Inhalt des Dokuments
AbsolventenSeminar • Numerische Mathematik
Verantwortliche Dozenten: 
Prof. Dr. Christian Mehl [1], Prof. Dr. Volker Mehrmann
[2] 

Koordination:  Ines
Ahrens [3] 
Termine: 
Do 10:0012:00 in MA 376 
Inhalt:  Vorträge von
Bachelor und Masterstudenten, Doktoranden, Postdocs und manchmal auch
Gästen zu aktuellen
Forschungsthemen 
Datum  Zeit  Raum  Vortragende(r)  Titel 

Do 17.10.  10:15 Uhr  MA 376  Vorbesprechung  
Do 24.10.  11:00 Uhr  MA
376  Paula Klimczok  Classification of TwoVariable Linear Differential
Equations with Large Delays 
Do 31.10.  10:15 Uhr  MA 376  Onkar Jadhav  Model order reduction for parametric high dimensional
interest rate models in the analysis of financial
risk 
Christian Mehl
[4]  Distance problems for dissipative
Hamiltonian pencils and related matrix polynomials  
Do 07.11.  10:15 Uhr  MA 376  
Do 14.11.  10:15 Uhr  MA 376  Julianne Chung  Computational
Methods for Large and Dynamic Inverse Problems 
Matthias Chung  Sampled Limited Memory Methods for Least Squares Problems
with Massive Data  
Do
21.11.  10:15 Uhr  MA
376  
Do 28.11.  10:15 Uhr  MA 376  Volker Mehrmann [5]  Stability
analysis of dissipative Hamiltonian differentialalgebraic
systems 
Do
05.12.  10:15 Uhr  MA
376  Rebekka Beddig  H_2 x L_infoptimal model reduction 
Do 12.12.  10:15 Uhr  MA 376  Christoph Zimmer  Exponential
Integrators for SemiLinear Parabolic Problems with Linear Constraints

Paul Schwerdtner
[6]  Robust Control for Large Sparse
Systems  
Do
19.12.  10:15 Uhr  MA
376  Attila Karsai  Computation of the Distance to Instability for Large Scale
Systems 
Benjamin
Unger  Semiexplicit Discretization Schemes
for WeaklyCoupled EllipticParabolic Problems  
Do 09.01.  10:15 Uhr  MA 376  Benjamin Unger  Nonlinear Galerkin Model Reduction for Systems with
Multiple Transport Velocities 
Do 16.01.  10:15 Uhr  MA 376  Karim Cherifi  Data driven Port
Hamiltonian realizations 
Do 23.01.  10:15 Uhr  MA 376  Philipp Krah
[7]  Wavelet Adaptive Proper Orthogonal
Decomposition with Application to Insects Flight 
Do 30.01.  10:15 Uhr  MA 376  Dorothea Hinsen  A
portHamiltonian approach for the modeling of power networks including
the telegraph equations 
Do 06.02.  10:15 Uhr  MA 376  Ines Ahrens
[8]  A success check for structural analysis
applied to delay DAEs 
Do 13.02.  10:15 Uhr  MA 376  Marine Froidevaux
[9]  PDE eigenvalue iterations with
applications in twodimensional photonic crystals 
Felix Black  Dealing with computational complexity in the shifted POD
reduced order model  
Do 27.02.  10:15 Uhr  MA 376  Pieter
Appeltans  Computing the robust (strong)
H_{∞}norm of uncertain timedelay systems 
Rückblick
 Absolventen Seminar SS 19 [10]
 Absolventen Seminar WS 18/19 [11]
 Absolventen Seminar SS 18 [12]
 Absolventen Seminar WS 17/18 [13]
 Absolventen Seminar SS 17 [14]
 Absolventen Seminar WS 16/17 [15]
 Absolventen Seminar SS 16 [16]
 Absolventen Seminar WS 15/16 [17]
 Absolventen Seminar SS 15 [18]
 Absolventen Seminar WS 14/15 [19]
 Absolventen Seminar SS 14 [20]
 Absolventen Seminar WS 13/14 [21]
 Absolventen Seminar SS 13 [22]
 Absolventen Seminar WS 12/13 [23]
 Absolventen Seminar SS 12 [24]
 Absolventen Seminar WS 11/12 [25]
Pieter Appeltans (KU Leuven)
Donnerstag, 27. Februar 2020
Computing the robust (strong) H_{∞}norm of uncertain timedelay systems
The relation between the Hinfinity norm and the distance to
instability is well known for linear time invariant state space models
with ordinary differential equations. In this talk I will extend this
result by showing that the robust (strong) Hinfinity norm of state
space models with discrete time delays and realvalued uncertainties
is related to the distance to instability of an associated singular
delay eigenvalue problem. Special attention will be paid to the
potential sensitivity of the Hinfinity norm of time delay systems
with respect to infinitesimal small perturbations on the delays. The
aforementioned relation is subsequently employed in a novel algorithm
for computing the robust strong Hinfinity norm of uncertain time
delay systems.
Marine Froidevaux (TU Berlin)
Donnerstag, 13. Februar 2020
PDE eigenvalue iterations with
applications in twodimensional photonic crystals
We consider PDE eigenvalue problems as they occur in the modeling of
twodimensional photonic crystals. In particular we consider different
models for the permittivity of the materials and discuss how to deal
with the occurring nonlinearities in the eigenvalue. Further, we
extend known iterative methods, the inverse power method as well as
the Newton iteration, to the infinitedimensional case and combine
them with adaptive mesh refinement to obtain substantial computational
speedups.
This is joint work with Robert Altmann (U
Augsburg).
Felix Black (TU Berlin)
Donnerstag, 13. Februar 2020
Dealing with computational
complexity in the shifted POD reduced order model
The proper orthogonal decomposition (POD) often fails to produce
lowdimensional surrogate models if the full order model exhibits
advective transport. The shifted POD remedies this problem by
introducing transformation operators that allow the modes to adapt to
the advection. The transformations are parametrized by timedependent
paths such that the projection onto the corresponding manifold leads
to an inherently nonlinear reducedorder model (ROM). The evaluation
of the ROM requires evaluations that scale with the original size of
the full order model, thus negating the potential speedup gained by
the lowrank description. In this talk, we discuss ideas of dealing
with the added computational complexity introduced by the shifted
POD.
Ines Ahrens (TU Berlin)
Donnerstag, 06. Februar 2020
A success check for structural analysis applied to delay DAEs
The solution of a delay differentialalgebraic equation (DDAE) may
depend on derivatives and future evaluations of some of its equations.
It is ubiquitous for theoretical and numerical aspects to understand
which equations need to be differentiated and/or shifted how
many times. Structural analysis determines the needed number of
differentiations and shifts. However, this method can fail and thus a
success check is necessary. In this talk, I will present ongoing
research how one can onstruct such a success check for DDAEs.
Dorothea Hinsen (TU Berlin)
Donnerstag, 30. Januar 2020
A portHamiltonian approach for the modeling of power networks including the telegraph equations
In recent years energy transition and the increasing electricity
demand have led to growing interest in modeling power networks, which
have to withstand unexpected contingencies as voltage or transient
instabilities. One way to approach modeling power networks is with
portHamiltonian 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 portHamiltonian
equations. However, the transmission lines are modeled
differentialalgebraic by the telegraph equations. This leads us to a
PDAE model, which we will discuss. In the end we will then combine
each component into one global portHamiltonian PDAE
model.
Philipp Krah (TU Berlin)
Donnerstag, 23. Januar 2020
Wavelet Adaptive Proper Orthogonal Decomposition with Application to Insects Flight
In this talk I will present some new results of the wavelet
adaptive proper orthogonal decomposition (wPOD). Given numerical or
experimental data, U = {u(x, μ_1 ), . . . , u(x, μ_N )} with u(·,
μ) : Ω → R^K, the wPOD combines a sparse representation of u in
the spatial domain Ω ⊂ R^d (d ∈ {2, 3}), using wavelet adaptation
methods, with the proper orthogonal decomposition, a well known model
order reduction technique to approximate the μdependence with a few
basis functions φ_n(x). The framework is well suited for experimental
methods like Particle Image Velocimetry or Direct Numerical
Simulations which are highly resolved in space and sampled with a
moderate number of parameters μ.
In my talk, I will
introduce the snapshot POD, which is the foundation of my algorithm
and explain the wavelet adaptation techniques. Furthermore, I will
explain the error estimation and present numerical results for
the flow around a cylinder (d=2) and the flight of a bumblebee (d=3).
Karim Cherifi (MPI Magdeburg)
Donnerstag, 16. Januar 2020
Data driven Port Hamiltonian realizations
Port Hamiltonian systems have gained a lot of attention in recent years due their interesting properties in modelling and control. They are particularly interesting for systems interconnection since they preserve their port Hamiltonian structure. However, to be able to benefit from this structure, one has to model the system in Port Hamiltonian framework. In this talk, we focus on the construction of minimal realizations of linear timeinvariant (LTI) portHamiltonian (pH) systems.The goal is to be able to compute the port Hamiltonian minimal realization directly from time domain input/output data of the system.
Benjamin Unger (TU Berlin)
Donnerstag, 09. Januar 2020
Nonlinear Galerkin Model Reduction for Systems with Multiple Transport Velocities
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs timedependent transformation operators and, especially, generalizes MFEM to arbitrary basis functions. The new framework is suitable to obtain a lowdimensional approximation with small errors even in situations when the Kolmogorov nwidths do not decay exponentially. In such cases, classical model order reduction techniques require much higher dimensions for a similar approximation quality. In this talk, we discuss the existence of optimal modes and the construction of the reduced order model. If time permits, we discuss aposteriori error estimation and the close connection to the symmetry reduction framework. The talk describes joint work with F. Black und P. Schulze (both TU Berlin).
Attila Karsai (TU Berlin)
Donnerstag, 19. Dezember 2019
Computation of the Distance to Instability for Large Scale Systems
Although dissipative Hamiltonian systems often are asymptotically stable in theory, in practice truncation and model errors can introduce perturbations such that this property is lost while the DH structure is kept. Without asymptotic stability, arbitrarily small perturbations can make these systems unstable. To cope with this problem, the stability analysis must focus on robust stability. In this talk, an overview of the computation of the distance to instability of dissipative Hamiltonian systems with focus on large scale systems is given. Further, techniques to speed up the computation are presented.
Benjamin Unger (TU Berlin)
Donnerstag, 19. Dezember 2019
Semiexplicit Discretization Schemes for WeaklyCoupled EllipticParabolic Problems
We study the timediscretization of an ellipticparabolic problem that is weakly coupled. This setting includes poroleasticity, thermoelasticity, as well as multiplenetwork models used in medical applications. We propose a semiexplicit Euler scheme in time combined with a finite element discretization in space, which decouples the system such that each time step requires the solution of two small and wellstructured linear systems rather than the solution of one large system. The decoupling improves the computational efficiency without decreasing the convergence rates. Our convergence proof is based on an interpretation of the scheme as an implicit method applied to a constrained partial differential equation with delay term. Here, the delay time equals the used step size. This connection also allows a deeper understanding of the weak coupling condition, which we accomplish to quantify explicitly.
Christoph Zimmer (TU Berlin)
Donnerstag, 12. Dezember 2019
Exponential Integrators for SemiLinear Parabolic Problems with Linear Constraints
Exponential integrators provide a powerful tool for the time
integration of spatial discretized partial differential equations
(PDEs), by allowing large time steps even for very restrictive CFL
conditions. On the other hand, the class of PDEs with additional
underling constraints (PDAEs) includes applications such as PDEs with
dynamical boundary conditions or the incompressible NavierStokes
equations.
In this talk, we construct and analyze exponential
integrators for semilinear parabolic PDAEs. Starting with semilinear
ordinary differential equations we explain the main idea behind
exponential integrators. Afterwards, we extend this idea to
differentialalgebraic equations and PDAEs. The resulting schemes only
require the solution of linear stationary saddle point problems in
each time step. Further, no linearization steps or regularizations of
the transient system are needed. The talk concludes with numerical
examples.
This is joint work with Robert Altmann.
Paul Schwerdtner (TU Berlin)
Donnerstag, 12. Dezember 2019
Robust Control for Large Sparse Systems
We present our ongoing work on the fixedorder robust controller
synthesis problem for large and sparse systems.
Fixedorder
methods in controller design use gradientbased optimization to
compute controllers, that minimize the Hinfinity norm of the
resulting closedloop transfer function. This requires many
computations of the Hinfinity norm of the different closedloop
transfer functions which is computationally demanding in the large
scale case.
We show, how the recently developed software
linorm_subsp for the computation of the Hinfinity norm can be
extended when used within an optimization loop to design fixedorder
controllers, efficiently.
However, linorm_subsp only converges to
a local maximum a given transfer function. Hence, the Hinfinity norm
is not always computed correctly. Therefore, we propose to complement
linorm_subsp with global certification to circumvent this problem and
give insights into the implementation of a global
certificate.
Rebekka Beddig (TU Berlin)
Donnerstag, 05. Dezember 2019
H_2 x L_infoptimal model reduction
In this talk, we discuss H_2 x L_infoptimal model reduction of parametric linear timeinvariant systems. The H_2 x L_inf error is defined as the maximum H_2error in the transfer function within a feasible parameter domain. We start with the computation of the H_2 x L_infnorm using Chebychev interpolation. The next step is to minimize the error with nonsmooth constrained optimization. For the optimization process we use a gradient with respect to the matrix elements of the reduced order model. To obtain an asymptotically stable reduced system we include a stability constraint. Numerical experiments illustrate this method.
Volker Mehrmann (TU Berlin)
Donnerstag, 28. November 2019
Stability analysis of dissipative Hamiltonian differentialalgebraic systems
PortHamiltonian differentialalgebraic systems are an important class of control systems that arise in all areas of science and engineering. When the system is linearized arround a stationary solution one gets a linear portHamiltonian differentialalgebraic system. Despite the fact that the system looks very unstructured at first sight, it has remarkable properties. Stability and passivity are automatic, Jordan structures for purely imaginary eigenvalues, eigenvalues at infnity, and even singular blocks in the Kronecker canonical form are very restricted. We will show several results and then apply them to the brake squeal problem.
Julianne Chung (TU Berlin)
Donnerstag, 14. November 2019
Computational Methods for Large and Dynamic Inverse Problems
In this talk, we describe efficient methods for uncertainty quantification for large, dynamic inverse problems. The first step is to compute a MAP estimate, and for this we describe efficient, iterative, matrixfree methods based on the generalized GolubKahan bidiagonalization. These methods can address illposedness and can handle many realistic scenarios, such as in passive seismic tomography or dynamic photoacoustic tomography, where the underlying parameters of interest may change during the measurement procedure. The second step is to explore the posterior distribution via sampling. We use the generalized GolubKahan bidiagonalization to derive an approximation of the posterior covariance matrix for "free" and describe preconditioned Lanczos methods to efficiently generate samples from the posterior distribution.
Matthias Chung (TU Berlin)
Donnerstag, 14. November 2019
Sampled Limited Memory Methods for Least Squares Problems with Massive Data
In this talk, we discuss massive least squares problems where the size of the forward model matrix exceeds the storage capabilities of computer memory or the data is simply not available all at once. We consider randomized rowaction methods that can be used to approximate the solution. We introduce a sampled limited memory rowaction method for least squares problems, where an approximation of the global curvature of the underlying least squares problem is used to speed up the initial convergence and to improve the accuracy of iterates. Our proposed methods can be applied to illposed inverse problem, where we establish sampled regularization parameter selection methods. Numerical experiments on very large superresolution and tomographic reconstruction examples demonstrate the efficiency of these sampled limited memory rowaction methods.
Onkar Jadhav (TU Berlin)
Donnerstag, 31. Oktober 2019
Model order reduction for parametric high dimensional interest rate models in the analysis of financial risk
The European Parliament has introduced regulations (No 1286/2014) on packaged retail investment and insurance products (PRIIPs). According to this regulation, PRIIP manufacturers must provide a key information document (KID) describing the risk and the possible returns of these products. The formation of a KID requires expensive valuations rising the need for efficient computations. To perform such valuations efficiently, we establish a model order reduction approach based on a proper orthogonal decomposition (POD) method. The study involves the computations of high dimensional parametric convectiondiffusion reaction partial differential equations. POD requires to solve the high dimensional model at some parameter values to generate a reducedorder basis. We propose a greedy sampling technique for the selection of the sample parameter set that is analyzed, implemented, and tested on the industrial data. The results obtained for the numerical example of a floater with cap and floor under the HullWhite model indicate that the MOR approach works well for the shortrate models.
Christian Mehl (TU Berlin)
Donnerstag, 31. Oktober 2019
Distance problems for dissipative Hamiltonian pencils and related matrix polynomials
We investigate the distance problems to singularity, higher index, and instability for dissipative Hamiltonian systems by developing a general framework for matrix polynomials with a special symmetry and positivity structure. As we will show, the mentioned distances can then be formulated as the distance to a common kernel of some of the coefficients of the given matrix polynomial.
Paula Klimczok (TU Berlin)
Donnerstag, 24. Oktober 2019
Classification of TwoVariable Linear Differential Equations with Large Delays
In this talk we will discuss the stability of linear differential equations of the form x’(t)=Ax(t)+Bx(t−τ) with a discrete delay τ and constant A and B. For a large delay τ the eigenvalues can be approximated by two sets: the asymptotic strongly unstable spectrum and the asymptotic continuous spectrum. We will characterise these sets in the case of A, B ∈ R^{2×2} and give conditions for the stability. Further, we will take a look on the computation of the eigenvalues.
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