# Colloquium on Applied Mathematics

The Institute of Mathematics at TUHH (E-10) hosts a colloquium series in Applied Mathematics. Each semester there are several talks, where most of them deal with one or more of the main areas of research at the institute (numerical solution of linear and nonlinear systems, numerics of large eigenvalue problems, numerical treatment of differential equations, nonlinear optimization, Fredholm and spectral theory).

If you want to be informed about talks by e-mail please subscribe to mailing-list "mathe-kolloquium".

## Talks

| 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 |

2022 |
---|

Asymptotic-preserving and hybrid finite-volume/Monte-Carlo methods for kinetic equations in the plasma edge of a fusion reactor Giovanni Samaey KU Leuven, 07/07/2022, 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 & Zoom Abstract: Nuclear fusion reactor design crucially depends on numerical simulation. The plasma can usually be modeled using fluid equations (for mass, momentum and energy). However, the reactor also contains neutral (non-charged) particles (which are important in its operation), of which both the position and velocity distribution is important. This leads to a Boltzmann-type transport equation that needs to be discretised with a Monte Carlo method. In high-collisional regimes, the Monte Carlo simulation describing the evolution of neutral particles becomes prohibitively expensive, because each individual collision needs to be tracked. |

Robot manipulation in real-time, in the real-world, and under uncertainty. Wisdom Agboh University of Leeds, 05/02/2022, 03:00 pm Zoom Abstract: Robots have the potential to disrupt many aspects of our lives, from healthcare to manufacturing. To realize this potential, a key challenge is real-time robot manipulation. Given a task, how can a robot quickly generate a motion plan to successfully complete it? How can the robot react in real-time to potential uncertainties in the real-world as it executes its plan? In this talk, we will overview recent developments at the University of Leeds, to realize real-time robot manipulation. These will include parallel-in-time integration methods that leverage parallel computing to significantly speed-up physics predictions for various robot manipulation tasks. It will also include learning-based and optimal control-based methods for robots to handle real-world uncertainties in object pose estimation and model parameters. We hope these recent advances will help accelerate the next generation of intelligent robots. |

Observability for the (anisotropic) Hermite semigroup from finite volume or decaying sensor sets Ivan Veselic TU Dortmund, Fakultät für Mathematik, Lehrstuhl LSIX, 02/07/2022, 03:00 pm Zoom Abstract: We study the observability and null control problem for |

2021 |
---|

A Hybrid Approach for Data-based Models Using a Least-squares Regression Malin Lachmann 11/22/2021, 03:00 pm E3.074 & zoom (talk via zoom) Abstract: An increased use of renewable energy could significantly contribute to decelerate climate change but cannot be realized easily since most renewable energy sources underlie volatile availability. Using of storage devices and scheduling consumers to times when energy is available can increase the amount of renewable energy that is used. For this purpose, adequate models that forecast the energy generation and consumption as well as the behavior of storage devices are essential. We present a computationally efficient modeling approach based on a least-squares problem that is extended by a hybrid model approach based on kmeans clustering and evaluate it on real-world data at the examples of modeling the state of charge of a battery storage and the temperature inside a milk cooling tank. The experiments indicate that the hybrid approach leads to better forecasting results, especially if the devices show a more complicated behavior. Furthermore, we investigate whether the behavior of the models is qualitatively realistic and find that the battery model fulfills this requirement and is thus suitable for the application in a smart energy management system. Even though forecasts for the hybrid milk cooling model have low error values, further steps need to be taken to avoid undesired effects when using this model in such a sophisticated system. |

The quest for the cortical algorithm Dr. Helmut Linde Merck KGaA, Darmstadt, Germany 10/21/2021, 03:00 pm Zoom (see below for link) Abstract: How will the next generation of Artificial Intelligence (AI) look like? Comparing today's AI algorithms with biological intelligence, one of the most remarkable differences is the ability of the human brain to somehow understand the 'essence' of things: A small child can easily identify any type of object after having seen only a few examples or recognize a song even when played on different instruments or in a different key. In other words: Brains are able to create abstract concepts of real-world entities - and today's algorithms are not. Additional information about the author: Helmut Linde is the Global Head of Data Science at Merck KGaA (Darmstadt, Germany). He is responsible to drive innovation in the field of artificial intelligence and to ensure that the company leverages the potential of these modern technologies. Before joining Merck, Helmut has held various leadership roles at the software company SAP in the area of data science, overseeing the development and implementation of customer-specific forecasting and optimization solutions. Helmut has an academic research background in mathematical physics. |

Some peculiar (and not very well known) aspects of Gauss quadrature rules Thibaut Lunet Université de Genève, 06/28/2021, 03:00 pm Zoom Abstract: Gauss quadrature rules are nowadays not only a powerful tool to compute integrals in many scientific applications, but also a numerical method that most people in the scientific community at least heard of at some point in there life. Additional information about the author: https://tuhh.zoom.us/j/81267321365?pwd=LzQ1cWtESXlRYXFpSFU3VkxPL08zdz09 |

A semi-implicit meshfree/particle scheme for the shallow water equations Dr. Adeleke Bankole Institute of Mathematics, Hamburg University, 03/15/2021, 03:00 pm Zoom meeting Abstract: This presentation introduces the semi-implicit Smoothed Particle Hydrodynamics (SPH) |

2020 |
---|

Novel Space-Time Finite Element Discretizations Prof. Dr. Marek Behr Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, 02/20/2020, 01:15 pm Room H - SBC5 - H0.03 Abstract: Moving-boundary flow simulations are an important design and analysis tool in many areas, including civil and biomedical engineering, as well as production engineering. Interface-capturing offers flexibility for complex free-surface motion, while interface-tracking is very attractive due to its mass conservation properties at low resolution. We focus on these alternatives in the context of flow simulations based on stabilized finite element discretizations of Navier-Stokes equations, including space-time formulations that allow extra flexibility concerning grid design at the interface. Additional information about the author: - Univ.-Prof. (C4) at the Chair for Computational Analysis of Technical Systems in the Faculty of Mechanical Engineering of the RWTH Aachen University since 2004 |

2019 |
---|

Parallel-in-Time PDE-constrained Optimization Dr. Sebastian Götschel Zuse Institut Berlin (ZIB), 12/19/2019, 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: Large-scale optimization problems governed by partial differential equations (PDEs) occur in a multitude of applications, for example in inverse problems for non-destructive testing of materials and structures, or in individualized medicine. Algorithms for the numerical solution of such PDE-constrained optimization problems are computationally extremely demanding, as they require multiple PDE solves during the iterative optimization process. This is especially challenging for transient problems, where methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the associated optimality system. The evaluation of the reduced gradient then requires one solve of the state equation forward in time, and one backward-in-time solve of the adjoint equation. In order to tackle real-life applications, it is not only essential to devise efficient discretization schemes, but also to use advanced techniques to exploit computer architectures and decrease the time-to-solution, which otherwise is prohibitively long. Additional information about the author: https://www.zib.de/members/goetschel |

Factorization and Symmetrization of stabilized Gaussian RBFs Sabine Le Borne Technische Universität Hamburg, Institut für Mathematik, Lehrstuhl Numerische Mathematik, Am Schwarzenberg-Campus 3, Gebäude E, 21073 Hamburg 07/11/2019, 04:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 |

Extrapolation spaces and Desch-Schappacher perturbations of bi-continuous semigroups Christian Budde Bergische Universität Wuppertal, Arbeitsgruppe Funktionalanalysis, 01/28/2019, 01:15 pm H0.08 Abstract: We construct extrapolation spaces for non-densely defined (weak) Hille--Yosida operators. In particular, we discuss extrapolation of bi-continuous semigroups. As an application we present a Desch--Schappacher type perturbation result for this kind of semigroups. This talk is based on joint work with B. Farkas. |

On eventual regularity properties of operator valued functions Marco Peruzzetto Christian-Albrechts-Universität zu Kiel, Arbeitsbereich Analysis, 01/24/2019, 01:30 pm D1.024 Abstract: For two Banach spaces $X,Y$ let $u:\mathbb{R}_{\geq 0}\rightarrow \mathcal{L}(X;Y)$ be an operator valued function and $\mathtt{P}$ a regularity property. Assume that each orbit $t\mapsto u(t)x$ has the regularity property $\mathtt{P}$ on some interval $(t_x,\infty)$ in general depending on $x\in X$. In this paper we prove a Baire-type theorem, which allows to remove the dependency of $x$ in certain situations. Afterwards, we provide some applications which are of interest in semigroup theory. In particular, we generalize and explain the result obtained by Bárta in his article ``\emph{Two notes on eventually differentiable families of operators}'' (Comment. Math. Univ. Carolin. 51,1 (2010), 19-24). |

2018 |
---|

Approximation techniques for passive mechanical control systems Ines Dorschky Fachbereich Mathematik, Universität Hamburg, 11/29/2018, 02:00 pm D1.024 Abstract: In this talk we study approximation techniques for input-output systems, which appear in the modeling process of mechanical systems. So, the focus will be on linear dynamical systems with a second derivative term. |

Observability for Systems in Banach spaces - Part II Christian Seifert 11/15/2018, 02:00 pm D1.024 Abstract: This talk is divided into two parts. The first part will be given on Thursday 08.11.18 by Dennis Gallaun. |

Observability for Systems in Banach spaces - Part I Dennis Gallaun 11/08/2018, 01:30 pm D1.024 Abstract: This talk is divided into two parts. The second part will be given on Thursday 15.11.18 by Christian Seifert. |

Series representations in spaces of vector-valued functions Karsten Kruse 10/18/2018, 01:45 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: It is a classical result that every $\mathbb{C}$-valued holomorphic function has a local power series representation. |

Existence and Uniqueness of the Harmonic Extension Approach to Fractional Powers of Linear Operators Jan Meichsner Institut fuer Mathematik, Lehrstuhl angewandte Analysis, TUHH, 10/11/2018, 02:00 pm D1.024 Abstract: This talk will be an extended version of the talk I gave on the SOTA 2018 in Poland. |

A glimpse on interpolation theory and interpolation with mixed boundary conditions Sebastian Bechtel Arbeitsgruppe Analysis, TU Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt 08/09/2018, 03:45 pm H0.09 Abstract: First, we give a short introduction to abstraction interpolation theory and |

Sparse Frequency Estimation Benedikt Diederichs Fachbereich Mathematik, Universität Hamburg, 07/12/2018, 03:45 pm tba Abstract: Prony's problem - estimating the frequencies of an exponential sum - and its higher dimensional |

A minimax principle in spectral gaps Albrecht Seelmann Fakultät für Mathematik - Technische Universität Dortmund, 06/28/2018, 03:45 pm Am Schwarzenberg-Campus (D), Room D1.021 Abstract: In [Doc. Math. 4 (1999),275--283], Griesemer, Lewis, and Siedentop devised an abstract minimax principle for eigenvalues in spectral gaps of perturbed self-adjoint operators. We show that this minimax principle can be adapted to the particular situation of bounded additive perturbations with hypotheses that are easier to check in this case. The latter is demonstrated in the framework of the Davis-Kahan sin(2\Theta) theorem. Additional information about the author: http://www.mathematik.tu-dortmund.de/lsix/people/seelmann/index.php |

Silvestre-Caffarelli approach to Fractional Powers of Linear Operators Jan Meichsner 06/07/2018, 03:45 pm tba Abstract: We are going to discuss (again) the approach of describing fractional powers of linear operators on |

On the stability of Prony's method Stefan Kunis Institut für Mathematik, Uni Osnabrück, 05/17/2018, 04:30 pm TUHH, Building A, Room A0.19 Additional information about the author: Academic positions |

2017 |
---|

Bi-stetige Halbgruppen Jan Meichsner Institut fuer Mathematik, Lehrstuhl angewandte Analysis, TUHH, 06/15/2017, 02:45 pm Room H - SBC5 H0.03 (noch unbestaetigt) Abstract: In dem Vortrag wird es um bi-stetige Halbgruppen gehen. Das Konzept geht auf die Dissertation |

The need for linear system solvers in dispersive wave modeling Jörn Behrens UHH, 01/26/2017, 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: Tsunami modeling is - to first (and very accurate) approximation - performed with the help of shallow water theory and equations. This is still the method of choice for many applications, including forecasting, hazard assessment and inundation modeling. However, for long propagation distances as well as highly nonuniform topographies dispersive effects become important. While truly dispersive model equations are fully three-dimensional and therefore expensive with respect to computational requirements, a common approach to dispersive modeling comprises a non-hydrostatic correction of shallow water equations. In order to derive this correction term, a linear system of equations needs to be solved in each time step - even when the time-stepping scheme is explicit. |

2016 |
---|

Nuklearität und Tensorprodukte Karsten Kruse 12/12/2016, 03:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: Im Vortrag wird es darum gehen, wie man eine vektorwertige Gleichung löst, wenn man die entsprechende Gleichung schon einmal skalarwertig gelöst hat. Typische Beispiele hierfür sind elliptische Differentialgleichungen. Hierbei geht es dann weniger darum, den Differentialoperator selbst zu untersuchen, sondern die Eigenschaften der Räume, auf denen er lebt. |

Fractional Powers of Linear Operators Jan Meichsner 11/24/2016, 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: Im wesentlichen ein 60 bis 90 minütiger Arbeitsstandbericht. Es werden grundlagen der Theorie fraktionaler Operatoren erläutert und danach auf die Problematik der Einführung durch harmonische Erweiterung eingegangen. |

Vier konkrete Anwendungen von Toeplitzoperatoren Albrecht Böttcher TU Chemnitz, 11/02/2016, 01:30 pm TUHH, Building A, Room A0.19 Abstract: Vier konkrete Anwendungen von Toeplitzoperatoren Additional information about the author: 214 Paper |

Solving the Vlasov equation in low-rank tensor format Dr. Katharina Kormann Technische Universität München, Zentrum Mathematik - M16, Boltzmannstraße 3, 85747 Garching, Germany 04/26/2016, 04:15 pm Am Schwarzenberg-Campus 3, Building A, Room A.0.01 und A.3.31 Abstract: The evolution of a plasma in external and self-consistent fields is modelled by the Vlasov equation for the distribution function in six dimensional phase space. Due to the high dimensionality and the development of small structures the numerical solution is very challenging. Grid-based methods |

Auxiliary Space Methods for Variational Problems in H{curl) Ralf Hiptmair ETH Zürich, 01/28/2016, 03:30 pm Am Schwarzenberg-Campus 1 (A), A1.20 Abstract: Auxiliary space preconditioning targets elliptic boundary value problems discetized by means of finite elements. The idea is to use a related discrete boundary value problem, for which efficient solvers are available, as a preconditioner. The connection between both problems is established by means of a suitable prolongation operator. |

2015 |
---|

Rational Arnoldi methods Prof. Lothar Reichel Department of Mathematical Sciences, Kent State University, Ohio, USA 09/18/2015, 02:00 pm Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: The standard Arnoldi method is one of the most popular schemes for reducing a large matrix A to a small one. The method requires the evaluation of matrix-vector products with A. Rational Arnoldi methods reduce the matrix A by both evaluating matrix-vector products and solving linear systems of equations with A. Rational Arnoldi methods are attractive to use when A has a structure that allows efficient solution linear systems of equations with A. They are commonly applied to the computation of an invariant subspace of A and to the approximation of matrix functions. We discuss implementations of rational Arnoldi methods and compares their properties. |

Interpolationsbasierte Reduzierte-Basis-Modellierung von Lösungskurven mit Umkehrpunkten Hagen Eichel Eröffnung des Promotionsverfahrens, 09/03/2015, 10:00 am Am Schwarzenberg-Campus 3 (E), Room 3.074 Abstract: Bei der numerischen Simulation physikalischer Prozesse treten häufig große parameterabhängige nichtlineare Gleichungssysteme auf. Zur Verringerung des Rechenaufwands werden oft Reduzierte-Basis-Methoden verwendet, die sich in lokale und globale Methoden unterscheiden lassen, wobei letztere Umkehrpunkte bezüglich des Parameters gewöhnlich nicht zulassen. In dieser Arbeit wird ein globaler, interpolationsbasierter Ansatz für Probleme mit Umkehrpunkten entwickelt und es werden die Vorteile und Grenzen dieser Methode aufgezeigt. |

Orthogonalization with a non-standard inner product and approximate inverse preconditioning Miro Rozložník Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic 03/19/2015, 03:00 pm Schwarzenbergstrasse 95E, Room 3.074 Abstract: One of the most important and frequently used preconditioning techniques for solving symmetric positive definite systems is based on computing the approximate inverse factorizations. It is also a well-known fact that such factors can be computed column-wise by the orthogonalization process applied to the unit basis vectors provided that we use a non-standard inner product induced by the positive definite system matrix A. In this contribution we consider the classical Gram-Schmidt algorithm (CGS), the modified Gram-Schmidt algorithm (MGS) and also yet another variant of sequential orthogonalization, which is motivated originally by the AINV preconditioner and which uses oblique projections. |

2014 |
---|

H²-matrix methods for boundary integral equations Steffen Börm Christian-Albrechts-Universität Kiel, 12/05/2014, 02:00 pm Schwarzenbergstrasse 95E, Room 3.074 Abstract: Boundary integral equations are an important tool for analyzing elliptic partial differential equations arising, e.g., in structural mechanics or the simulation of acoustic or electromagnetic fields. Standard discretization techniques lead to large and densely populated matrices that require special algorithms. |

Recursive Low-Rank Truncation Wolfgang Hackbusch Max-Planck-Institut für Mathematik in den Naturwissenschaften, 11/13/2014, 03:30 pm Schwarzenbergstrasse 93, Room A1.20 Abstract: The best approximation of a matrix by a low-rank matrix can be obtained by the singular value decomposition. For large-sized matrices this approach is too costly. Instead one may use a block decomposition. Approximating the smaller |

Domain Decomposition for elliptic PDE eigenvalue problems Lars Grasedyck RWTH Aachen, 06/30/2014, 03:00 pm Schwarzenbergstrasse 95E, Room 3.074 Abstract: We consider the solution of a rather simple class of eigenvalue problems $Ax=\lambda{Mx}$ for symmetric positive definite matrices $A$,$M$ that stem, e.g., from the discretisation of a PDE eigenvalue problem. Thus, the problem is in principle simple, but the matrices $A$ and $M$ are large-scale and we would like to compute all relevant eigenvalues, where relevant is to be understood in the sense that all eigenvalues should be computed that can be captured by the discretisation of the continuous PDE eigenvalue problem. |

A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations Leo Rebholz 06/24/2014, 03:30 pm Schwarzenbergstrasse 95E, Room 3.074 Abstract: We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin/Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter $\gamma$, converge to the associated coupled method solution with rate $\gamma^{-1}$ as $\gamma\rightarrow \infty$. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters can dramatically improve accuracy. |

Preconditioners for time-dependent PDE-constrained optimization Martin Stoll MPI Magdeburg, 04/24/2014, 04:00 pm Schwarzenbergstrasse 95E, Room 3.074 |

2013 |
---|

On the Role of the Helmholtz Decomposition in Mixed Methods for Incompressible Flows and a New Variational Crime Alexander Linke WIAS Berlin, 10/17/2013, 02:15 pm Schwarzenbergstrasse 95E, Room 3.074 Abstract: According to the Helmholtz decomposition, the irrotational parts of the momentum balance equations of the incompressible Navier-Stokes equations are balanced by the pressure gradient. Unfortunately, nearly all mixed methods for incompressible flows violate this fundamental property, resulting in the well-known numerical instability of poor mass conservation. The origin of this problem is the lack of L2-orthogonality between discretely divergence-free velocities and irrotational vector fields. Therefore, a new variational crime for the nonconforming Crouzeix-Raviart element is proposed, where divergence-free, lowest-order Raviart-Thomas velocity reconstructions reestablish L2-orthogonality. This approach allows to construct a cheap flow discretization for general 2d and 3d simplex meshes that possesses the same advantageous robustness properties like divergence-free flow solvers. In the Stokes case, optimal a-priori error estimates for the velocity gradients and the pressure are derived. Moreover, the discrete velocity is independent of the continuous pressure. Several detailed linear and nonlinear numerical examples illustrate the theoretical findings. |

Numerical Treatment of Tensors Wolfgang Hackbusch Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig 07/04/2013, 02:00 pm Schwarzenbergstraße 95H, Room H0.03 Abstract: The numerical treatment of tensors and the use of tensors for various numerical problem has rapidly increased in the last time. It is now applied to many fields in analysis (treatment of pdes, representation of multivariate functions, etc.). The key for an efficient numerical treatment is a suitable format. We discuss the various formats, their properties, and operations with tensors. |

H-Matrizen für Finite-Differenzen Matrizen Dominik Enseleit UHH, UHH 05/29/2013, 01:30 pm Schwarzenbergstrasse 95E, Room 1.050 Abstract: Die Technik der Hierarchischen Matrizen H-Matrizen) ermöglicht die Berechnung einer approximativen H-Inversen oder H-LU-Zerlegung in fast linearer Komplexität und kann auf diese Weise zur effizienten Lösung linearer Gleichungssysteme eingesetzt werden. Vor der Verwendung der H-Matrix-Technik ist zu untersuchen, ob eine H-Matrix Approximation der Inversen bzw. der Faktoren der LU-Zerlegung existiert. |

Titchmarsh-Weyl theory for elliptic differential operators on unbounded domains Jussi Behrndt TU Graz, Österreich 01/22/2013, 03:00 pm Schwarzenbergstrasse 95E, Room 1.050 Abstract: In this talk we describe the spectral properties of selfadjoint Schrödinger operators on unbounded domains with |

2012 |
---|

Robust successive computation of eigenpairs for nonlinear eigenvalue problems Cedric Effenberger École polytechnique fédérale de Lausanne EPFL, Lausanne 12/12/2012, 03:00 pm Schwarzenbergstrasse 95E, Room 1.050 Abstract: We consider eigenvalue problems which are nonlinear in the eigenvalue |

Invariant pairs for nonlinear eigenvalue problems Prof. Dr. Daniel Kressner École polytechnique fédérale de Lausanne EPFL, Lausanne 11/28/2012, 03:00 pm Schwarzenbergstrasse 95E, Room 1.050 Abstract: The concept of invariant subspaces is fundamental to linear eigenvalue problems and provides an important theoretical foundation in the design of numerical eigenvalue solvers. It turns out that there is no straightforward extension of this concept to eigenvalue problems that are nonlinear in the eigenvalue parameter. One obstacle is that eigenvectors belonging to different eigenvalues may become linearly dependent in the nonlinear case. Invariant pairs offer an elegant way to avoid this obstacle and appear to be the most natural extension of invariant subspaces. In this talk, we give an overview of the properties of invariant pairs and explain how they can be used in the design of numerical algorithms for nonlinear eigenvalue problems, as they arise for example in band diagram calculations for photonic crystals and fluid-structure interaction problems. |

Schrödinger-Operatoren mit kompakter Resolvente Peter Stollmann TU Chemnitz, TU Chemnitz, Fakultät für Mathematik, 09107 Chemnitz 10/24/2012, 03:00 pm Schwarzenbergstrasse 95, Room 1.050 Abstract: Ein klassischer Satz von Friedrichs besagt, dass Schrödingeroperatoren kompakte Resolvente besitzen, wenn das zugrundeliegende Potential bei Unendlich gegen Unendlich geht. In diesem Vortrag werden wir einen einfachen Beweis einer Verallgemeinerung präsentieren, basierend auf einer gemeinsamen Arbeit mit D. Lenz (Jena) und D. Wingert. |

The Lanczos algorithms and their relations to formal orthogonal polynomials, Padé approximation, continued fractions, and the qd algorithm Martin Gutknecht ETH Zurich; Seminar for Applied Mathematics, LEO D3 (Leonhardstrasse 27), 8092 Zurich, Switzerland 03/14/2012, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: In their seminal 1952 paper on the conjugate gradient (CG) method Hestenes and Stiefel pointed out that their method, which is applicable to linear systems of equations with symmetric positive definite matrix only, is closely related to certain orthogonal polynomials, the corresponding Gauss quadrature formulas, certain continued fractions, and their convergents (or `partial sums'). The latter can be seen to be Padé approximants of a function that involves the resolvent of the matrix. |

Solving large nonsymmetric linear systems with IDR(s) on a geographically separated cluster of parallel computers Martin van Gijzen Delft University of Technology; Faculty of Electrical Engineering, Mathematics and Computer Science, Mekelweg 4; 2628 CD Delft; The Netherlands 02/29/2012, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: The IDR(s) method is a family of fast algorithms for iteratively solving large nonsymmetric linear systems. In the talk we will discuss an IDR(s) variant that is specifically tuned for parallel and grid computing. In particular in grid computing the inner product is a bottleneck operation. We will discuss three techniques that we have used to alleviate this bottleneck in IDR(s). Firstly, the efficient and stable IDR(s)-biortho method is reformulated in such a way that it has a single global synchronisation point per iteration step. Secondly, the so-called test matrix is chosen so that the work, communication, and storage involving this matrix is minimised in multi-cluster environments. Finally, a methodology is presented for a-priori estimation of the optimal value of s using only problem and machine--based parameters. We will also discuss a preconditioned version of IDR(s) that is particularly suited for grid computing. We will illustrate our results with numerical experiments on the DAS--3 Grid computer, which consists of five cluster computers located at geographically separated places in the Netherlands. |

2011 |
---|

The Lanczos Algorithm in Finite-Precision Arithmetic Ivo Panayotov Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, England 03/16/2011, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: The Lanczos algorithm was introduced in 1950 as means of solving eigenvalue problems. Despite its apparent elegance, the algorithm was initially neglected by the scientific community because it was observed to depart from its theoretical properties due to the effects of finite-precision computer arithmetic. The algorithm regained popularity several decades later when it was shown that despite its departure from theory, it nevertheless produces highly accurate eigenvalue estimates. |

2010 |
---|

On the motion of several rigid bodies in an incompressible non-Newtonian fluid Prof. Sarka Necasova Institute of Mathematics of the Academy of Sciences, Praha, Czech Republic 02/03/2010, 01:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: The motion of one or several rigid bodies in a viscous fluid occupying a bounded domain $\Omega in R^3$ represents an interesting theoretical problem featuring, among others, possible contacts of two or more solid objects. We consider the motion of several rigid bodies in a non-Newtonian fluid of a power-law type. Our main result establishes the existence of global-in-time solutions of the associated evolutionary system, when collisions of two or more rigid objects do not appear in a finite time unless they were present initially. |

A self-similar solution for the porous medium equation in a two-component domain Prof. Jan Filo Comenius University, Bratislava, Slovak Republic 01/27/2010, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: We solve a particular system of nonlinear ODEs defined on the two different components of the real line connected by the nonlinear contact condition |

2009 |
---|

Inverse iteration for purely imaginary eigenvalues with application to the detection of Hopf Bifurcations in large scale problems Prof. Dr. Karl Meerbergen Katholieke Universiteit, Leuven 12/16/2009, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: The detection of a Hopf bifurcation in a large scale dynamical system that depends on a physical parameter often consists of computing the right-most eigenvalues of a sequence of large sparse eigenvalue problems. Guckenheimer et. al. (SINUM, 34, (1997) pp. 1-21) proposed a method that computes a value of the parameter that corresponds to a Hopf point without actually computing right-most eigenvalues. This method utilises a certain sum of Kronecker products and involves the solution of matrices of squared dimension, which is impractical for large scale applications. However, if good starting guesses are available for the parameter and the purely imaginary eigenvalue at the Hopf point, then efficient algorithms are available. In this paper, we propose a method for obtaining such good starting guesses, based on finding purely imaginary eigenvalues of a two-parameter eigenvalue problem (possibly arising after a linearisation process). The problem is formulated as an inexact inverse iteration method that requires the solution of a sequence of Lyapunov equations with low rank right hand sides. It is this last fact that makes the method feasible for large systems. The power of our method is tested on numerical examples. |

The generalized Riemann problem (GRP) method for compressible fluid flows Prof. Jiequan Li School of Mathematics, Capital Normal University, Beijing, China 09/02/2009, 04:15 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: In this talk I will briefly review the generalized Riemann problem (GRP) method for compressible fluid flows. There were originally two versions of this method: |

ON THE CONTROL OF NUMERICAL EFFECTS OF DISPERSION AND DISSIPATION PREVAILING IN FINITE DIFFERENCE SCHEMES Dr. Bippine Appadu University of Mauritius, Reduit, Mauritius 09/02/2009, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: In CFD, Atmospheric Sciences and Computational Aeroacoustics, many problems involve regions of discontinuity. When used to solve problems involving regions of shocks, dispersive schemes give rise to oscillations while dissipative schemes cause smearing, close to these regions of sharp gradients. |

Discrete Empirical Interpolation for Nonlinear Model Reduction Prof. D. C. Sorensen Rice University, Houston, Texas 07/10/2009, 10:00 am Schwarzenbergstrasse 95, Building D, Room D1025 Abstract: A dimension reduction method called Discrete Empirical Interpolation (DEIM) will be presented and shown to dramatically reduce the computational complexity of the popular Proper Orthogonal Decomposition (POD) method for constructing reduced-order models for unsteady and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. |

IDR in variations Prof. Martin Gutknecht Seminar for Applied Mathematics, ETH Zurich 01/28/2009, 03:00 pm Schwarzenbergstrasse 95, Room 3.053 Abstract: The Induced Dimension Reduction (IDR) method is a Krylov space method for solving linear systems that was first developed by Sonneveld around 1979 and documented on three and a half pages of a 1980 proceedings paper by Wesseling and Sonneveld. Soon after IDR, Sonneveld introduced his widely applied Conjugate Gradient Squared (CGS) algorithm. Then, in 1990, van der Vorst suggested Bi-CGSTAB that he claimed to improve both those methods. |