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## Absolventen-Seminar • Numerische Mathematik

Verantwortliche Dozenten: | Prof. Dr. Christian Mehl, Prof. Dr. Volker Mehrmann |
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Koordination: | Benjamin Unger, Dr. Matthias Voigt |

Termine: | Do 10:00-12:00 in MA 376 |

Inhalt: | Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen |

Datum | Zeit | Raum | Vortragende(r) | Titel |
---|---|---|---|---|

Do 19.10. | 10:15 Uhr | MA 376 | Vorbesprechung | |

Do 26.10. | 10:15 Uhr | MA 376 | Ines Ahrens | A generalization of the Pantelides algorithm for DAEs with delay [abstract] |

Murat Manguoglu | Parallel Solution of Sparse Underdetermined Linear Least Squares Problems [abstract] | |||

Do 02.11. | 10:15 Uhr | MA 376 | no seminar | |

Do 09.11. | 10:15 Uhr | MA 376 | Philibert Pinkert | Correction of different errors in vehicular probe data to generate high definition maps [abstract] |

Benjamin Unger | Model reduction for linear systems with low-rank switching [abstract] | |||

Do 16.11. | 10:15 Uhr | MA 376 | Riccardo Morandin | Model Hierarchy and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form [abstract] |

Felix Black | Model order reduction for transport phenomena illustrated with the 1D advection equation [abstract] | |||

Do 23.11. | 10:15 Uhr | MA 376 | Marko Hajba | |

Matko Ljulj | ||||

Do 30.11. | 10:15 Uhr | MA 376 | ||

Do 07.12. | 10:15 Uhr | MA 376 | Murat Manguoglu | |

Benjamin Unger | ||||

Do 14.12. | 10:15 Uhr | MA 376 | Matthew Salewski | |

Christian Mehl | ||||

Do 21.12. | 10:15 Uhr | MA 376 | Philipp Schulze | |

Jeroen Stolwijk | ||||

Do 11.01. | 10:15 Uhr | MA 376 | Carlo Cassina | |

Marine Froidevaux | ||||

Do 18.01. | 10:15 Uhr | MA 376 | Arbi Moses Badlyan | |

David Noben | ||||

Do 25.01. | 10:15 Uhr | MA 376 | David Kohn | |

Christoph Zimmer | ||||

Do 01.02. | 10:15 Uhr | MA 376 | Daniel Bankmann | |

Sofia Bikopoulou | ||||

Do 08.02. | 10:15 Uhr | MA 376 | Sarah Hauschild | |

Andres Gonzales Zumba | ||||

Di 15.02. | 10:15 Uhr | MA 376 | Hannes Gernandt | |

Volker Mehrmann |

# Rückblick

- Absolventen Seminar SS 17
- Absolventen Seminar WS 16/17
- Absolventen Seminar SS 16
- Absolventen Seminar WS 15/16
- Absolventen Seminar SS 15
- Absolventen Seminar WS 14/15
- Absolventen Seminar SS 14
- Absolventen Seminar WS 13/14
- Absolventen Seminar SS 13
- Absolventen Seminar WS 12/13
- Absolventen Seminar SS 12
- Absolventen Seminar WS 11/12

### Ines Ahrens (TU Berlin)

Donnerstag, 26. Oktober 2017

** A generalization of the Pantelides algorithm for DAEs with delay**

The strangeness index for DAEs is based on the derivative array, which consists of the system itself plus its time derivatives. Index reduction is performed by selecting certain important equations from the derivative array. In a large-scale setting with high index, this might become computationally infeasible. However, if it is known a priori which equations of the original systems need to be differentiated, then the computational cost can be reduced. One way to determine these equations is by means of the Pantelides algorithm.

If the DAE features in addition a delay term then taking derivatives might not be sufficient and instead, the derivative array must additionally be shifted in time thus increasing the computational complexity even further. In this talk I will explain how one can modify the Pantelides algorithm such that it determines the equations which need to be shifted and/or differentiated. This is joint work with Benjamin Unger.

### Murat Manguoglu (Middle East Technical University)

Donnerstag, 26. Oktober 2017

**Parallel Solution of Sparse Underdetermined Linear Least Squares Problems**

Sparse underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and computational finance. In this talk, we introduce a parallel algorithm for obtaining the minimum 2-norm solution of sparse underdetermined system of equations. The proposed algorithm assumes a generalized banded form where the coefficient matrix has a column overlapped block structure in which the blocks are sparse. The blocks are handled independently by any existing solver and a smaller reduced system is formed and needs to be solved before obtaining the minimum norm solution of the original system in parallel. We implement the proposed algorithm by using the message passing paradigm. We show the parallel scalability of the proposed algorithm and compare it against an existing state-of-the-art solver on both shared and distributed memory platforms. This is a joint work with F. Sukru Torun (Bilkent University) and Cevdet Aykanat (Bilkent University).

### Philibert Pinkert (TU Berlin)

Donnerstag, 09. November 2017

**Correction of different errors in vehicular probe data to generate high definition maps**

High definition maps play an important role in enabling highly automated driving as well as other applications. Since the standard method to generate these maps is rather expensive, we want to create a highway map using the abundantly available sensor data of ordinary vehicles, which are driving on the road for another purpose than generating a map. The drawback about this data is its low precision and other serious errors that need to be corrected first.

One of the errors is a temporal offset between the different sensors. I will show how I correct this offset by minimizing an error function. Another error causes the traces on curvy parts of the road to be farther away from their actual position than on straight parts. I will present my progress on finding a model for this error assuming it is a side effect of the Kalman Filter in the GPS module and fitting it to the data. Finally, I will talk about my ideas on how to generate a map using the corrected sensor data.

### Benjamin Unger (TU Berlin)

Donnerstag, 09. November 2017

**Model reduction for linear systems with low-rank switching**

In this talk we present a new strategy for model reduction of linear switched systems. The main idea is to derive an abstract model without switching - called the envelope system - that is able to reproduce the behavior of the switched system if a suitable feedback is supplied. That advantage of this formalism is that one can use standard MOR techniques. Moreover, the envelope system has a physical interpretation that describes the energy that comes with switching between different models. If additionally the subsystems of the switched system are port-Hamiltonian systems, that this structure can be preserved in the reduced model. This talk describes joint work with Philipp Schulze (TU Berlin).

### Riccardo Morandin (TU Berlin)

Donnerstag, 16. November 2017

**Model Hierarchy and Synchronicity Analysis of Power Network Models in Port-Hamiltonian form **

In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an important task that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model.

In this talk we present the first draft of a model hierarchy for power networks. In particular, we present a new energy-based formulation of the Kuramoto model as port-Hamiltonian system of differential-algebraic equations. This leads to a very robust representation of the system with respect to disturbances, and it encodes the underlying physics, such as the dissipation inequality or the deviation from synchronicity, directly in the structure of the equations.

This talk describes joint work with Volker Mehrmann (TU Berlin), Simona Olmi (TU Berlin) and Eckehard Schöll (TU Berlin).

### Felix Black (TU Berlin)

Donnerstag, 16. November 2017

**Model Order Reduction for transport phenomena illustrated with the 1D advection equation**

In many physical applications such as thermodynamics and fluid dynamics, transport phenomena are observed. Transport phenomena usually describe the advection of mass, energy, or other physical quantities without diffusion. Unfortunately, they also present a challenge for classical model order reduction (MOR) techniques, in cases where the solution exhibits high gradients, e.g., a shock.

The goal of my master thesis is to analyse and compare MOR techniques that are tailored to advection-dominated problem models by means of the 1D wave equation and the 1D Burgers' equation. In this talk, we will instead use the 1D advection equation, for simplicity, and investigate some of the MOR techniques which will be considered later in the thesis.

The methods under investigation are

(1) a modified version of Proper Orthogonal Decomposition (POD) that is able to preserve port-Hamiltonian structure,

(2) a symmetry reduction approach, and

(3) an extended finite element method (XFEM).

The effectiveness of the methods will be demonstrated via numerical examples.