@article{8751,
abstract = {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 the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.},
author = {Peitz, Sebastian and Dellnitz, Michael},
issn = {2297-8747},
journal = {Mathematical and Computational Applications},
number = {2},
title = {{A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}},
doi = {10.3390/mca23020030},
volume = {23},
year = {2018},
}
@inbook{8574,
author = {Liebendörfer, Michael and Kuklinski, Christiane and Hochmuth, Reinhard},
booktitle = {Beiträge zum Mathematikunterricht 2018},
editor = {Didaktik der Mathematik der Universität Paderborn, Fachgruppe},
pages = {1175--1178},
publisher = {WTM-Verlag},
title = {{Auswirkungen von innovativen Vorlesungen für Lehramtsstudierende in der Studieneingangsphase}},
year = {2018},
}
@inproceedings{7766,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2018},
publisher = {WTM-Verlag},
title = {{Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen}},
year = {2018},
}
@article{10142,
author = {Steffen, Eckhard},
journal = {Australasian Journal of Combinatorics},
number = {1},
pages = {153--160},
title = {{Approximating Vizing’s independence number conjecture}},
volume = {71},
year = {2018},
}
@inproceedings{8757,
abstract = {A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non‐smooth objective functionals. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results.},
author = {Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan},
booktitle = {PAMM},
issn = {1617-7061},
pages = {51--54},
title = {{POD-based multiobjective optimal control of PDEs with non-smooth objectives}},
doi = {10.1002/pamm.201710015},
year = {2018},
}
@inproceedings{8575,
abstract = {The transition from high school to university mathematics has proven to be difficult for many students but especially for pre-service secondary teachers. To support these students at mastering this transition, various universities have introduced support measures of various kinds. The WiGeMath project developed a taxonomy that makes it possible to describe and compare these measures concerning their goals as well as their frame characteristics. We will exemplify the use of the taxonomy in the description of one specific innovative measure that was part of the WiGeMath evaluations. Moreover, we will present first results concerning the goal-fulfilment of this measure concerning affective characteristics of the student cohort and their predominant beliefs.},
author = {Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Lankeit, Elisa and Neuhaus, Silke and Schaper, Niclas and Schürmann, Mirko},
booktitle = {Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018)},
editor = {Durand-Guerrier, V. and Hochmuth, R. and Goodchild, S. and Hogstad, N.M.},
keyword = {Beliefs., Motivational developments, Novel approaches to teaching, Teacher education, Transition to and across university mathematics},
pages = {527--536},
publisher = {INDRUM Network, University of Agder},
title = {{Evaluating Innovative Measures in University Mathematics – The Case of Affective Outcomes in a Lecture focused on Problem-Solving}},
year = {2018},
}
@article{10129,
abstract = {There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.},
author = {Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard},
journal = {The Electronic Journal of Combinatorics},
keyword = {Cubic graph, Tait coloring, Snark, Boole coloring, Berge's conjecture, Tutte's 5-flow conjecture},
number = {4},
title = {{Measures of Edge-Uncolorability of Cubic Graphs}},
volume = {25},
year = {2018},
}
@unpublished{16292,
abstract = {In a recent article, we presented a framework to control nonlinear partial
differential equations (PDEs) by means of Koopman operator based reduced models
and concepts from switched systems. The main idea was to transform a control
system into a set of autonomous systems for which the optimal switching
sequence has to be computed. These individual systems can be approximated very
efficiently by reduced order models obtained from data, and one can guarantee
equality of the full and the reduced objective function under certain
assumptions. In this article, we extend these results to continuous control
inputs using convex combinations of multiple Koopman operators corresponding to
constant controls, which results in a bilinear control system. Although
equality of the objectives can be carried over when the PDE depends linearly on
the control, we show that this approach is also valid in other scenarios using
several flow control examples of varying complexity.},
author = {Peitz, Sebastian},
booktitle = {arXiv:1801.06419},
title = {{Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data}},
year = {2018},
}
@book{8576,
author = {Liebendörfer, Michael},
isbn = {978-3-658-22506-3 978-3-658-22507-0},
publisher = {Springer Fachmedien Wiesbaden},
title = {{Motivationsentwicklung im Mathematikstudium}},
doi = {10.1007/978-3-658-22507-0},
year = {2018},
}
@inbook{8569,
author = {Biehler, Rolf and Hochmuth, Reinhard and Schaper, Niclas and Kuklinski, Christiane and Lankeit, Elisa and Leis, Elena and Liebendörfer, Michael and Schürmann, Mirko},
booktitle = {3. Auswertungsworkshop der Begleitforschung. Dokumentation der Projektbeiträge.},
editor = {Hanft, Anke and Bischoff, Franziska and Kretschmer, Stefanie},
pages = {32--41},
publisher = {Carl von Ossietzky Universität Oldenburg},
title = {{Verbundprojekt WiGeMath: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase}},
year = {2018},
}
@article{8571,
author = {Frühbis-Krüger, Anne and Liebendörfer, Michael},
journal = {Computeralgebra-Rundbrief},
number = {63},
title = {{Minisymposium CAS in der Hochschullehre - ein Blick in die Praxis}},
year = {2018},
}
@article{10132,
author = {Jin, Ligang and Mazzuoccolo, Giuseppe and Steffen, Eckhard},
issn = {1234-3099},
journal = {Discussiones Mathematicae Graph Theory},
pages = {165--175},
title = {{Cores, joins and the Fano-flow conjectures}},
doi = {10.7151/dmgt.1999},
volume = {38},
year = {2018},
}
@inbook{8754,
abstract = {In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed in such a way that the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.},
author = {Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan},
booktitle = {Reduced-Order Modeling (ROM) for Simulation and Optimization},
isbn = {9783319753188},
pages = {47--72},
title = {{Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}},
doi = {10.1007/978-3-319-75319-5_3},
year = {2018},
}
@unpublished{16293,
abstract = {Kernel transfer operators, which can be regarded as approximations of
transfer operators such as the Perron-Frobenius or Koopman operator in
reproducing kernel Hilbert spaces, are defined in terms of covariance and
cross-covariance operators and have been shown to be closely related to the
conditional mean embedding framework developed by the machine learning
community. The goal of this paper is to show how the dominant eigenfunctions of
these operators in combination with gradient-based optimization techniques can
be used to detect long-lived coherent patterns in high-dimensional time-series
data. The results will be illustrated using video data and a fluid flow
example.},
author = {Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar},
booktitle = {arXiv:1805.10118},
title = {{Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions}},
year = {2018},
}
@inbook{8572,
author = {Frühbis-Krüger, Anne and Kemper, Gregor and Koepf, Wolfram and Liebendörfer, Michael},
booktitle = {Beiträge zum Mathematikunterricht 2018},
pages = {83--84},
publisher = {WTM-Verlag},
title = {{CAS in der Hochschullehre - Ein Blick in die Praxis}},
year = {2018},
}
@article{6571,
author = {Jurgelucks, Benjamin and Claes, Leander and Walther, Andrea and Henning, Bernd},
issn = {1055-6788},
journal = {Optimization Methods and Software},
pages = {1--21},
title = {{Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation}},
doi = {10.1080/10556788.2018.1435652},
year = {2018},
}
@inproceedings{6595,
author = {Feldmann, Nadine and Jurgelucks, Benjamin and Claes, Leander and Henning, Bernd},
booktitle = {Messtechnische Anwendungen von Ultraschall},
title = {{Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden}},
year = {2018},
}
@article{8755,
abstract = {Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.},
author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof},
issn = {0951-7715},
journal = {Nonlinearity},
number = {7},
pages = {3359--3380},
title = {{Tensor-based dynamic mode decomposition}},
doi = {10.1088/1361-6544/aabc8f},
volume = {31},
year = {2018},
}
@unpublished{16294,
abstract = {Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al.~have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and --
more importantly -- problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving.},
author = {Ober-Blöbaum, Sina and Peitz, Sebastian},
booktitle = {arXiv:1809.06238},
title = {{Explicit multiobjective model predictive control for nonlinear systems with symmetries}},
year = {2018},
}
@inproceedings{8750,
abstract = {In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.},
author = {Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael},
booktitle = {Numerical and Evolutionary Optimization – NEO 2017},
isbn = {9783319961033},
issn = {1860-949X},
title = {{A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}},
doi = {10.1007/978-3-319-96104-0_2},
year = {2018},
}
@inproceedings{8559,
author = {Liebendörfer, Michael and Hochmuth, Reinhard},
booktitle = {Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings},
editor = {Göller, Robin and Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-Georg},
pages = {286--293},
publisher = {Universität Kassel},
title = {{Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations}},
year = {2017},
}
@inproceedings{6572,
author = {Jurgelucks, Benjamin and Feldmann, Nadine and Claes, Leander and Henning, Bernd and Walther, Andrea},
booktitle = {Proceedings of Meetings on Acoustics},
pages = {030010},
title = {{Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity}},
doi = {10.1121/2.0000707},
year = {2017},
}
@article{8756,
abstract = {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.},
author = {Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael},
issn = {2405-8963},
journal = {IFAC-PapersOnLine},
number = {1},
pages = {8674--8679},
title = {{A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles}},
doi = {10.1016/j.ifacol.2017.08.1526},
volume = {50},
year = {2017},
}
@inproceedings{8752,
abstract = {In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.},
author = {Peitz, Sebastian and Dellnitz, Michael},
booktitle = {NEO 2016},
isbn = {9783319640624},
issn = {1860-949X},
pages = {159--182},
title = {{Gradient-Based Multiobjective Optimization with Uncertainties}},
doi = {10.1007/978-3-319-64063-1_7},
year = {2017},
}
@inbook{8570,
author = {Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Kuklinski, Christiane and Khellaf, Sarah and Colberg, Christoph and Schürmann, Mirko and Rothe, Lukas},
booktitle = {Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1 – 5, 2017)},
editor = {Dooley, T. and Gueudet, Ghislaine},
keyword = {Ziele der Lehre},
pages = {2177--2184},
publisher = {DCU Institute of Education & ERME},
title = {{A framework for goal dimensions of mathematics learning support in universities}},
year = {2017},
}
@inproceedings{7767,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2017},
editor = {Kortenkamp, Ulrich and Kuzle, Ana},
publisher = {WTM-Verlag},
title = {{Sinnkonstruktion beim Erkunden von Mustern und Strukturen}},
year = {2017},
}
@article{8564,
author = {Liebendörfer, Michael and Schukajlow, Stanislaw},
issn = {1863-9690, 1863-9704},
journal = {ZDM},
number = {3},
pages = {355--366},
title = {{Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?}},
doi = {10.1007/s11858-016-0827-3},
volume = {49},
year = {2017},
}
@phdthesis{10594,
abstract = {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
the set of optimal compromises (the Pareto set) between the conflicting objectives.
Since – in contrast to the solution of a single objective optimization problem – the
Pareto set generally consists of an infinite number of solutions, the computational
effort 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
are costly to evaluate. Consequently, this thesis is devoted to the identification and
exploitation of structure both in the Pareto set and the dynamics of the underlying
model as well as to the development of efficient algorithms for solving problems with
additional parameters, with a high number of objectives or with PDE-constraints.
These three challenges are addressed in three respective parts.
In the first part, predictor-corrector methods are extended to entire Pareto sets.
When certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent
space can be approximated numerically which yields a direction for the predictor
step. In the corrector step, the predicted set converges to the Pareto set at a new
parameter value. The resulting algorithm is applied to an example from autonomous
driving.
In the second part, the hierarchical structure of Pareto sets is investigated. When
considering a subset of the objectives, the resulting solution is a subset of the Pareto
set 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
way, the “skeleton” of a Pareto set can be computed and due to the exponential
increase in computing time with the number of objectives, the computations of
these subsets are significantly faster which is demonstrated using an example from
industrial laundries.
In the third part, PDE-constrained multiobjective optimal control problems are
addressed by reduced order modeling methods. Reduced order models exploit the
structure in the system dynamics, for example by describing the dynamics of only the
most 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
algorithms. Both scalarization and set-oriented approaches are coupled with reduced
order modeling. Convergence results are presented and the numerical benefit is
investigated. The algorithms are applied to semi-linear heat flow problems as well
as to the Navier-Stokes equations.
},
author = {Peitz, Sebastian},
title = {{ Exploiting structure in multiobjective optimization and optimal control}},
year = {2017},
}
@inproceedings{8566,
author = {Göller, Robin and Liebendörfer, Michael},
booktitle = {Beiträge zum Mathematikunterricht 2016},
editor = {für Didaktik der Mathematik, Gesellschaft},
keyword = {\_tablet, Abschreiben},
pages = {321--324},
publisher = {WTM-Verlag für wissenschaftliche Texte und Medien},
title = {{Eine alternative Einstiegsvorlesung in die Fachmathematik – Konzept und Auswirkungen}},
doi = {http://dx.doi.org/10.17877/DE290R-17398},
year = {2016},
}
@inproceedings{7765,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2016},
publisher = {WTM-Verlag},
title = {{Erkunden mathematischer Strukturen anstatt Interpretation in Modellen – Ein innermathematischer Zugang zu negativen Zahlen}},
year = {2016},
}
@inbook{8555,
author = {Kolter, Jana and Liebendörfer, Michael and Schukajlow, Stanislaw},
booktitle = {Lehren und Lernen von Mathematik in der Studieneingangsphase},
editor = {Hoppenbrock, Axel and Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-Georg},
isbn = {978-3-658-10260-9 978-3-658-10261-6},
pages = {567--583},
publisher = {Springer Fachmedien Wiesbaden},
title = {{Mathe – nein danke? Interesse, Beliefs und Lernstrategien im Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach}},
year = {2016},
}
@inproceedings{8562,
author = {Colberg, Christoph and Biehler, Rolf and Hochmuth, Reinhard and Schaper, Niclas and Liebendörfer, Michael and Schürmann, Mirko},
booktitle = {Beiträge zum Mathematikunterricht 2016},
pages = {213--216},
publisher = {WTM-Verlag für wissenschaftliche Texte und Medien},
title = {{Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase}},
doi = {http://dx.doi.org/10.17877/DE290R-17376},
year = {2016},
}
@article{8567,
author = {Liebendörfer, Michael and Göller, Robin},
journal = {Mitteilungen der Deutschen Mathematiker-Vereinigung},
keyword = {\_tablet, Abschreiben},
number = {4},
pages = {230--233},
title = {{Abschreiben von Übungsaufgaben in traditionellen und innovativen Mathematikvorlesungen}},
volume = {24},
year = {2016},
}
@inproceedings{8758,
abstract = {In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intelligent cruise control in order to extend the vehicle range, i.e. to minimize energy consumption, by computing the optimal torque profile for a given track. On the one hand, a path-based linear model with strong simplifications regarding the vehicle dynamics is used. On the other hand, a nonlinear model is employed in which the dynamics of the mechanical and electrical subsystem are modeled.},
author = {Eckstein, Julian and Peitz, Sebastian and Schäfer, Kai and Friedel, Patrick and Köhler, Ulrich and Molo, Mirko Hessel-von and Ober-Blöbaum, Sina and Dellnitz, Michael},
booktitle = {Procedia Technology},
issn = {2212-0173},
pages = {465--472},
title = {{A Comparison of two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles}},
doi = {10.1016/j.protcy.2016.08.059},
year = {2016},
}
@phdthesis{33,
abstract = {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.},
author = {Steinle, Tobias},
title = {{Modeling and simulation of metallic, particle-damped spheres for lightweight materials}},
year = {2016},
}
@inproceedings{6570,
author = {Jurgelucks, Benjamin and Claes, Leander},
booktitle = {AD2016 The 7th International Conference on Algorithmic Differentiation},
location = {Christ Church, Oxford, United Kingdom},
pages = {99--102},
title = {{Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation}},
year = {2016},
}
@inproceedings{8759,
abstract = {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.},
author = {Peitz, Sebastian and Gräler, Manuel and Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler, Ansgar},
booktitle = {Procedia Technology},
issn = {2212-0173},
pages = {483--490},
title = {{Multiobjective Model Predictive Control of an Industrial Laundry}},
doi = {10.1016/j.protcy.2016.08.061},
year = {2016},
}
@inproceedings{34,
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},
booktitle = {Progress in Industrial Mathematics at ECMI},
issn = {2212-0173},
pages = {633--641},
publisher = {Springer International Publishing},
title = {{Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control}},
doi = {10.1007/978-3-319-23413-7_87},
volume = {22},
year = {2016},
}
@inbook{8565,
author = {Liebendörfer, Michael and Göller, Robin},
booktitle = {Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2014 Beiträge zum gleichnamigen Symposium am 7. & 8. November 2014 an der Westfälischen Wilhelms-Universität Münster},
editor = {Paravicini, Walther and Schnieder, Jörn},
isbn = {978-3-942197-99-1},
pages = {119--141},
publisher = {WTM-Verlag für wissenschaftliche Texte und Medien},
title = {{Abschreiben - ein Problem in mathematischen Lehrveranstaltungen?}},
year = {2016},
}
@inbook{8558,
author = {Colberg, Christoph and Schürmann, Mirko and Biehler, Rolf and Hochmuth, Reinhard Karl and Schaper, Niclas and Liebendörfer, Michael},
booktitle = {Working Paper Studieneingangsphase Perspektiven aus der Begleitforschung zum Qualitätspakt Lehre},
editor = {Hanft, Anke and Bischoff, Franziska and Prang, Bianca},
pages = {19--22},
publisher = {Carl von Ossietzky Universität Oldenburg},
title = {{Projekt WiGeMath: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase}},
year = {2016},
}
@article{8560,
author = {Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-Georg and Göller, Robin and Hoppenbrock, Axel and Liebendörfer, Michael and Püschl, Juliane},
issn = {1027-488X},
journal = {EMS Newsletter},
number = {102},
pages = {49--50},
title = {{Research in University Mathematics Education: The khdm}},
doi = {10.4171/NEWS/102/14},
volume = {12},
year = {2016},
}
@inproceedings{6569,
author = {Jurgelucks, Benjamin and Claes, Leander},
booktitle = {2nd Seminar on Ferroic Functional Materials & 12th International Workshop on Direct and Inverse Problems in Piezoelectricity},
title = {{Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation}},
year = {2016},
}
@article{1774,
abstract = {In this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.},
author = {Peitz, Sebastian and Dellnitz, Michael},
issn = {1617-7061},
journal = {PAMM},
number = {1},
pages = {613--614},
publisher = {WILEY-VCH Verlag},
title = {{Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction}},
doi = {10.1002/pamm.201510296},
volume = {15},
year = {2015},
}
@article{1769,
abstract = {Große zylindrische Stahlprüflinge werden mittels der Methode der finiten Differenzen im Zeitbereich (engl. finite differences in time domain, FDTD) simulativ untersucht. Dabei werden Pitch-Catch-Messanordnungen verwendet. Es werden zwei Bildgebungsansätze vorgestellt: ersterer basiert auf dem Imaging Principle nach Claerbout, letzterer basiert auf gradientenbasierter Optimierung eines Zielfunktionals.},
author = {Hegler, Sebastian and Statz, Christoph and Mütze, Marco and Mooshofer, Hubert and Goldammer, Matthias and Fendt, Karl and Schwarzer, Stefan and Feldhoff, Kim and Flehmig, Martin and Markwardt, Ulf and E. Nagel, Wolfgang and Schütte, Maria and Walther, Andrea and Meinel, Michael and Basermann, Achim and Plettemeier, Dirk},
journal = {tm - Technisches Messen},
number = {9},
pages = {440--450},
publisher = {Walter de Gruyter},
title = {{Simulative Ultraschall-Untersuchung von Pitch-Catch-Messanordnungen für große zylindrische Stahl-Prüflinge und gradientenbasierte Bildgebung}},
doi = {doi:10.1515/teme-2015-0031},
volume = {82},
year = {2015},
}
@inproceedings{8563,
author = {Liebendörfer, Michael and Hochmuth, Reinhard},
booktitle = {Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education},
editor = {Krainer, Konrad and Vondrová, Nad'a},
publisher = {Charles University in Prague, Faculty of Education and ERME},
title = {{Perceived Autonomy in the First Semester of Mathematics Studies}},
year = {2015},
}
@article{8568,
author = {Braun, Eileen Angélique and Liebendörfer, Michael and Schorcht, Sebastian},
journal = {Mitteilungen der Gesellschaft für Didaktik der Mathematik},
number = {98},
pages = {60--61},
title = {{Initiative Bottom-Up-Nachtreffen zum Doktorandenkolloquium der GDM}},
volume = {41},
year = {2015},
}
@inproceedings{8760,
abstract = {n this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.},
author = {Peitz, Sebastian and Dellnitz, Michael},
booktitle = {PAMM},
issn = {1617-7061},
pages = {613--614},
title = {{Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction}},
doi = {10.1002/pamm.201510296},
year = {2015},
}
@inproceedings{1781,
abstract = {In light of an increasing awareness of environmental challenges, extensive research is underway to develop new light-weight materials. A problem arising with these materials is their increased response to vibration. This can be solved using a new composite material that contains embedded hollow spheres that are partially filled with particles. Progress on the adaptation of molecular dynamics towards a particle-based numerical simulation of this material is reported. This includes the treatment of specific boundary conditions and the adaption of the force computation. First results are presented that showcase the damping properties of such particle-filled spheres in a bouncing experiment.},
author = {Steinle, Tobias and Vrabec, Jadran and Walther, Andrea},
booktitle = {Proc. Modeling, Simulation and Optimization of Complex Processes (HPSC)},
editor = {Bock, Hans Georg and Hoang, Xuan Phu and Rannacher, Rolf and Schlöder, Johannes P.},
isbn = {978-3-319-09063-4},
pages = {233--243},
publisher = {Springer International Publishing},
title = {{Numerical Simulation of the Damping Behavior of Particle-Filled Hollow Spheres}},
doi = {10.1007/978-3-319-09063-4_19},
year = {2014},
}
@inproceedings{8554,
author = {Liebendörfer, Michael and Hochmuth, Reinhard and Kolter, Jana and Schukajlow, Stanislaw},
booktitle = {Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education an the 36th Conference of the North American Chapter of the Psychology of Mathematics Education},
editor = {Nicol, C. and Oesterle, S. and Liljedahl, Peter and Allan, D.},
pages = {153},
publisher = {PME},
title = {{The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers}},
volume = {6},
year = {2014},
}
@inbook{8561,
author = {Liebendörfer, Michael and Hochmuth, Reinhard and Schreiber, Stephan and Göller, Robin and Kolter, Jana and Biehler, Rolf and Kortemeyer, Jörg and Ostsieker, Laura},
booktitle = {Beiträge zum Mathematikunterricht 2014},
editor = {Roth, Jürgen and Ames, J.},
pages = {739--742},
publisher = {WTM-Verlag},
title = {{Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen}},
year = {2014},
}
@inbook{8550,
author = {Liebendörfer, Michael and Ostsieker, Laura},
booktitle = {Mit Werkzeugen Mathematik und Stochastik lernen – Using Tools for Learning Mathematics and Statistics},
editor = {Wassong, Thomas and Frischemeier, Daniel and Fischer, Pascal R. and Hochmuth, Reinhard and Bender, Peter},
isbn = {978-3-658-03103-9 978-3-658-03104-6},
pages = {453--462},
publisher = {Springer Fachmedien Wiesbaden},
title = {{Mathematik als Werkzeug: Sicht- und Arbeitsweisen von Studierenden am Anfang ihres Mathematikstudiums}},
year = {2014},
}
@article{8557,
author = {Liebendörfer, Michael},
journal = {Oberwolfach Reports},
number = {4},
pages = {3132--3135},
title = {{Self-determination and interest development of first-year mathematics students}},
volume = {11},
year = {2014},
}
@inproceedings{8761,
abstract = {In this contribution, the range extension problem of electric vehicles is addressed. To this aim, an intelligent cruise control is developed based on the formulation of an optimal control problem. Solutions of this optimal control problem are energy efficient accelerator pedal position profiles. They can be computed numerically by a direct optimal control method using sequential quadratic programming. The approach is applied to two different driving scenarios. The results show that the energy efficiency is increased by using optimal control for both an artificial and a realistic scenario.},
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},
booktitle = {Procedia Technology},
issn = {2212-0173},
pages = {285--294},
title = {{Development of an Intelligent Cruise Control Using Optimal Control Methods}},
doi = {10.1016/j.protcy.2014.09.082},
volume = {15},
year = {2014},
}
@inbook{8547,
author = {Göller, Robin and Kortemeyer, Jörg and Liebendörfer, Michael and Biehler, Rolf and Hochmuth, Reinhard and Krämer, Jana and Ostsieker, Laura and Schreiber, Stephan},
booktitle = {Beiträge zum Mathematikunterricht 2013: Vorträge auf der 47. Tagung für Didaktik der Mathematik},
editor = {Greefrath, Gilbert},
pages = {360--363},
publisher = {WTM-Verlag},
title = {{Instrumentenentwicklung zur Messung von Lernstrategien in mathematikhaltigen Studiengängen}},
year = {2013},
}
@inbook{8551,
author = {Liebendörfer, Michael and Hochmuth, Reinhard},
booktitle = {Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education},
editor = {Lindmeier, Anke and Heinze, Aiso},
pages = {240},
title = {{Interest and Self-Determination in the Transition to Studying Mathematics}},
volume = {5},
year = {2013},
}
@inproceedings{8549,
author = {Kolter, Jana and Liebendörfer, Michael},
booktitle = {Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr},
pages = {101--102},
title = {{Mathe – nein danke? Interesse im und am Mathematikstudium bei Grundschullehramtsstudierenden mit Pflichtfach}},
year = {2013},
}
@inproceedings{8553,
author = {Liebendörfer, Michael and Hochmuth, Reinhard},
booktitle = {Proceedings of the 8th {Conference} of European Research in Mathematics Education},
editor = {Ubuz, Behiye and Haser, Çiğdem} and Mariotti, Maria Alessandra},
isbn = {978-975-429-315-9},
pages = {2386--2395},
publisher = {Middle East Technical University},
title = {{Interest in Mathematics and the First Steps at the University}},
year = {2013},
}
@inproceedings{3980,
abstract = {
Paper Abstract
High harmonic generation is investigated for a two-band model of a semiconductor nanostructure. Similar to an atomic two-level system, the semiconductor emits high harmonic radiation. We show how one can specifically enhance the emission for a given frequency by applying a non-trivially shaped laser pulse. Therefore, the semiconductor Bloch equations including the interband and additionally the intraband dynamics are solved numerically and the spectral shape of the input pulse is computed via an optimization algorithm. It is demonstrated that desired emission frequencies can be favored even though the overall input power is kept constant. We also suggest special metallic nano geometries to achieve enhanced localized optical fields. They are found by geometric optimization.},
author = {Reichelt, Matthias and Hildebrandt, Andre and Walther, Andrea and Förstner, Jens and Meier, Torsten},
booktitle = {Ultrafast Phenomena and Nanophotonics XVI},
isbn = {9780819489036 },
keyword = {tet_topic_shg},
pages = {82601L},
publisher = {Proc. SPIE 8260},
title = {{Engineering high harmonic generation in semiconductors via pulse shaping}},
doi = {10.1117/12.906338},
year = {2012},
}
@inproceedings{8548,
author = {Liebendörfer, Michael and Hochmuth, Reinhard},
booktitle = {Beiträge zum Mathematikunterricht 2012 : Vorträge auf der 46. Tagung für Didaktik der Mathematik},
pages = {545--548},
publisher = {WTM-Verlag},
title = {{Mathematikinteresse im 1. Studiensemester}},
volume = {1},
year = {2012},
}
@article{8556,
abstract = {We consider the space of complete rank two collineations. Starting from its description as a limit of GIT-quotients of a Grassmanian G(2, n) by a certain {\textbackslash}documentclass\{article\}{\textbackslash}usepackage\{amssymb\}{\textbackslash}begin\{document\}{\textbackslash}pagestyle\{empty\}\${\textbackslash}mathbb \{C\}{\textasciicircum}*\${\textbackslash}end\{document\}-action, we determine the Cox ring by means of toric ambient modifications.},
author = {Hausen, Jürgen and Liebendörfer, Michael},
issn = {1522-2616},
journal = {Mathematische Nachrichten},
number = {8-9},
pages = {974--980},
title = {{The Cox ring of the space of complete rank two collineations}},
doi = {10.1002/mana.201100043},
volume = {285},
year = {2012},
}
@inproceedings{8552,
author = {Biehler, Rolf and Hoppenbrock, Axel and Klemm, Juliane and Liebendörfer, Michael and Wassong, Thomas},
booktitle = {CETL-MSOR Conference 2011},
title = {{Training of student teaching assistants and e-learning via math-bridge – Two projects at the German Centre for Higher Mathematics Education}},
year = {2012},
}
@article{10171,
author = {Steffen, Eckhard},
journal = {Discrete Mathematics},
pages = {2757--2759},
title = {{Nearly nowhere-zero r-flow graphs}},
volume = {312},
year = {2012},
}