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Numerische MathematikAbsolventen Seminar SS 19

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Absolventen-Seminar • Numerische Mathematik

Absolventen-Seminar
Verantwortliche Dozenten:
Prof. Dr. Christian MehlProf. Dr. Volker Mehrmann
Koordination:
Ines Ahrens
Termine:
Do 10:00-12:00 in MA 376
Inhalt:
Vorträge von Bachelor- und Masterstudenten, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen
Sommersemester 2019 Vorläufige Terminplanung
Datum
Zeit
Raum
Vortragende(r)
Titel
Do 11.04.
10:15
Uhr
MA 376
no seminar
Do 18.04.
10:15
Uhr
MA 376
Vorbesprechung
Benjamin Unger
Feedback regularization of DAEs via delays [abstract]
Do 25.04.
10:15 Uhr
MA 376
Volker Mehrmann
Numerical analysis of finite element systems modeling elastic stents [abstract]
Do 02.05.
10:15
Uhr
MA 376
Christoph Zimmer
On the solvability of port-Hamiltonian partial differential equation with linear constraints  [abstract]
Paul Van Dooren
Role modeling using a low rank similarity matrix [abstract]
Do 09.05.
10:15
Uhr
MA 376
Michal Wojtylak
The gap distance between linear pencils [abstract]
Paul Schwerdtner
Structure Preserving or Realization Independent H-infinity Approximation [abstract]
Do
16.05.
10:15
Uhr
MA 376
Ninoslav Truhar
On an Eigenvector-Dependent Nonlinear Eigenvalue Problem from Perspective of Relative Perturbation Theory [abstract]
Dorothea Hinsen
A modeling of a power network with the telegraph equations [abstract]
Do
23.05.
10:15
Uhr
MA 376
Jennifer Przybilla
Model Reduction of Differential-Algebraic Systems by Parameter-Dependent Balanced Truncation [abstract]
Riccardo Morandin
Energy-based hierarchical modeling of power networks [abstract]
Do 30.05.
10:15
Uhr
MA 376
no seminar
Do 06.06.
10:15
Uhr
MA 376
Pia Marie Lutum
Michelle Stahl
Do 13.06.
10:15
Uhr
MA 376
Serhiy Yanchuk


Daniel Bankmann
Do 20.06.
10:15
Uhr
MA 376
Philipp Schulze
Philipp Krah
Do 27.06.
10:15 Uhr
MA 376
Marine Froidevaux
Arbi Moses Badlyan
Do 04.07.
10:15
Uhr
MA 376
Ines Ahrens
Felix Black
Do 11.07.
10:15
Uhr
MA 376

Abstracts zu den Vorträgen:

Jennifer Przybilla (TU Berlin)

Donnerstag, 23. Mai 2019

Model Reduction of Differential-Algebraic Systems by Parameter-Dependent Balanced Truncation

In this talk we will deal with the application of balanced truncation for parameter-dependent differential-algebraic systems. For this, we have to solve parameter-dependent Lyapunov equations, which we do with the help of the reduced-basis method. In order to use this method, we first have to deal with the algebraic parts of the system and make the system strictly dissipative in order to apply error estimators in the reduced basis method.

Riccardo Morandin (TU Berlin)

Donnerstag, 23. Mai 2019

Energy-based hierarchical modeling of power networks

Recent developments in the energy market require new mathematical models and suitable algorithms for the efficient usage of the existing networks. Starting from these real-world problems, it is necessary to concentrate on methods for large-scale energy networks and, in particular, address optimization and stability analysis, model predictive control, model-order reduction, uncertainty quantification, and related topics on energy networks. The abstract setting allows for consideration of applications arising from both, gas and power networks.


Our framework of choice is the one of port-Hamitlonian descriptor systems, or pHDAEs. These are energy-based equations with a special structure, that guarantees several beneficial properties, e.g. inherent stability and passivity, physical interpretation of variables, simple interconnection, structure-preserving model reduction, robust numerical integration and simplification of feedback stabilization.


In this talk we present a model hierarchy for some components of a power grid, specifically synchronous generators and transmission lines, where all equations presented are pHDAEs. Furthermore, we show how these components can be easily interconnected to form a larger network, while preserving the port-Hamiltonian structure. To do so, we apply Kirchhoff's laws and exploit the common structure of the electrical components, in a way that can be easily extended to other devices and more complex models.

Dorothea Hinsen (TU Berlin)

Donnerstag, 16. Mai 2019

A modeling of a power network with the telegraph equations

In recent years energy transition and the increasing electricity demand have led to growing interest in modeling power networks, which withstand unexpected occurrences as voltage or transient instabilities.

One way to approach modeling power networks is with port-Hamiltonian systems.

The power networks we are dealing with consist of generators, loads and transmission lines.

In this talk we discuss an approach to a power network model, where the generators and the loads are described with port-Hamiltonian equations.

However, the transmission lines are depicted with the telegraph equations. This leads us to a PDAE model, which we will discuss.

Ninoslav Truhar (Josip Juraj Strossmayer University of Osijek)

Donnerstag, 16. Mai 2019

On an Eigenvector-Dependent Nonlinear Eigenvalue Problem from Perspective of Relative Perturbation Theory

The talk contains two part. I the first part we consider the eigenvector-dependent nonlinear eigenvalue problem (NEPv) H(V) V = V Λ, where H(V) ∈ Cn,n is an Hermitian matrix-valued function of V ∈ Cn,k with orthonormal columns, i.e., VH V = Ik, k < n (usually k ≪ n). We present the conditions on existence and uniqueness for the solvability of NEPv using the well known results of the relative perturbation theory. Our results are motiveted by the results on NEPv presented in Y. Cai, L.-H. Zhang, Z. Bai, and R.-C. Li, On an eigenvector-dependent nonlinear eigenvalue problem, SIAM J. Matrix Anal. Appl. 2018, where among the other results one can find conditions for existence and uniqueness for the solvability of an NEPv. These results are based on well-known standard perturbation theory for Hermitian matrices. The differences between so called standard perturbation theory approach, and our new (relative perturbation theory) approach have been illustrated in several numerical examples.

In the second part we present an upper and a lower bound for the the Frobenius norm of the matrix sin(Θ), of the sines of canonical angles between unperturbed and perturbed eigenspaces of a regular generalized Hermitian eigenvalue problem A x = λ B x  where A and B are Hermitian n × n matrices, under a feasible non Hermitian perturbation. As one application of the obtained bounds we present the corresponding upper and the lower bounds for eigenspaces of a matrix pair (A,B) obtained by a linearization of regular quadratic eigenvalue problem ( λ2 M + λ D + K ) u = 0, where M is positive definite and D and K are semidefinite. We also apply obtained upper and lower bounds to the important problem which considers the influence of adding a damping on mechanical systems. The new results show that for certain additional damping the upper bound can be too pessimistic, but the lower bound can reflect a behaviour of considered eigenspaces properly.

Michal Wojtylak (Jagiellonian University, Krakow)

Donnerstag, 09. Mai 2019

The gap distance between linear pencils

We introduce a new distance between linear pencils, which is based on their graphs ker[A,-E]. Several basic properties of this distance will be shown. Next, we will formulate the problem of distance to singularity and compare it with the original one given by Byers, He and Mehrmann in 1998. The talk is based on a joint work: Berger, Gernandt, Trunk, Winkler, MW, LAA 2019.

Paul Schwerdtner (TU Berlin)

Donnerstag, 09. Mai 2019

Structure Preserving or Realization Independent H-infinity Approximation

In this talk we revisit linorm_subsp, an algorithm that is used to compute the H-infinity norm of transfer functions of large-scale dynamical systems and show how it can be made more efficient for irrational transfer functions using an inner loop outer loop strategy.
Then, we present a greedy interpolation approach to address the H-infinity model order reduction problem that is using the evaluation of the H-infinity norm computation provided by linorm_subsp.
Starting from an initial reduced order model, we compute the H-infinity norm of the error transfer function and then place an new interpolation point where this H-infinity norm is attained. In this way, we construct a sequence of reduced order models aiming at minimizing the H-infinity norm of the error transfer function.
Using interpolation for this allows to either preserve the given model structure or construct surrogate models with a structure defined by the user to approximate the given system, respectively.

Christoph Zimmer (TU Berlin)

Donnerstag, 02. Mai 2019

On the solvability of port-Hamiltonian partial differential equation with linear constraints 

Through its natural approach of energy as underlying quantity and its many nice properties, port-Hamiltonan (pH) systems rose as a popular modeling tool for dynamical system like electrical, mechanical, and hydrodynamical ones. Therefore, it is not surprising that the concept was extended to non-autonomous systems, to descriptor systems and to infinite dimensional systems. In this talk, we investigate non-autonomous semi-explicit pH descriptor systems. Mainly focusing on the existence of solution, we will start with finite dimensional systems. Afterwards, we will transfer the used tricks to the infinite dimensional case and prove the existence of solutions as well as their smoothness.

Paul Van Dooren (Catholic University of Louvain)

Donnerstag, 02. Mai 2019

Role modeling using a low rank similarity matrix

Community detection is a popular approach used analyze large  networks and obtain relevant statistical properties by finding  community structures in networks. However, community detection  algorithms cannot be used to find non-community structures in  networks, such as cyclic graph structures which appear in food  web networks. The role extraction problem represents large  networks by a smaller, general graph structure, called role  graphs. In this presentation, we analyze the neighborhood  pattern similarity measure used to solve the role extraction  problem. We show theoretically that under certain assumptions  the role graphs can be recovered from a low-rank factorization  of the similarity matrix due to the relationship between the  dominant eigenvalues of the similarity matrix and the number of  roles. We also show how it applies to the detection of  overlapping communities and bipartite communities.

Volker Mehrmann (TU Berlin)

Donnerstag, 25. April 2019

 Numerical analysis of finite element systems modeling elastic stents

A new model description for the numerical simulation of elastic stents is proposed. Based on the new formulation an inf-sup inequality for the finite element discretization is proved and the proof of the inf-sup inequality for the continuous problem is simplified. The new formulation also leads to faster simulation times despite an increased number of variables. The techniques also simplify the analysis and numerical solution of the evolution problem describing the movement of the stent under external forces. The results are illustrated via numerical examples, see [1].

[1] L. Grubišić, M. Ljulj, V. Mehrmann, and J. Tambača, Modeling and discretization methods for the numerical simulation of elastic stents, arxiv.org/1812.10096, Preprint 01-2019, Institute of Mathematics, TU Berlin, submitted for publication, 2019.

Benjamin Unger (TU Berlin)

Donnerstag, 18. April 2019

Feedback regularization of DAEs via delays

We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations arise naturally, if a feedback controller is applied to a descriptor system, since the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise smooth distributions and an algorithm to determine whether a DDAE is delay-regular. As a consequence, we show that a DAE can be regularized by a feedback if and only if it can be regularized by a delayed feedback. This is joint work with Stephan Trenn (University of Groningen).

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