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## Absolventen-Seminar • Numerische Mathematik

Verantwortliche Dozenten: | Prof. Dr. Christian Mehl, Prof. Dr. Volker Mehrmann |
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Koordination: | Dr. Agnieszka Międlar |

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 20.10.11 | 10:15 Uhr | MA 376 | Ute Kandler | (Abstract) |

im Anschluss | Manuel Baumann | (Abstract) | ||

Do 27.10.11 | 10:15 Uhr | MA 376 | Nicola Guglielmi (U L'Aquila) | |

Do 03.11.11 | 10:15 Uhr | MA 376 | Federico Poloni | (Abstract) |

im Anschluss | Philip Losse | (Abstract) | ||

Do 10.11.11 | 10:15 Uhr | MA 376 | Sarosh Mumtaz Quraishi | (Abstract) |

Do 17.11.11 | 10:15 Uhr | MA 376 | Manideepa Saha | (Abstract) |

Do 24.11.11 | 10:15 Uhr | MA 376 | Jan Heiland | (Abstract) |

Do 01.12.11 | 10:15 Uhr | MA 376 | André Gaul | (Abstract) |

Do 15.12.11 | 10:15 Uhr | MA 376 | Christian Schröder | (Abstract) |

Do 05.01.12 | 10:15 Uhr | MA 376 | Robert Altmann | (Abstract) |

Do 12.01.12 | 10:15 Uhr | MA 376 | Phi Ha | (Abstract) |

Do 19.01.12 | 10:15 Uhr | MA 376 | Volker Mehrmann | (Abstract) |

Do 26.01.12 | 10:15 Uhr | MA 376 | Lena Scholz | |

im Anschluss | 10:15 Uhr | MA 376 | Andreas Steinbrecher | |

Do 02.02.12 | 10:15 Uhr | MA 376 | Helia Neroomandrad | |

im Anschluss | Kristin Steinberg | |||

Do 09.02.12 | 10:15 Uhr | MA 376 | Christian Mehl | |

Do 16.02.12 | 10:15 Uhr | MA 376 | Tobias Brüll | |

im Anschluss | Ann-Kristin Baum |

## Rückblick

- Diplomanden- und Doktorandenseminar SS 2011
- Diplomanden- und Doktorandenseminar WS 2010/11
- Diplomanden- und Doktorandenseminar SS 2010
- Diplomanden- und Doktorandenseminar WS 2009/10
- Diplomanden- und Doktorandenseminar SS 2009
- Diplomanden- und Doktorandenseminar WS 2008/09
- Diplomanden- und Doktorandenseminar SS 2008
- Diplomanden- und Doktorandenseminar WS 2007/08
- Diplomanden- und Doktorandenseminar SS 2007
- Diplomanden- und Doktorandenseminar WS 2006/07
- Diplomanden- und Doktorandenseminar SS 2006
- Diplomanden- und Doktorandenseminar WS 2005/06
- Diplomanden- und Doktorandenseminar SS 2005

### Federico Poloni

**The benefits of changing identity (in Lagrangian subspaces and doubling algorithms) **

Thu, 03.11.2011, 10:15 Uhr in MA 376

Abstract:

We prove that every Lagrangian subspace is spanned by some row permutation of [I;X], where I is the nxn identity matrix and X is symmetric/Hermitian (up to some sign changes) with all its entries bounded in modulus by \sqrt{2}. With respect to the usual representation as span of [I;X], allowing the row permutation lets us obtain this entrywise bound on X, which ensures that the basis is computationally tame.

Small modifications of this result can be adapted to provide representations of symplectic and Hamiltonian pencils, and can be used to implement a pencil arithmetic primitive that is used in the context of doubling algorithms for algebraic Riccati equations. In particular, we obtain for the first time a doubling variant that has the potential to be *structure-preserving* and *computationally stable* at the same time.

### Philip Losse

**The H_infinity Optimal Control Problem for Descriptor Systems**

Thu, 03.11.2011, 10:15 Uhr in MA 376

Abstract :

The H_infinity control problem is studied for linear constant coefficient descriptor systems.

Necessary and sufficient optimality conditions as well as controller formulas are derived in

terms of deflating subspaces of even matrix pencils for problems of arbitrary index. A structure

preserving method for computing these subspaces is introduced. In combination these results

allow the derivation of a numerical algorithm with advantages over the classical methods.

### Sarosh Mumtaz Quraishi

**Wavelet based multiscale FEM for problems in structural mechanics**

Thu, 10.11.2011, 10:15 Uhr in MA 376

Abstract:

In this talk we will review wavelets arising from finite element basis functions and use them for discretizing PDEs from structural mechanics. In particular we are interested wavelets that are orthogonal with respect to the operator of the PDE in the weak formulation. These wavelets result in a scale-decoupled finite element system. We explore commonly used basis functions like Lagrange and Hermite interpolating functions, B-spline and subdivision surfaces.

Finally we illustrate some practical examples like beam and plate deformation which are modeled by fourth order differential equations.

### Manideepa Saha

**Combinatorial bases for the generalized null space and height-level characteristic of an $M_\vee$"-matrix **

Thu, 17.11.2011, 10:15 Uhr in MA 376

Abstract:

An $M_{\vee}$-matrix has the form $A=sI-B$, with $0\leq\rho(B)\leq s$

and $B$ an eventually nonnegative matrix. We studied the relation between the combinatorial structure and the spectral structure of the generalized nullspace of a special subclass of such matrices. We also focus on the interretation between level and height characteristic of such matrices and give some necessary and sufficient condition for their equality.

### Jan Heiland

**Optimal Control of Flows - I Try a Differential Algebraic Matrix Riccati Equation Approach**

Thu, 24.11.2011, 10:15 Uhr in MA 376

Abstract:

Optimal control problems are basically formulated via some state equations that include a control term and a cost functional that specifies which controls are optimal. For flow problems the state equations are given by partial differential-algebraic equations (PDAEs).

The basis for the numerical analysis of optimal control problems governed by partial differential equations with algebraic constraints is the linear time varying differential-algebraic equation (DAE) system. This is due to the fact that sooner or later a numerical solution procedure approximates the PDAEs by a linearization and a space discretization. Therefore I am going to present some ideas related to time-varying linear DAE systems and quadratic cost functionals.

In view of the considered flow problem I will concentrate on semi-explicit linear DAEs of differentiation index 2, where the control acts only in the dynamic part of the equations.

The associated Euler-Lagrange equations that provide necessary and sometimes sufficient conditions for the optimality of a control are given by a boundary value problem. This boundary value problem appears to be a differential-algebraic equation system. Thus a solution may not exist because of inconsistency or lacking smoothness of the data.

For the semi-explicit equations and suitable cost functionals necessary conditions for a solution are readily identified. To find a solution of the boundary value problem I try a Riccati-like decoupling of the solution components. Having considered the necessary conditions one ends up with a semi-explicit differential algebraic matrix Riccati equation.

### André Gaul

**Spectral transformations for GMRES**

Thu, 01.12.2011, 10:15 Uhr in MA 376

Abstract:

In this talk I will share some thoughts with you about work in progress on the solution of linear algebraic systems with a nonsingular and possibly non-normal matrix A. For a large and sparse matrix I consider a projection-based transformation introduced by Erlangga and Nabben in 2008 for the GMRES method (IMO the term 'preconditioning' is misleading for a non-normal matrix and I thus stick to 'transformation'). If a basis of an A-invariant subspace is known, I will show how the spectrum, the eigenvector conditioning and the singular values can be modified with this transformation to directly improve well-known convergence bounds for GMRES.

### Christian Schröder

**A Tale of Abuse and a Fresh Start **

Thu, 15.12.2011, 10:15 Uhr in MA 376

Abstract:

A standard way to solve a linear system of equations, Ax=b, are projection methods with growing search space dimension (like GMRES). But after, say, m_max iterations no further search space basis vectors can be stored. A standard remedy is to restart the method with the current approximation of x. This is a waste of information and

we want to restart with a search space of dimension larger than 1.

The question is: which directions in the search space should be kept and

which can be safely discarded without harming convergence speed to much?

In this talk I present an approach to this question based on rewriting the subspace iteration as quasi Newton method.

This is work in progress - so much in fact that the numerical examples are not yet done. On Thursday I will know if it works ... and so will you ... if you come.

### Robert Altmann

**Strangeness-free Elastodynamics**

Thu, 05.01.2012, 10:15 Uhr in MA 376

Abstract:

As preparation for the simulation of flexible multibody systems in a

space-time adaptive scheme, we first look at a single flexible body. This field is then called elastodynamics. The inclusion of Dirichlet boundary conditions as contraints and a semi-discretization in space will lead to a DAE of index 3.

### Phi Ha

**Analysis and Remodeling Delay Differential Algebraic Equations**

Thu, 12.01.2012, 10:15 Uhr in MA 376

Abstract:

This talk aims at Delay Differential Algebraic Equations of Neutral and Retarded type with linear time invariant matrix coefficients (LTI DDAEs). We introduce condensed forms of matrix triples and use these forms to investigate structural properties of the system like solvability, regularity, consistency and smoothness requirements. Furthermore, for numerical purpose we also consider a numerically stable method to determine a strangeness-free formulation for a solution procedure.

### Volker Mehrmann

**Approximation of spectral intervals and leading directions for differential-algebraic equations **

Thu, 19.01.2012, 10:15 Uhr in MA 376

Abstract:

This talk is devoted to the numerical approximation of Lyapunov and

Sacker-Sell spectral intervals for linear differential-algebraic equations (DAEs). The spectral analysis for DAEs is improved and the concepts of leading directions and solution subspaces (generalizing the concepts of eigenvectors and invaraint subspaces) associated with spectral intervals are extended to DAEs. Numerical methods based on smooth singular value decompositions are introduced for computing all or only some spectral intervals and their associated leading directions. The numerical algorithms are discussed in detail and numerical examples are presented to illustrate the theoretical results.

This is joint work with Vu Hoang Linh