for Partial Differential Equations</i> 34, no. 2 (2017): 518–54. <a href=\"https://doi.org/10.1002/num.22212\">https://doi.org/10.1002/num.22212</a>.","ama":"Kovács B, Power Guerra CA. Maximum norm stability and error estimates for the evolving surface finite element method. <i>Numerical Methods for Partial Differential Equations</i>. 2017;34(2):518-554. doi:<a href=\"https://doi.org/10.1002/num.22212\">10.1002/num.22212</a>"},"page":"518-554","intvolume":"        34","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis","Analysis"],"publication":"Numerical Methods for Partial Differential Equations","date_created":"2023-07-10T11:40:00Z","publisher":"Wiley","title":"Maximum norm stability and error estimates for the evolving surface finite element method","issue":"2","year":"2017"},{"title":"Emptiness problems for integer circuits","date_created":"2024-07-16T11:09:20Z","author":[{"first_name":"D.","last_name":"Barth","full_name":"Barth, D."},{"full_name":"Beck, M.","last_name":"Beck","first_name":"M."},{"first_name":"T.","full_name":"Dose, T.","last_name":"Dose"},{"first_name":"Ch.","last_name":"Glaßer","full_name":"Glaßer, Ch."},{"first_name":"L.","last_name":"Michler","full_name":"Michler, L."},{"first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc","id":"106108"}],"date_updated":"2024-07-24T07:24:26Z","citation":{"ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. <i>Emptiness Problems for Integer Circuits</i>.; 2017.","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. <i>Emptiness Problems for Integer Circuits</i>. https://eccc.weizmann.ac.il/report/2017/012, 2017.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, <i>Emptiness problems for integer circuits</i>. https://eccc.weizmann.ac.il/report/2017/012, 2017.","bibtex":"@book{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, place={https://eccc.weizmann.ac.il/report/2017/012}, title={Emptiness problems for integer circuits}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2017} }","mla":"Barth, D., et al. <i>Emptiness Problems for Integer Circuits</i>. 2017.","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Emptiness Problems for Integer Circuits, https://eccc.weizmann.ac.il/report/2017/012, 2017.","apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2017). <i>Emptiness problems for integer circuits</i>."},"place":"https://eccc.weizmann.ac.il/report/2017/012","year":"2017","language":[{"iso":"eng"}],"extern":"1","user_id":"106108","department":[{"_id":"102"}],"_id":"55293","status":"public","type":"report"},{"type":"conference","publication":"42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)","editor":[{"full_name":"Larsen, Kim G.","last_name":"Larsen","first_name":"Kim G."},{"full_name":"Bodlaender, Hans L.","last_name":"Bodlaender","first_name":"Hans L."},{"first_name":"Jean-Francois","last_name":"Raskin","full_name":"Raskin, Jean-Francois"}],"status":"public","_id":"55292","user_id":"106108","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","department":[{"_id":"102"}],"language":[{"iso":"eng"}],"extern":"1","year":"2017","citation":{"ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems for integer circuits. In: Larsen KG, Bodlaender HL, Raskin J-F, eds. <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>. Vol 83. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum für Informatik; 2017:33:1–33:14. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. “Emptiness Problems for Integer Circuits.” In <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited by Kim G. Larsen, Hans L. Bodlaender, and Jean-Francois Raskin, 83:33:1–33:14. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness problems for integer circuits,” in <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, 2017, vol. 83, p. 33:1–33:14, doi: <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>.","apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2017). Emptiness problems for integer circuits. In K. G. Larsen, H. L. Bodlaender, &#38; J.-F. Raskin (Eds.), <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i> (Vol. 83, p. 33:1–33:14). Schloss Dagstuhl–Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>","mla":"Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited by Kim G. Larsen et al., vol. 83, Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017, p. 33:1–33:14, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>.","bibtex":"@inproceedings{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Emptiness problems for integer circuits}, volume={83}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2017.33\">10.4230/LIPIcs.MFCS.2017.33</a>}, booktitle={42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, publisher={Schloss Dagstuhl–Leibniz-Zentrum für Informatik}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, editor={Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois}, year={2017}, pages={33:1–33:14}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, in: K.G. Larsen, H.L. Bodlaender, J.-F. Raskin (Eds.), 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2017, p. 33:1–33:14."},"page":"33:1–33:14","intvolume":"        83","date_updated":"2024-07-24T07:25:35Z","publisher":"Schloss Dagstuhl–Leibniz-Zentrum für Informatik","date_created":"2024-07-16T11:09:20Z","author":[{"first_name":"D.","full_name":"Barth, D.","last_name":"Barth"},{"last_name":"Beck","full_name":"Beck, M.","first_name":"M."},{"first_name":"T.","full_name":"Dose, T.","last_name":"Dose"},{"first_name":"Ch.","full_name":"Glaßer, Ch.","last_name":"Glaßer"},{"first_name":"L.","last_name":"Michler","full_name":"Michler, L."},{"first_name":"Marc","full_name":"Technau, Marc","id":"106108","orcid":"0000-0001-9650-2459","last_name":"Technau"}],"volume":83,"title":"Emptiness problems for integer circuits","doi":"10.4230/LIPIcs.MFCS.2017.33"},{"status":"public","type":"journal_article","publication":"Comput. Methods Funct. Theory","language":[{"iso":"eng"}],"_id":"55275","user_id":"106108","department":[{"_id":"102"}],"year":"2017","citation":{"ama":"Technau M, Technau N. A Loewner equation for infinitely many slits. <i>Comput Methods Funct Theory</i>. 2017;17(2):255–272. doi:<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>","chicago":"Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many Slits.” <i>Comput. Methods Funct. Theory</i> 17, no. 2 (2017): 255–272. <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">https://doi.org/10.1007/s40315-016-0179-6</a>.","ieee":"M. Technau and N. Technau, “A Loewner equation for infinitely many slits,” <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, pp. 255–272, 2017, doi: <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>.","mla":"Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many Slits.” <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, 2017, pp. 255–272, doi:<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>.","short":"M. Technau, N. Technau, Comput. Methods Funct. Theory 17 (2017) 255–272.","bibtex":"@article{Technau_Technau_2017, title={A Loewner equation for infinitely many slits}, volume={17}, DOI={<a href=\"https://doi.org/10.1007/s40315-016-0179-6\">10.1007/s40315-016-0179-6</a>}, number={2}, journal={Comput. Methods Funct. Theory}, author={Technau, Marc and Technau, N.}, year={2017}, pages={255–272} }","apa":"Technau, M., &#38; Technau, N. (2017). A Loewner equation for infinitely many slits. <i>Comput. Methods Funct. Theory</i>, <i>17</i>(2), 255–272. <a href=\"https://doi.org/10.1007/s40315-016-0179-6\">https://doi.org/10.1007/s40315-016-0179-6</a>"},"page":"255–272","intvolume":"        17","issue":"2","title":"A Loewner equation for infinitely many slits","doi":"10.1007/s40315-016-0179-6","date_updated":"2024-07-24T07:24:37Z","author":[{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108"},{"first_name":"N.","full_name":"Technau, N.","last_name":"Technau"}],"date_created":"2024-07-16T11:08:06Z","volume":17},{"abstract":[{"text":"We describe a practical algorithm to solve the constructive membership problem for discrete two-generator subgroups of SL₂(R) or PSL₂(R). This algorithm has been implemented in Magma for groups defined over real algebraic number fields.","lang":"eng"}],"publication":"Journal of Algebra","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"year":"2017","title":"The constructive membership problem for discrete two-generator subgroups of SL(2,R)","date_created":"2023-03-07T08:28:11Z","publisher":"Elsevier BV","status":"public","type":"journal_article","extern":"1","user_id":"93826","department":[{"_id":"102"}],"_id":"42791","citation":{"ama":"Kirschmer M, Rüther MG. The constructive membership problem for discrete two-generator subgroups of SL(2,R). <i>Journal of Algebra</i>. 2017;480:519-548. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>","chicago":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i> 480 (2017): 519–48. <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>.","ieee":"M. Kirschmer and M. G. Rüther, “The constructive membership problem for discrete two-generator subgroups of SL(2,R),” <i>Journal of Algebra</i>, vol. 480, pp. 519–548, 2017, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>.","short":"M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548.","mla":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i>, vol. 480, Elsevier BV, 2017, pp. 519–48, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>.","bibtex":"@article{Kirschmer_Rüther_2017, title={The constructive membership problem for discrete two-generator subgroups of SL(2,R)}, volume={480}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">10.1016/j.jalgebra.2017.02.029</a>}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Kirschmer, Markus and Rüther, Marion G.}, year={2017}, pages={519–548} }","apa":"Kirschmer, M., &#38; Rüther, M. G. (2017). The constructive membership problem for discrete two-generator subgroups of SL(2,R). <i>Journal of Algebra</i>, <i>480</i>, 519–548. <a href=\"https://doi.org/10.1016/j.jalgebra.2017.02.029\">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>"},"page":"519-548","intvolume":"       480","publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"doi":"10.1016/j.jalgebra.2017.02.029","author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"first_name":"Marion G.","full_name":"Rüther, Marion G.","last_name":"Rüther"}],"volume":480,"date_updated":"2023-04-04T09:10:14Z"},{"main_file_link":[{"url":"http://nbn-resolving.de/urn:nbn:de:hbz:466:2-24042"}],"title":"Modeling and simulation of metallic, particle-damped spheres for lightweight materials","supervisor":[{"last_name":"Walther","full_name":"Walther, Andrea","first_name":"Andrea"},{"first_name":"Jadran","full_name":"Vrabec, Jadran","last_name":"Vrabec"}],"date_created":"2017-07-26T15:19:44Z","author":[{"full_name":"Steinle, Tobias","last_name":"Steinle","first_name":"Tobias"}],"date_updated":"2022-01-06T06:59:09Z","citation":{"apa":"Steinle, T. (2016). <i>Modeling and simulation of metallic, particle-damped spheres for lightweight materials</i>.","bibtex":"@book{Steinle_2016, title={Modeling and simulation of metallic, particle-damped spheres for lightweight materials}, author={Steinle, Tobias}, year={2016} }","short":"T. Steinle, Modeling and Simulation of Metallic, Particle-Damped Spheres for Lightweight Materials, 2016.","mla":"Steinle, Tobias. <i>Modeling and Simulation of Metallic, Particle-Damped Spheres for Lightweight Materials</i>. 2016.","ieee":"T. Steinle, <i>Modeling and simulation of metallic, particle-damped spheres for lightweight materials</i>. 2016.","chicago":"Steinle, Tobias. <i>Modeling and Simulation of Metallic, Particle-Damped Spheres for Lightweight Materials</i>, 2016.","ama":"Steinle T. <i>Modeling and Simulation of Metallic, Particle-Damped Spheres for Lightweight Materials</i>.; 2016."},"year":"2016","language":[{"iso":"eng"}],"department":[{"_id":"27"},{"_id":"104"},{"_id":"155"}],"user_id":"24135","_id":"33","status":"public","abstract":[{"text":"Lightweight materials play an ever growing role in today's world. Saving on the mass of a machine will usually translate into a lower energy consumption. However, lightweight applications are prone to develop performance problems due to vibration induced by the operation of the machine. The Fraunhofer Institute for Manufacturing Technology and Advanced Materials in Dresden conducts research into the damping properties of composite materials. They are experimenting with hollow, particle filled spheres embedded in the lightweight material. Such a system is the technical motivation of this thesis. Ultimately, a numerical experiment to derive the coefficient of restitution is required. The simulation developed in this thesis is based on a discrete element method to track the individual particle and sphere trajectories. Based on a potential based approach for the particle interactions deployed in molecular dynamics, the behavior of the particles can be controlled effectively. The simulated volume is using reflecting boundaries and encloses the hollow sphere. In this work, a highly flexible memory structure was used with a linked cell approach to cope with the highly flexible mass of particles. This allows for a linear complexity of the method in regard to the particle number by reducing the computational overhead of the interaction computation. Multiple numerical experiments show the great effect the particles have on the damping behavior of the system.","lang":"eng"},{"text":"In vielen technischen Anwendungen spielt heute der Leichtbau eine große Rolle, denn durch Gewichtseinsparungen lässt sich auch Energie einsparen. Allerdings birgt der Leichtbau die Gefahr einer erhöhten Störanfälligkeit gegenüber Vibrationen, die durch die Operation von Maschinen entstehen können. Das Fraunhofer Institut für Fertigungstechnik und Angewandte Materialforschung in Dresden beschäftigt sich mit den Möglichkeiten einer Schwingungsdämpfung durch Verbundwerkstoffe. Dabei wird in die Leichtbaustruktur eine Vielzahl von Hohlkugeln eingebracht, die mit Keramikpartikeln gefüllt sind. Diese Fragestellung bildet die technische Motivation für diese Arbeit. Ziel ist, ein Experiment zur Bestimmung des Restitutionskoeffizienten numerisch nachzubilden. Die Simulation basiert auf einer Diskreten Elemente Methode um die Trajektorien der einzelnen Partikel und der Kugel berechnen zu können. Basierend auf einem Potentialansatz für die Interaktionsberechnung in der Molekulardynamik kann das Reibungsverhalten vielfältig angepasst werden. Das Simulationsvolumen wird durch reflektierende Randbedingungen abgeschlossen und umfasst die Kugelhülle. Dazu kam eine hochflexible Speicherstruktur zum Einsatz, um die heterogene Verteilung der Partikel im Raum mit einer effizienten Linked Cell Methode abbilden zu können. Dadurch wird eine in der Partikelzahl lineare Komplexität erreicht. Umfangreiche numerische Experimente zeigen den großen Effekt der Partikelfüllung auf das Dämpfungsverhalten.","lang":"ger"}],"type":"dissertation"},{"series_title":"Mathematics in Industry","user_id":"24135","department":[{"_id":"27"},{"_id":"101"}],"_id":"34","type":"conference","publication":"Progress in Industrial Mathematics at ECMI","status":"public","date_created":"2017-07-26T15:25:33Z","author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"last_name":"Eckstein","full_name":"Eckstein, Julian","first_name":"Julian"},{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"last_name":"Friedel","full_name":"Friedel, Patrick","first_name":"Patrick"},{"first_name":"Christian","last_name":"Horenkamp","full_name":"Horenkamp, Christian"},{"full_name":"Köhler, Ulrich","last_name":"Köhler","first_name":"Ulrich"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Sebastian","last_name":"Tiemeyer","full_name":"Tiemeyer, Sebastian"}],"volume":22,"publisher":"Springer International Publishing","date_updated":"2022-01-06T06:59:14Z","doi":"10.1007/978-3-319-23413-7_87","title":"Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control","publication_identifier":{"issn":["2212-0173"]},"citation":{"ieee":"M. Dellnitz <i>et al.</i>, “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control,” in <i>Progress in Industrial Mathematics at ECMI</i>, 2016, vol. 22, pp. 633–641.","chicago":"Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel, Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” In <i>Progress in Industrial Mathematics at ECMI</i>, 22:633–41. Mathematics in Industry. Cham: Springer International Publishing, 2016. <a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">https://doi.org/10.1007/978-3-319-23413-7_87</a>.","ama":"Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In: <i>Progress in Industrial Mathematics at ECMI</i>. Vol 22. Mathematics in Industry. Cham: Springer International Publishing; 2016:633-641. doi:<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>","short":"M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler, S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Progress in Industrial Mathematics at ECMI, Springer International Publishing, Cham, 2016, pp. 633–641.","mla":"Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” <i>Progress in Industrial Mathematics at ECMI</i>, vol. 22, Springer International Publishing, 2016, pp. 633–41, doi:<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>.","bibtex":"@inproceedings{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016, place={Cham}, series={Mathematics in Industry}, title={Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>}, booktitle={Progress in Industrial Mathematics at ECMI}, publisher={Springer International Publishing}, author={Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016}, pages={633–641}, collection={Mathematics in Industry} }","apa":"Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler, U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In <i>Progress in Industrial Mathematics at ECMI</i> (Vol. 22, pp. 633–641). Cham: Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">https://doi.org/10.1007/978-3-319-23413-7_87</a>"},"page":"633-641","intvolume":"        22","place":"Cham","year":"2016"},{"year":"2016","citation":{"apa":"Nüske, F., Schneider, R., Vitalini, F., &#38; Noé, F. (2016). Variational tensor approach for approximating the rare-event kinetics of macromolecular systems. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.4940774\">https://doi.org/10.1063/1.4940774</a>","mla":"Nüske, Feliks, et al. “Variational Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems.” <i>The Journal of Chemical Physics</i>, 054105, 2016, doi:<a href=\"https://doi.org/10.1063/1.4940774\">10.1063/1.4940774</a>.","bibtex":"@article{Nüske_Schneider_Vitalini_Noé_2016, title={Variational tensor approach for approximating the rare-event kinetics of macromolecular systems}, DOI={<a href=\"https://doi.org/10.1063/1.4940774\">10.1063/1.4940774</a>}, number={054105}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Schneider, Reinhold and Vitalini, Francesca and Noé, Frank}, year={2016} }","short":"F. Nüske, R. Schneider, F. Vitalini, F. Noé, The Journal of Chemical Physics (2016).","ama":"Nüske F, Schneider R, Vitalini F, Noé F. Variational tensor approach for approximating the rare-event kinetics of macromolecular systems. <i>The Journal of Chemical Physics</i>. 2016. doi:<a href=\"https://doi.org/10.1063/1.4940774\">10.1063/1.4940774</a>","ieee":"F. Nüske, R. Schneider, F. Vitalini, and F. Noé, “Variational tensor approach for approximating the rare-event kinetics of macromolecular systems,” <i>The Journal of Chemical Physics</i>, 2016.","chicago":"Nüske, Feliks, Reinhold Schneider, Francesca Vitalini, and Frank Noé. “Variational Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems.” <i>The Journal of Chemical Physics</i>, 2016. <a href=\"https://doi.org/10.1063/1.4940774\">https://doi.org/10.1063/1.4940774</a>."},"publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","title":"Variational tensor approach for approximating the rare-event kinetics of macromolecular systems","doi":"10.1063/1.4940774","date_updated":"2022-01-06T06:55:20Z","author":[{"first_name":"Feliks","id":"81513","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske"},{"last_name":"Schneider","full_name":"Schneider, Reinhold","first_name":"Reinhold"},{"last_name":"Vitalini","full_name":"Vitalini, Francesca","first_name":"Francesca"},{"full_name":"Noé, Frank","last_name":"Noé","first_name":"Frank"}],"date_created":"2021-04-30T16:54:43Z","status":"public","publication":"The Journal of Chemical Physics","type":"journal_article","article_number":"054105","extern":"1","language":[{"iso":"eng"}],"_id":"21937","department":[{"_id":"101"}],"user_id":"81513"},{"publication_status":"published","publication_identifier":{"issn":["2212-0173"]},"year":"2016","citation":{"apa":"Peitz, S., Gräler, M., Henke, C., Molo, M. H., Dellnitz, M., &#38; Trächtler, A. (2016). Multiobjective Model Predictive Control of an Industrial Laundry. In <i>Procedia Technology</i> (pp. 483–490). <a href=\"https://doi.org/10.1016/j.protcy.2016.08.061\">https://doi.org/10.1016/j.protcy.2016.08.061</a>","bibtex":"@inproceedings{Peitz_Gräler_Henke_Molo_Dellnitz_Trächtler_2016, title={Multiobjective Model Predictive Control of an Industrial Laundry}, DOI={<a href=\"https://doi.org/10.1016/j.protcy.2016.08.061\">10.1016/j.protcy.2016.08.061</a>}, booktitle={Procedia Technology}, author={Peitz, Sebastian and Gräler, Manuel and Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler, Ansgar}, year={2016}, pages={483–490} }","short":"S. Peitz, M. Gräler, C. Henke, M.H. Molo, M. Dellnitz, A. Trächtler, in: Procedia Technology, 2016, pp. 483–490.","mla":"Peitz, Sebastian, et al. “Multiobjective Model Predictive Control of an Industrial Laundry.” <i>Procedia Technology</i>, 2016, pp. 483–90, doi:<a href=\"https://doi.org/10.1016/j.protcy.2016.08.061\">10.1016/j.protcy.2016.08.061</a>.","ama":"Peitz S, Gräler M, Henke C, Molo MH, Dellnitz M, Trächtler A. Multiobjective Model Predictive Control of an Industrial Laundry. In: <i>Procedia Technology</i>. ; 2016:483-490. doi:<a href=\"https://doi.org/10.1016/j.protcy.2016.08.061\">10.1016/j.protcy.2016.08.061</a>","chicago":"Peitz, Sebastian, Manuel Gräler, Christian Henke, Mirko Hessel-von Molo, Michael Dellnitz, and Ansgar Trächtler. “Multiobjective Model Predictive Control of an Industrial Laundry.” In <i>Procedia Technology</i>, 483–90, 2016. <a href=\"https://doi.org/10.1016/j.protcy.2016.08.061\">https://doi.org/10.1016/j.protcy.2016.08.061</a>.","ieee":"S. Peitz, M. Gräler, C. Henke, M. H. Molo, M. Dellnitz, and A. Trächtler, “Multiobjective Model Predictive Control of an Industrial Laundry,” in <i>Procedia Technology</i>, 2016, pp. 483–490."},"page":"483-490","date_updated":"2022-01-06T07:04:00Z","date_created":"2019-03-29T13:35:59Z","author":[{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427"},{"first_name":"Manuel","full_name":"Gräler, Manuel","last_name":"Gräler"},{"first_name":"Christian","full_name":"Henke, Christian","last_name":"Henke"},{"full_name":"Molo, Mirko Hessel-von","last_name":"Molo","first_name":"Mirko Hessel-von"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Ansgar","last_name":"Trächtler","full_name":"Trächtler, Ansgar"}],"title":"Multiobjective Model Predictive Control of an Industrial Laundry","doi":"10.1016/j.protcy.2016.08.061","type":"conference","publication":"Procedia Technology","abstract":[{"lang":"eng","text":"In a wide range of applications, it is desirable to optimally control a system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario."}],"status":"public","_id":"8759","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}]},{"department":[{"_id":"49"},{"_id":"104"}],"user_id":"11829","_id":"6569","project":[{"name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"}],"language":[{"iso":"eng"}],"type":"misc","status":"public","date_created":"2019-01-09T14:37:18Z","author":[{"first_name":"Benjamin","last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin"},{"id":"11829","full_name":"Claes, Leander","orcid":"0000-0002-4393-268X","last_name":"Claes","first_name":"Leander"}],"date_updated":"2022-01-06T07:03:12Z","title":"Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation","citation":{"bibtex":"@book{Jurgelucks_Claes_2016, place={Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen}, title={Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation}, author={Jurgelucks, Benjamin and Claes, Leander}, year={2016} }","short":"B. Jurgelucks, L. Claes, Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers Using Algorithmic Differentiation, Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen, 2016.","mla":"Jurgelucks, Benjamin, and Leander Claes. <i>Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers Using Algorithmic Differentiation</i>. 2016.","apa":"Jurgelucks, B., &#38; Claes, L. (2016). <i>Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation</i>. Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen.","ieee":"B. Jurgelucks and L. Claes, <i>Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation</i>. Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen, 2016.","chicago":"Jurgelucks, Benjamin, and Leander Claes. <i>Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers Using Algorithmic Differentiation</i>. Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen, 2016.","ama":"Jurgelucks B, Claes L. <i>Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers Using Algorithmic Differentiation</i>. Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen; 2016."},"place":"Workshop on Direct and Inverse Problems in Piezoelectricity, Erlangen","year":"2016"},{"project":[{"_id":"90","name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums"}],"_id":"6570","user_id":"11829","department":[{"_id":"49"},{"_id":"104"}],"language":[{"iso":"eng"}],"type":"conference","publication":"AD2016 The 7th International Conference on Algorithmic Differentiation","status":"public","date_updated":"2022-01-06T07:03:12Z","date_created":"2019-01-09T14:37:19Z","author":[{"first_name":"Benjamin","full_name":"Jurgelucks, Benjamin","last_name":"Jurgelucks"},{"first_name":"Leander","id":"11829","full_name":"Claes, Leander","last_name":"Claes","orcid":"0000-0002-4393-268X"}],"title":"Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation","conference":{"name":"AD2016 The 7th International Conference on Algorithmic Differentiation","location":"Christ Church, Oxford, United Kingdom"},"year":"2016","citation":{"ieee":"B. Jurgelucks and L. Claes, “Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation,” in <i>AD2016 The 7th International Conference on Algorithmic Differentiation</i>, Christ Church, Oxford, United Kingdom, 2016, pp. 99–102.","chicago":"Jurgelucks, Benjamin, and Leander Claes. “Optimisation of Triple-Ring-Electrodes on Piezoceramic Transducers Using Algorithmic Differentiation.” In <i>AD2016 The 7th International Conference on Algorithmic Differentiation</i>, 99–102, 2016.","ama":"Jurgelucks B, Claes L. Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation. In: <i>AD2016 The 7th International Conference on Algorithmic Differentiation</i>. ; 2016:99-102.","mla":"Jurgelucks, Benjamin, and Leander Claes. “Optimisation of Triple-Ring-Electrodes on Piezoceramic Transducers Using Algorithmic Differentiation.” <i>AD2016 The 7th International Conference on Algorithmic Differentiation</i>, 2016, pp. 99–102.","bibtex":"@inproceedings{Jurgelucks_Claes_2016, title={Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation}, booktitle={AD2016 The 7th International Conference on Algorithmic Differentiation}, author={Jurgelucks, Benjamin and Claes, Leander}, year={2016}, pages={99–102} }","short":"B. Jurgelucks, L. Claes, in: AD2016 The 7th International Conference on Algorithmic Differentiation, 2016, pp. 99–102.","apa":"Jurgelucks, B., &#38; Claes, L. (2016). Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation. In <i>AD2016 The 7th International Conference on Algorithmic Differentiation</i> (pp. 99–102). Christ Church, Oxford, United Kingdom."},"page":"99-102"},{"date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-16T05:37:11Z","author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"first_name":"Julian","full_name":"Eckstein, Julian","last_name":"Eckstein"},{"full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp","first_name":"Kathrin"},{"first_name":"Patrick","last_name":"Friedel","full_name":"Friedel, Patrick"},{"first_name":"Christian","full_name":"Horenkamp, Christian","last_name":"Horenkamp"},{"last_name":"Köhler","full_name":"Köhler, Ulrich","first_name":"Ulrich"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian"},{"last_name":"Tiemeyer","full_name":"Tiemeyer, Sebastian","first_name":"Sebastian"}],"title":"Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control","doi":"10.1007/978-3-319-23413-7_87","publication_identifier":{"isbn":["9783319234120","9783319234137"],"issn":["1612-3956","2198-3283"]},"publication_status":"published","place":"Cham","year":"2016","citation":{"ama":"Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In: <i>Mathematics in Industry</i>. Cham; 2016. doi:<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>","chicago":"Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel, Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” In <i>Mathematics in Industry</i>. Cham, 2016. <a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">https://doi.org/10.1007/978-3-319-23413-7_87</a>.","ieee":"M. Dellnitz <i>et al.</i>, “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control,” in <i>Mathematics in Industry</i>, Cham, 2016.","mla":"Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control.” <i>Mathematics in Industry</i>, 2016, doi:<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>.","short":"M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler, S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Mathematics in Industry, Cham, 2016.","bibtex":"@inbook{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016, place={Cham}, title={Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">10.1007/978-3-319-23413-7_87</a>}, booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016} }","apa":"Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler, U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control. In <i>Mathematics in Industry</i>. Cham. <a href=\"https://doi.org/10.1007/978-3-319-23413-7_87\">https://doi.org/10.1007/978-3-319-23413-7_87</a>"},"_id":"16579","department":[{"_id":"101"}],"user_id":"15701","language":[{"iso":"eng"}],"publication":"Mathematics in Industry","type":"book_chapter","status":"public"}]