@article{16964,
author = {Hochmuth, Reinhard and Liebendörfer, Michael and Biehler, Rolf and Eichler, Andreas},
journal = {Neues Handbuch Hochschullehre},
pages = {117--138},
title = {{Das Kompetenzzentrum Hochschuldidaktik Mathematik (khdm)}},
volume = {95},
year = {2020},
}
@article{16965,
author = {Schürmann, Mirko and Schaper, Niclas and Liebendörfer, Michael and Biehler, Rolf and Lankeit, Elisa and Hochmuth, Reinhard and Ruge, Johanna and Kuklinski, Christiane},
journal = {dghd-Newsletter},
pages = {25--29},
title = {{Ein Kurzbericht aus dem Forschungsprojekt WiGeMath-Lernzentren als Unterstützungsmaßnahme für mathematikbezogenes Lernen in der Studieneingangsphase}},
volume = {01/2020},
year = {2020},
}
@inbook{17994,
abstract = {In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.},
author = {Gerlach, Raphael and Ziessler, Adrian},
booktitle = {Advances in Dynamics, Optimization and Computation},
editor = {Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin},
isbn = {9783030512637},
issn = {2198-4182},
pages = {55--85},
publisher = {Springer},
title = {{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}},
doi = {10.1007/978-3-030-51264-4_3},
volume = {304},
year = {2020},
}
@article{19938,
abstract = {We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of the breaking of umbilic bifurcations by nonysmplectic integrators. We discover extra structure induced from certain types of boundary value problems, including classical Dirichlet problems, that is useful to locate bifurcations. Geodesics connecting two points are an example of a Hamiltonian boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator that easily computes geodesics and their bifurcations. Finally, we study the periodic pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian systems. It is not preserved by either symplectic on nonsymplectic integrators, but in some circumstances symplecticity greatly reduces the error. },
author = {McLachlan, Robert I and Offen, Christian},
journal = {Foundations of Computational Mathematics},
number = {6},
pages = {1363--1400},
title = {{Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation}},
doi = {10.1007/s10208-020-09454-z},
volume = {20},
year = {2020},
}
@article{10595,
abstract = {In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.},
author = {Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael},
issn = {0925-5001},
journal = {Journal of Global Optimization},
number = {4},
pages = {891--913},
title = {{On the hierarchical structure of Pareto critical sets}},
doi = {10.1007/s10898-019-00737-6},
volume = {73},
year = {2019},
}
@inproceedings{13107,
abstract = {In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.},
author = {Schumacher, Jan and Rezat, Sebastian},
booktitle = {Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)},
editor = {Jankvist, Uffe Thomas and Van den Heuvel-Panhuizen, Marja and Veldhuis, Michiel},
keyword = {diagrammatic reasoning, hypothetical learning trajectory, induction extrapolatory method, integers, negative numbers, permanence principle, semiotics},
location = {Utrecht},
publisher = {Freudenthal Group & Freudenthal Institute, Utrecht University and ERME},
title = {{A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers}},
year = {2019},
}
@inbook{16966,
author = {Kuklinski, Christiane and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Lankeit, Elisa and Leis, Elena and Schürmann, Mirko},
booktitle = {Proceedings of {CERME} 11},
title = {{Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students}},
year = {2019},
}
@book{13139,
editor = {Rezat, Sebastian and Fan, Lianghuo and Hattermann, Mathias and Schumacher, Jan and Wuschke, Holger},
location = {Paderborn},
pages = {392},
publisher = {Universitätsbibliothek Paderborn},
title = {{Proceedings of the Third International Conference on Mathematics Textbook Research and Development: 16-19 September 2019 Paderborn, Germany}},
doi = {10.17619/UNIPB/1-768},
year = {2019},
}
@unpublished{16296,
abstract = {Multiobjective optimization plays an increasingly important role in modern
applications, where several objectives 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 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 as
is the case for models governed by partial differential equations (PDEs). To
decrease the numerical effort to an affordable amount, surrogate models can be
used to replace the expensive PDE evaluations. Existing multiobjective
optimization methods using model reduction are limited either to low parameter
dimensions or to few (ideally two) objectives. In this article, we present a
combination of the reduced basis model reduction method with a continuation
approach using inexact gradients. The resulting approach can handle an
arbitrary number of objectives while yielding a significant reduction in
computing time.},
author = {Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan},
booktitle = {arXiv:1906.09075},
title = {{ROM-based multiobjective optimization of elliptic PDEs via numerical continuation}},
year = {2019},
}
@article{16708,
abstract = { In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to
the computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.
To this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for
the computation of such objects of finite dimensional systems with the results obtained in the work
of Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis
of partial differential equations and illustrate its feasibility by computing unstable manifolds of the
one-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential
equation.
},
author = {Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael},
issn = {1536-0040},
journal = {SIAM Journal on Applied Dynamical Systems},
pages = {1265--1292},
title = {{The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}},
doi = {10.1137/18m1204395},
year = {2019},
}