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## Colloquium of the Modeling, Numerics, Differential Equations Group

Responsible Persons: | All Professors of the Modeling • Numerics • Differential Equations Group |
---|---|

Coordination: | Dr. Philipp Petersen, Mones Raslan |

Dates: | Tue 16-18 Uhr in MA 313 and by appointment |

Content: | Talks by visitors and sometimes also our faculty on current resesarch topics |

Contact: | kolloquium-mnd@math.tu-berlin.de |

### Description

The colloquium of the Modeling, Numerics, Differential Equations Group at the institute of mathematics is a conventional colloquium attracting a broad audience consisting of professors and research assistants of all associated work groups, in particular applied functional analysis, numerical linear algebra, and partial differential equations. Graduate students are also attending the colloquium.

For these reasons we look forward to talks aimed at non-specialists that can be be enjoyed by graduate students.

Datum date | Zeit time | Raum room | Vortragende(r) speaker | Titel title | Einladender invited by |
---|---|---|---|---|---|

23.10.2018 | 16:15 | MA 313 | Ronald W. Hoppe (Universität Augsburg / University of Houston) Rolf D. Grigorieff | Numerical Solution of Second and Fourth Order Total Variation Flow Problems | Kolloquium zum 80. Geburtstag von Rolf D. Grigorieff |

06.11.2018 | 16:15 | MA 313 | Robert Calderbank (Duke University) | Golay, Heisenberg and Weyl | G. Kutyniok |

13.11.2018 | 16:15 | MA 313 | David Šiška (University of Edinburgh) | Exponential Convergence of Policy Improvement Algorithm for Controlled Diffusions | E. Emmrich |

04.12.2018 | 16:15 | MA 313 | María Soledad Aronna (Escola de Matemática Aplicada Rio de Janeiro) | On second order optimality conditions for control-affine problems | F. Tröltzsch |

08.01.2019 | 16:15 | MA 313 | Herbert Egger (TU Darmstadt) | On the systematic approximation of evolution problems with dissipation, Hamiltonian, or gradient structure | V. Mehrmann |

15.01.2019 | 16:15 | MA 313 | |||

22.01.2019 | 16:15 | MA 313 | Volker Mehrmann (TU Berlin) | Stability through structure for port-Hamiltonian differential-algebraic systems | B. Zwicknagl |

29.01.2019 | 16:15 | MA 313 | Paul Kotyczka (TU München) | Discrete-time port-Hamiltonian systems: A definition based on symplectic integration | V. Mehrmann |

05.02.2019 | 16:15 | MA 313 | Raphael Kruse (TU Berlin) | On randomized time-stepping methods for non-autonomous evolution equations with time-irregular coefficients | M. Voigt |

12.02.2019 | 16:15 | MA 313 | Heiner Olbermann (UC Louvain) | Paper crumpling - at the crossroads of differential geometry, calculus of variations and materials science | B. Zwicknagl |

## Rückblick

- Kolloquium ModNumDiff Sommer 2018
- Kolloquium ModNumDiff Winter 2017/2018
- Kolloquium ModNumDiff Sommer 2017
- Kolloquium ModNumDiff Winter 2016/17
- Kolloquium ModNumDiff Sommer 2016
- Kolloquium ModNumDiff Winter 2015/16
- Kolloquium ModNumDiff Sommer 2015
- Kolloquium ModNumDiff Winter 2014/15
- Kolloquium ModNumDiff Sommer 2014
- Kolloquium ModNumDiff Winter 2013/14
- Kolloquium ModNumDiff Sommer 2013
- Kolloquium ModNumDiff Winter 2012/13
- Kolloquium ModNumDiff Sommer 2012
- Kolloquium ModNumDiff Winter 2011/12
- Kolloquium ModNumDiff Sommer 2011

# Abstracts

**Ronald W. Hoppe ****(Universität Augsburg / University of Houston)**

Numerical Solution of Second and Fourth Order Total Variation Flow Problems

**María Soledad Aronna (Escola de Matemática Aplicada Rio de Janeiro)**

In this talk I will present the main features of first and second order optimality conditions for optimal control problems of ordinary differential equations that are affine with respect to the control and nonlinear with respect to the state. Assuming the presence of control constraints, I will present a second order sufficient condition for optimality and a numerical scheme in the form of a shooting method.

**David Siska (University of Edinburgh)**

*Exponential Convergence of Policy Improvement Algorithm for Controlled Diffusions*

In this talk I will present the main features of first and second order optimality conditions for optimal control problems of ordinary differential equations that are affine with respect to the control and nonlinear with respect to the state. Assuming the presence of control constraints, I will present a second order sufficient condition for optimality and a numerical scheme in the form of a shooting method.

**Herbert Egger (TU Darmstadt)**

*On the systematic approximation of evolution problemswith dissipation, Hamiltonian, or gradient structure.*

A general framework for the numerical approximation of evolution

problems is presented that allows

to preserve an underlying dissipative, Hamiltonian, or gradient

structure. The approach is based on rewriting

the evolution problem in a particular form that complies with the

underlying structure and its variational

formulation. The underlying structure is then preserved automatically

under Galerkin projection in space,

which allows to deduce important structural properties for appropriate

discretization schemes including

projection based model reduction methods.

For the time-discretization, we consider two different approaches

depending on the underlying geometric

structure, i.e., discontinuous Galerkin and Petrov-Galerkin

approximations. Again, the basic structure of

the problem is inherited automatically by the proposed discretization

schemes.

The presented framework is rather general and allows the numerical

approximation of a wide range of applications,

including nonlinear partial differential equations and port-Hamiltonian

systems. Several examples will be discussed

for illustration and some connections to other discretization approaches

will be revealed.