HGS MathComp Curriculum
|info||Finite Element Methods in Scientific Computing||Prof. Wolfgang Bangerth||March 19th -30th 2012||ECTS-Points: 6|
|Abstract: The course is intended to give students a perspective on the practical aspects of the finite element method, in particular on how typical finite element software is structured, on algorithmic details of how to efficiently implement it, and the pre- and postprocessing steps necessary in the scientific computing workflow. One of the most important lessons learned over the past decade is that due to their size, modern numerical software cant be written from scratch for each new project, and must instead build on existing software libraries that handle most of what constitutes the finite element method as well as linear algebra and|
parallel communication. Applications then only have to implement things like bilinear forms, outer nonlinear solution loops, and linear solvers specialized to the application.
The course will use a large Open Source finite element library and other open source tools for the entire workflow. The library, deal.II, can be found at http://www.dealii.org and is developed mainly at Texas A&M University in collaboration with other researchers worldwide. It is used as the standard research and teaching tool for numerical computing in the Department of Mathematics. It supports the discretization of arbitrary partial differential equations and runs on machines from laptops to supercomputers with more than 10,000 processors.
The first part of the course will be used to review the basic mathematical concepts used in this software, such as finite element theory and iterative solvers.
The rest of the course will be used for projects in which students are guided through the implementation of an application related to their research project or interests. Part of this will be teaching the use of modern software engineering practices, such as the use of revision control management systems (e.g. Subversion), writing documentation, and writing tests for automated testsuites. The goal is the development of a code that a) helps in the research of a student, and
b) may be used as the starting point for future generations of students. It may also be converted into a tutorial for deal.II.
An outline of topics to be covered is as follows:
* Basics of finite element methods
* Structure of finite element codes
* Assembling linear systems of equations and algorithmic aspects
* Iterative solvers for large linear systems
* Adaptive mesh refinement
* Vector-valued and mixed problems
* Nonlinear problems
* Postprocessing, visualization, and parallelization aspects
* Collaborative software development, e.g. through the use of subversion
* Software engineering practices for large-scale software, e.g. automated build and test systems, tools for documentation
* Additional topics may be chosen based on student interests.
This course is intended for students of mathematics involved in research.
Link for more information
|Time: 9:15||Location: INF 368, R 532
|info||Introductory Course on Stochastic Biological Systems: Modeling, Simulation and Parameter Estimation||Christoph Zimmer, Andreas Sommer, Prof. Dr. Ursula Kummer||March 20, 2012, 09:00-18:00||ECTS-Points: 1|
|Abstract: Target audience: |
Students with interest in stochastic modeling approaches. No previous knowledge necessary.
Biological systems are often modeled as systems of ordinary differential equations. This approach focuses on the time dependent development of the concentrations of the species in the model. Under certain circumstances, for example small number of molecules or intrinsic stochastic fluctuations, it is necessary to consider these in the modeling approach, as the introduction of stochasticity can alter both qualitative and quantitative behavior of the model. This course will show examples in which modeling with ordinary differential equations is not appropriate, and introduce stochastic differential equations and Markov jump processes as means to cope with stochasticity.
The day starts with a lecture on modeling with ordinary differential equations to have a common starting point, followed by a basic introduction to stochastic differential equations (Ito; calculus) and simple simulation methods are introduced. In the second part of the morning session, the modeling with Markov processes is physically motivated and, for simulation, the standard algorithm of Gillespie is shown.
Although simulation algorithms exists for a long time, parameter estimation in stochastic settings is still a field of ongoing research. Some new results will be discussed here. The day will be completed with a practical lesson on how to perform stochastic simulations with Copasi and Matlab.
Registration please contact:
|Time: 9:00||Location: Bioquant Building, INF 267, room 042
|info||Brachiation mechanics and robotics: analysis, simulation, and construction||Prof. Dr. M. Coleman, Prof. Dr. K. Mombaur||March 26-30, 2012; Preliminary discussion: March 21, 2012, 11:00||ECTS-Points: 4|
|Abstract: Study braciation mechanics in theory and practice. |
Plase sign up for this course until March 15 by sending and email to firstname.lastname@example.org
This course will be a brief introduction to brachiation mechanics and robotics. The course will involve studying simple mechanical/ mathematical models, simulating the models on the computer, and building physical models using construction toys and very basic construction materials.
Prerequisites: Introductory dynamics and system dynamics, elementary linear algebra including linear equation solution and eigenvalues/eigenvectors, elementary ordinary differential equations, basic MATLAB skills including ODE simulation, linear equation solving, eigenvalue-eigenvector calculation, basic graphics.
|Time: 11:00||Location: IWR Robotics Lab
|info||Parameter Estimation and Optimum Experimental Design||Dr. Stefan Körkel, Dr. Mario Mommer||April 10-13, 2012, 9:00-16:00||ECTS-Points: 5|
|Abstract: Topic of this course are methods for optimization based modelling. It consists of nine lectures about nonlinear process models, parameter estimation and nonlinear optimum experimental design for parameter estimation and model discrimination. Aim is to make the participants familiar with modeling concepts, formulation of optimization problems|
in model validation and numerical approaches and methods for the solution. The final day of the four-day course is intended as exchange of experiences between modelers, users and developers of the methods.
|Time: 9:00||Location: IWR, INF 368, R. 432
|info||Mechanisms of biological pattern formation: mathematical models versus experimental findings||Prof. Dr. Anna Marciniak-Czochra and Dr. Mihaela Zigman (Center of Organismal Studies, University of Heidelberg)||Preliminary discussion: April 19, .2012, 14.00||ECTS-Points: 6|
|Abstract: To celebrate the centenary of Allan Turing´s birth and the 60th anniversary of his famous paper ,,The Chemical Basis of Morphogenesis__, which settled foundations of mathematical theory of biological and chemical pattern formation, we organize an interdisciplinary seminar aimed to bring together graduate and undergraduate students from mathematics and natural sciences interested in mathematical models and methods as well as biological theories of pattern formation.|
The topics of the seminar will include a classical reaction-diffusion theory, as proposed by Turing in his seminal paper and then applied eg. in the activator-inhibitor models, and more recent approaches such as models based on the existence of multiple steady states and switches in the intracellular dynamics and models involving biomechanical interactions within the tissue. Models and related theoretical concepts will be presented and discussed on examples of symmetry breaking and pattern formation in the model organisms of developmental biology (eg. Hydra and Drosophila) as well as in plants.
|Time: 14:00||Location: INF 294, SR 214
|info||Modeling of Plant Growth and Scientific Visualization||Somporn Chuai-Aree (Meng)||May 10-11, 14-15, 2012; 10:15-12:15 & 14:00-16:00||ECTS-Points: 3|
|Abstract: Plant growth modeling is a challenging topic involving multidisciplinary aspects such as computer science, computer graphics, computer simulation and visualization, mathematical modeling, etc. It plays a big role in agriculture and industry. This course provides information from the basic level of structural and functional plant growth modeling to the advanced level for plant growth simulation. |
The course consists of the following topics:
- Lindenmayer systems (L-systems),
- particle transportation system,
- growth function,
- plant growth simulation,
- leaf vein generator,
- root growth simulation,
- leaf shape recognition using artificial neural networks,
- plant growth measurement using image processing and region growth method,
- visualization method in plant growth,
- PlantVR software.
L-systems are used to represent the plant structure. The classes of L-systems such as deterministic and stochastic L-system are described in the course. The particle transportation method (PTM) is used to simulate the leaf vein and plant structure. The course will show some examples in each topic.
Please register here:
Link for more information
|Time: 10:15||Location: Bioquant, INF 267; seminar room 43
|info||Practical parameter estimation methods||Prof. Wolfgang Bangerth||July 9th-20th 2012||ECTS-Points: 6|
|Abstract: Mathematical models are used throughout all of the natural sciences, engineering, biology and many other areas including the social sciences to describe, understand, and optimize natural and man-made systems. All such models contain parameters specific to this particular system. For example, to describe population growth, we need to know the growth rate; to model the flight of air planes, we need to know the density and viscosity of air; to simulate the nervous system, we need to know the excitation potential of neurons; or to model financial markets, we need to know the statistics of volatility.|
Accurate modeling therefore requires us to determine these parameters from observations or experiments. This is the realm of the mathematical field of parameter estimation. This class will discuss the mathematical basics of parameter estimation as well as many practical aspects of its application to problems in the applied sciences. The target audience is graduate students from the non-mathematical sciences interested in modeling in their area, as well as interested mathematics graduate students. I intend to cover the following basic areas, with details to be determined (and
to be adjusted based on the audience):
* Examples of parameter estimation problems
* Mathematical formulation of parameter estimation problems as optimization problems
* Methods of solving parameter estimation problems
* Inverse problems: Parameter estimation for differential equations
* Assessing the accuracy of parameter estimates
* A different viewpoint: Bayesian inversion
Depending on demand, the class may involve student presentations on how to apply these techniques to their own areas of research.
Link for more information
|Time: 9:15||Location: INF 368, R 432 (preliminary)
|info||Atomistic-to-Continuum Modeling and Computing||Prof. Mitchell Luskin||July 17th- Aug 9th 2012; Tuesdays 16:00 & Thursdays 11:00||ECTS-Points: 2|
|Abstract: Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long-range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis has clarified the relation between the various methods and their sources of error. This lecture will begin by introducing the physical and mathematical background and then presenting the current state of numerical analysis for atomistic-to-continuum coupling methods.|
Dates and Places:
Thursday, July 19th, 11:00 IWR, room 432
Tuesday, July 24th, 31st & Aug 7th, 16:00 IWR, room 532
Thursday, July 26th, Aug 2nd and 9th, 11:00 IWR, room 432
Link for more information
|Time: 11:00||Location: IWR, INF 368, Room 432 & 532
|info||Parallel Computing||Prof. Peter Bastian, Dr. Stefan Lang, Dr. Olaf Ippisch||July 30 - Aug.2, 2012||ECTS-Points: 3|
|Abstract: The students learn|
- to understand and use current parallel computers
- plan and assess parallel agorithms
Hardware architecture of parallel computers
- open MP
- Parallel Algorithms
- Efficiency and Scalability
Prerequisites: Basis C++ programming
Please register untill 25 July: http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=75
|Time: 9:00||Location: IWR INF 368 and OMZ U011/U012
|info||Practical Image Processing||PD Dr. Christoph Garbe||30. July - 3. August 2012; 9:00-12:00 and 13:30-16:00||ECTS-Points: 3|
|Abstract: Objectives& Goals|
Today, a plethora of image processing algorithms exists, ranging from very basic and easy to implement to highly sophisticated. At the same time, imaging sensors are becoming increasingly wide spread and are quickly being adopted by new application domains. To the practitioner it is often unclear which processes can be automated by image processing routines and which type of algorithm is best suited to solve the problem at hand. At the same time, image processing algorithms make implicit or explicit assumptions with respect to the data or the models used. Using image processing routines in a software package as a black box entails the risk to choose wrong parameters or or an algorithms in which some assumptions are violated. This may lead to inaccurate or downright wrong results.
In this short course, basic image processing tasks such as image enhancement / denoising, feature detection, object segmentation and -classification as well as motion estimation will be introduced. The concepts of the different approaches will be detailed. The focus will be on understanding how the algorithms work and which assumptions are made. We will skip over stringent mathematical proofs. This short course will introduce the basic algorithms but also give an overview of current state-of-the-art approaches. The course is aimed at practitioners from all fields, but the main examples will be from the field of biology, fluid mechanics and environmental sciences. The course will consist of lectures in the morning and hands on practicals in the afternoon. Basic programming skills are advantageous.
|Time: 9:00||Location: HCI, Speyerer Str. 6, SR 2.22 and PC-Pool
|info||Vernetzungen und Verstrickungen: Digital Humanities and the New Sience of Complex Networks||Dr. Maximilian Schich & Dr. Katharina Zweig||10.09.-12.09.2012||ECTS-Points: not yet determined|
|Abstract: In den letzten Jahren haben die vermehrten Sozialkontakte durch neue Medien, insbesondere Smart Phones und soziale Netzwerkplattformen, unser privates Leben verändert, und gleichzeitig werden in den Medien immer mehr die globalen Vernetzungen und Verstrickungen in und zwischen den nationalen Markt- und Arbeitssystemen sichtbar gemacht. Die Datenflut nimmt uns die Sicht und schärft gleichzeitig die Sicht anderer auf uns. Wie können diese Strukturen quantitativ bestimmt und untersucht werden? Welchen Einfluss haben Netzwerkstrukturen auf die unser Verhalten, die Kunst und die Sprache, und welchen Einfluss hat unser Verhalten, die Sprache oder die Kunst auf unsere Netzwerke? In diesem Kompaktkurs werden wir uns zuerst mit sogenannten Netzwerkphänomenen beschäftigen: den Small-World-Effekt und das The rich get richer-Phänomen, zusammen mit Netzwerkmodellen, die ihre Herkunft erklären. Dann werden verschiedene Methoden vorgestellt, mit denen Netzwerke quantitativ beschrieben und visualisiert werden können. Im letzten Teil des Kompaktkurses werden die Studierenden Referate über Anwendungen der Netzwerkanalysemethoden auf Fragen im Bereich der Digital Humanities, der Kunstgeschichte, der Lebensmittelforschung, und den Sprachwissenschaften vorstellen, und weitere Anwendungsmöglichkeiten werden wir gemeinsam diskutieren.|
(Der Kurs wird möglicherweise teilweise in Englisch abgehalten.)
Link for more information
|Time: 9:00||Location: Marsilius Kolleg, Hauptstr. 232-234, 69117 Heidelberg
||ECTS-Points: not yet determined|
|info||DUNE Spring Course 2012||Prof. Dr. Peter Bastian, Dr. Stefan Lang, Dr. Olaf Ippisch, Dr. Markus Blatt,||March 19th - March 23rd, 2012||ECTS-Points: 3|
|Abstract: The Distributed and Unified Numerics Environment (DUNE) is a software framework for the numerical solution of partial differential equations with grid-based methods. Using generic programming techniques it strives for both high flexibility (efficiency of the programmer) and high performance|
(efficiency of the program). DUNE provides, among other things, a large variety of local mesh refinement techniques, a scalable parallel programming model, an ample collection of finite element methods and efficient linear solvers.
This one week course will provide an introduction to the most important DUNE modules. At the end the attendees will have a solid knowledge of the simulation workflow from mesh generation and implementation of finite element and finite volume methods to visualization of the results. Successful participation requires knowledge of object-oriented programming using C++ including generic programming with templates. A solid background on numerical methods for the solution of PDEs is expected.
Registration deadline: Sunday February 26 2012
Dates: March 19 2012 - March 23 2012
Interdisciplinary Center for Scientific Computing University of Heidelberg,
Im Neuenheimer Feld 350/368
69120 Heidelberg, Germany
Fee: The fee for this course is 200 EUR including course material, coffee and lunch breaks as well as course dinner on Wednesday.
For registration and further information see http://conan.iwr.uni-heidelberg.de/dune-workshop/index.html
- know advanced C++ programming concepts
- get an introduction to the DUNE grid interface
-can use PDELAB to solve differnet kinds of partial differential equations
- Advanced C++ programming
- DUNE grid interface
- PDELAB for stationary and instationary (non)linear second order PDE
Prerequisites: Good C++ programming skills
Link for more information
|Time: 9:00||Location: IWR INF 368 R 432 and OMZ U011/U012
|info||Modeling of biological processes with COPASI||Prof. Dr. Ursula Kummer, Christoph Zimmer||July 10 & 11,2012||ECTS-Points: 1|
|Abstract: Objectives and Goals:|
Introduction to the modeling of cellular systems like metabolic networks and signalling cascades.
This will be done by using the software COPASI and learning about relevant methods in this context, including ODE based modeling, sensitivity analysis, elementary modes and complexity reduction.
The course aims at computational people who are interested in venturing into biological applications.
Please register here:
|Time: 9:00||Location: Bioquant Building
|Key Competence Courses|
|info||Poster Design||Dr. Ben Brüggemann||April 24th 2012; 09:00-17:00||ECTS-Points: 1|
The participants learn to produce appealing and effective scientific posters to communicate their research outcomes to the scientific community.
Contents of a poster:
* Defining the story.
* Choosing a suitable amount of information.
* Following a line of argumentation.
* Title and poster sections.
* Fonts and font sizes.
* Color scheme.
* What program to choose?
* Printing a poster.
* Each participant can give a short presentation of an existing poster, with peer and trainer feedback for the presentation and the poster.
|Time: 9:00||Location: IWR, Room 520
|info||Assessment Center Training (in German)||Michael Müller, Maximilian Scheidt||July 4, 2012, 10:00-18:00||ECTS-Points: 1|
|Abstract: Das Training bietet die Möglichkeit die einzelnen Bausteine eines Assessment Centers zu durchlaufen. Die Teilnehmer trainieren Selbstpräsentation, Gruppendiskussion, Rollenspiele, Postkorbübung sowie Logiktests aus Gruppenauswahlverfahren. Sie bekommen eine dezidierte Auswertung ihrer Selbstpräsentation und des Rollenspiels per Videoanalyse Darüber hinaus erhalten die Teilnehmer Informationen zu den Erwartungen der Personalverantwortlichen.|
Besonderen Wert wird auf den Part des Auftretens und der Rhetorik gelegt. Den Teilnehmern wird ein besseres Gefühl für bewusstes Einsetzen von Körper und Sprache vermittelt.
In einem separaten Gespräch erhält jeder Teilnehmer ein ausführliches, individuelles Feedback, um sich weiter verbessern zu können.
Please register here:
|Time: 10:00||Location: INF 368, Room 520
|info||Project Management Tailored for Doctoral Thesis||Andreas Lowinger||Aug 1st & 2nd 2012 + review end of Sept. (0.5 day)||ECTS-Points: 2|
|Abstract: Working as a PhD student you have the challenging task of developing research findings and write you doctoral thesis within three years. This alone is a demanding job. In addition, it is vital to the scientific process that your findings are presented to the scientific community. For most PhD students this is the first big project in their professional life and it could have a crucial impact on their future professional career. PhD students are highly motivated when they start their PhD studies but may underestimate the need for professional management for this three-year project ,,doctoral thesis´´|
This seminar demonstrates how to approach the doctoral thesis in a professional way. Project management tools and techniques are used, tailored to the specific situation of PhD students. You will learn how to set a project vision, define clear objectives, gain buy-in from your supervisor and other colleagues in your group, and how to develop a project plan, which is structured and at the same time flexible enough to easily adjust to unexpected findings. You will establish a ,,controlling cycle´´ which helps you to recognise risks and problems as early as possible, and you will learn how to manage critical situations and deal with ups and downs. Furthermore, networking with colleagues, supervisors and other people is an important topic of this seminar.
Throughout the seminar, you will work on your own doctoral thesis and share your experience with others. This seminar is most beneficial for PhD students who are in the early phases of their doctoral thesis. At the end of the seminar you will have established a strategy on how to approach your own doctoral thesis. During the follow-up REVIEW we will share experience and best practices and deal with open questions from the first module.
This seminar will help you to make the most effective use of your three years and finish your doctoral thesis on time. You will also learn and practise the basic concepts of project management - which are required in industry and research institutions.
Link for more information
|Time: 9:00||Location: IWR, INF 368, Room 520
|Workshops & Schools|
|info||Probabilistic forecasting of high-impact extreme weather events||Prof. Dr. Tilmann Gneiting, Dr. Thordis L. Thorarinsdottir||April 25, 2012||ECTS-Points: 0|
|Abstract: Accurate forecasts of severe weather events are of crucial societal relevance and require the joint effort of atmospheric and mathematical scientists. High-impact extreme weather events, such as heavy rainfall and/or strong winds are very often associated with intensive atmospheric fronts with strong gradients or deep moist convection. These events are governed by mesoscale atmospheric dynamics, operating on horizontal scales ranging from a few to several hundred kilometers. The understanding of these dynamics and their inclusion in modern numerical weather prediction models is under constant development while statistical simulation methods are called for to explore the interacting dynamics that happen at subgrid-scales. Similarly, statistical post-processing of the outputs of the numerical weather prediction models is an essential component of precise forecasts which aims to correct for possible biases and the imperfect representation of uncertainty in the forecast. This workshop will bring together academic atmospheric scientists and mathematicians, as well as atmospheric scientists from the German Weather Service to discuss the current challenges in predicting severe weather events and to further strengthen the connections between the two disciplines. |
|Time: 8:30||Location: Internationales Wissenschaftsforum Heidelberg, Hauptstrasse 242
|info||Modeling, Simulation, and Optimization of Uncertain Systems||Dr. Christian Kirches||June 4th-6th 2012||ECTS-Points: 2|
|Link for more information||Time: 9:00||Location: Heidelberg Academy of Sciences
|info||Solid State Electrochemistry for Energy Storage and Conversion||T. Carraro, W. Chueh, F, Ciucci, G. Gregori||ECTS-Points: 2|
|Abstract: This interdisciplinary workshop covers mathematical modeling and numerical methods applied to electrochemistry as well as the latest advances in experimental techniques and novel ionic materials |
Link for more information
|Time: 13:00||Location: IWR, INF 368, room 432, 69120 Heidelberg
|info||Discovering new horizons with deal.II||Thomas Wick, Bärbel Janssen, Matthias Maier||ECTS-Points: 3|
|Abstract: The workshop focuses topics like:|
- Use cases and applications of the library
- What users think would be useful directions for the library to go into, things that are missing, and possibly getting people together who can help implement those parts
- Newer parts of the library (e.g. massively parallel computing, multiphysics coupling, etc) and how these could help in your programs.
We invite talks and plan discussions by users and existing developers in the following areas:
- use cases and applications of the library
- what users think would be useful directions for the library to go into, things that are missing, and possibly getting people together who can help implement those parts
- newer parts of the library (e.g. hp, multithreading,
optimization, etc) and how these could help in your programs.
Timo Heister (Texas A&M University)
Bärbel Janssen (University of Bern)
Matthias Maier (Heidelberg University)
Thomas Wick (Heidelberg University)
Link for more information
|Time: 8:00||Location: Interdisciplinary Center for Scientific Computing, INF 368, room 432
|info||3rd Workshop on Measurement and Computation of Turbulent Spray Combustion (TCS 3)||Prof. Dr. Eva Gutheil||Sept.2, 2012||ECTS-Points: 1|
Link for more information
|Time: 10:00||Location: Rottmannsaal, Heidelberg-Handschuhsheim
|info||2nd Workshop on Engine Combustion (ECN 2 - Engine Combustion Network)||Prof. Dr. Eva Gutheil||Sept. 7 & 8, 2012||ECTS-Points: 1|
(PDF) ||Time: 9:00||Location: INF 252
|info||Spring School: Theory of compressible and dissipative MHD flows in high energy physics (part I)||Dr. Ahmad Hujeirat||April 2-5, 2012||ECTS-Points: 3|
|Abstract: In this course the physical and mathematical properties of fluid flows in high energy physics will be studied. The properties of Euler and Navier-Stokes type flows, the transition to turbulence, the effects of compressibility, viscosity, resistivity and conductivity and superfluidity in MHD-flows will be analyzed. A general introduction to the numerical aspects and treatment of dissipative flows will be discussed as well.|
Registration & further information are available on:
Topics of the course: Mathematical treatment of hyperbolic, parabolic and elliptical equations, the different types of boundary conditions, linear versus non-linear equations, Euler and Navier- Stokes equations and the corresponding fluid numbers, the concept of compressibility (strongly & weakly incompressible flows), characterizing the involved time and length-scales, incorporating the effects of magnetic fields. Basics in finite difference and finite volume methods, explicit versus implicit solution procedures.
|Time: 9:00||Location: Room 432 INF 368
|info||PRACE Spring School: Development of Petascale Applications||Various||May 16 - 18, 2012||ECTS-Points: 2|
|Abstract: Registration deadline: March 31, 2012|
ICM, University of Warsaw is one of the organizing institutions of thevPRACE Spring School that will take place from the 16th to the 18th of May 2012 in Cracow, Poland. In this three-day event, called School for Developers of Petascale Applications, the participants will learn how to create efficient and scalable parallel codes for PRACE Tier-0
Link for more information
|Time: 8:00||Location: Kraków, Poland
|info||Nichtlineare optimale Kontrollprobleme: Einführung||Dr. Thomas Lorenz||Mo 14:00-16:00||ECTS-Points: 4|
|Abstract: Großgebiet: Nichtlineare Analysis|
Inhalt: Gewöhnliche Differenzialgleichungen stellen eine weit verbreitete Grundlage zur Systembeschreibung dar sowohl in den Naturwissenschaften, der Ökonomie als auch dem Ingenieurwesen. Dabei bieten häufig Parameter eine direkte Möglichkeit, auf das System Einfluss zu nehmen und es zu steuern. Das einfache Beispiel eines Schalters macht bereits deutlich, dass diese Parameter im Allgemeinen nicht als stetig (in der Zeit) angenommen werden können.
Diese Vorlesung bietet einen Einstieg in gewöhnliche Differenzialgleichungen, die zusätzlich von einem Parameter abhängen, der (nur) integrierbar von der Zeit abhängt und dessen Werte in einer vorgegebenen Kontrollmenge liegen müssen.
Unter den Lösungen eines solchen sog. Kontrollsystems sind insbesondere jene von Interesse, die ein vorgegebenes Funktional maximieren (bzw. minimieren). Auf der Suche nach den optimalen Kontrollen werden notwendige Bedingungen vorgestellt, die sich mit Hilfe der Hamiltonfunktion oder des Pontryagin_schen Maximumprinzips formulieren lassen.
Literatur: wird bekanntgegeben
Voraussetzungen: Grundvorlesungen Analysis und Lineare Algebra
Zielgruppe: Studierende im Hauptstudium Mathematik (inkl. Lehramt)
Bemerkungen: Die Kontrolltheorie dient in dieser Vorlesung als ein Beispiel für den Schritt von bekannten Resultaten aus dem Grundstudium (insbesondere dem Satz von Picard-Lindelöf über gewöhnliche Differenzialgleichungen) zu entsprechenden Ergebnissen unter deutlichen schwächeren Annahmen.
Dabei soll der Blick für relevante Aspekte in der analytischen Vorgehensweise geschärft werden.
Link for more information
|Time: 14:00||Location: INF 294, AM HS 134
|info||Statistical Forecasting||Prof. Dr. Tilmann Gneiting||Tuesdays||ECTS-Points: 6|
|Abstract: To have a firm understanding of the statistical theory of forecasting, and the ability to design, implement and evaluate prediction techniques.|
Basic notions: statistical decision theory, probabilistic and point forecasts, prediction spaces, information bases, calibration and sharpness
Proper scoring rules and consistent scoring functions
Times series forecasts and spatial prediction
Statistical postprocessing of ensemble forecasts; combining numerical and statistical approaches
Applications and case studies in meteorology, economics and other disciplines
Prerequisites: Statistik I or equivalent; Wahrscheinlichkeitstheorie I or equivalent
|Time: 9:00||Location: INF 294, HS -101
|info||Computer Graphics II (ICG2)||Dr. Susanne Krömker||Wednesdays and Fridays, 11:15-12:45||ECTS-Points: 6|
|Abstract: To have a firm command of programmable graphics hardware with C for graphics and advanced packages for global rendering methods using numerical algorithms for solving nonlinear systems of equations|
Shaders based on Bidirectional Reflectance Distribution Function (BRDF)
Programmable Graphics Hardware with C for graphics (Cg)
2. Advanced Methods for Global Rendering
Radiosity versus Raytracing
3. Rendering of Large Data Sets
Data Reduction and Splines
Prerequisites: Introduction to Applied Computer Science (IPR), Programming Course (IPK), Computer Graphics 1 (ICG1)
Preliminary discussion: Wednesday, April 18, 11:15 h, IWR, R 532
|Time: 11:15||Location: IWR, R 532 and OMZ, R U012
|info||Numerical Methods in Continuum Mechanics||Prof. Dr. Rolf Rannacher||Wed. 11-13, Fr. 9-11||ECTS-Points: 6|
|Abstract: This special lecture of the master program, also suitable for doctoral students working in this field.|
Continuum mechanical models are used to describe the flow of liquids and gases (Navier-Stokes equations) and the deformation of elastic bodies (Lame-Navier equations). First, the derivation of these equations from physical principles and their solution properties are discussed. Then, for their numerical solution, especially examines the method of finite elements, with emphasis on the treatment of transient cases.
This lecture is held in German.
|Time: 11:00||Location: INF 293, URZ, SR 215
|info||Reaction-diffusion equations and pattern formation||Prof. Dr. Anna Marciniak-Czochra||Preliminary discussion: April 26,2012; Lecture: Thursdays 9:30-11:00||ECTS-Points: 6|
|Abstract: The lectures will be devoted to the analysis of systems of reaction-diffusion equations and their applications to describe processes of pattern formation.|
After presenting classical analytical results concerning existence, uniqueness and regularity of solutions, we will provide a set of tools allowing a comparison between the dynamics of reaction-diffusion models and their ODEs counterparts, such as comparison principle and theory of bounded invariant rectangles. Then, we will focus on the analysis of mechanisms of pattern formation based on Turing-type instability and hysteresis. The last part of the course will be devoted to the models of coupled reaction-diffusion equations and ordinary dierential equations (models with degenerated diusion). Analytical framework will be illustrated by several examples of the applications, including classical Turing patters, spike patterns in the models with degenerated diffusion and transition layers arising from multistability effects.
|Time: 9:30||Location: INF SR 042
|info||3D-Acquisition - Equipment Studies & Surveying||Carsten Casselmann (UFG/Archaeology), Markus Forbriger (Geography), Hubert Mara (IWR)||April 16th 2012; 09:00-17:00||ECTS-Points: not yet determined|
|Abstract: Introduction and practical exercises with new 3D technologies for applications in Cultural Heritage and Geodesy.|
Acquiring knowledge in 3D-acquisition technologies and data-processing from larges objects (e.g. building, landscapes) to small objects (e.g. coins, ceramics, cuneiform tablets).
Prerequisites: Vermessungskunde (I/II) - Basic knowledge/course about surveying technology (e.g. Geodesy)
|Time: 9:00||Location: tba
||ECTS-Points: not yet determined|
|info||Nonlinear Parameterestimation||Prof. Dr. H. G. Bock, Dr. Johannes P. Schlöder||Preliminary discussion: April 16, 2012, 16:15||ECTS-Points: 3|
|Time: 16:15||Location: IWR, INF 368, Room 432
|info||Simulation of Multiphase Flows||Prof. Dr. Eva Gutheil||Mondays 9.15 - 10.45||ECTS-Points: 3|
|Time: 9:15||Location: INF 368, SR 248
|info||Quantum Dynamics and Electronic Structure of Molecular Systems||Prof. Dr. Lorenz Cederbaum||Mondays 14.15-15.45||ECTS-Points: 0|
|Time: 14:15||Location: INF 229, SR 108/110
|info||Quadratic Programming||Dr. Christian Kirches, Dr. Andreas Potschka||regular meetings Tuesdays, 2-6pm||ECTS-Points: 3|
|Abstract: In the seminar ,,Quadratic Programming´´ we will consider finite dimensional optimization problems, so called Quadratic Programs (QPs), which comprise a quadratic objective function and linear equality and inequality constraints. This important problem class has many applications to real world problems and arises as a subproblem in iterative methods for more general optimization problems. The seminar attendees will present original research and review papers, which cover theoretical results, applications, and numerical approaches for the solution of QPs. The language of the seminar will be English, unless all attendees are fluent in German. ||Time: 14:00||Location: INF 368, R 532 (preliminary)
|info||Theoretical and Computational Chemistry||Prof. Dr. Andreas Dreuw||Thursdays 16:00-18:00||ECTS-Points: 3|
|Time: 14:15||Location: INF 368 / IWR R 432