Search result: Catalogue data in Autumn Semester 2014

Computational Science and Engineering Master Information
Electives
NumberTitleTypeECTSHoursLecturers
151-0113-00LApplied Fluid DynamicsW4 credits2V + 1UJ.‑P. Kunsch
AbstractApplied Fluid Dynamics
The methods of fluid dynamics play an important role in the description of a chain of events, involving the release, spreading and dilution of dangerous fluids in the environment.
Tunnel ventilation systems and strategies are studied, which must meet severe requirements during normal operation and in emergency situations (tunnel fires etc.).
ObjectiveGenerally applicable methods in fluid dynamics and gas dynamics are illustrated and practiced using selected current examples.
ContentOften experts fall back on the methodology of fluid dynamics when involved in the construction of environmentally friendly processing and incineration facilities, as well as when choosing safe transport and storage options for dangerous materials. As a result of accidents, but also in normal operations, dangerous gases and liquids may escape and be transported further by wind or flowing water.
There are many possible forms that the resulting damage may take, including fire and explosion when flammable substances are mixed. The topics covered include: Emissions of liquids and gases from containers and pipelines, evaporation from pools and vaporization of gases kept under pressure, the spread and dilution of waste gas plumes in the wind, deflagration and detonation of inflammable gases, fireballs in gases held under pressure, pollution and exhaust gases in tunnels (tunnel fires etc.)
Lecture notesnot available
Prerequisites / NoticeRequirements: successful attendance at lectures "Fluiddynamik I und II", "Thermodynamik I und II"
151-0709-00LStochastic Methods for Fluid DynamcisW4 credits3GD. W. Meyer-Massetti
AbstractThe course provides an introduction into stochastic methods that are applicable for example for the description and modeling of turbulent and subsurface flows. Moreover, mathematical techniques are presented that are used to quantify uncertainty in fluid flows and other physical systems.
ObjectiveBy the end of the course you should be able to mathematically describe random quantities and their effect on physical systems. Moreover, you should be able to develop basic stochastic models for engineering applications.
Content- Probability theory, single and multiple random variables, mappings of random variables
- Stochastic differential equations, Ito calculus, PDF evolution equations
- Polynomial chaos and other expansion methods
All topics are illustrated with application examples related mostly to turbulent flows and subsurface flows.
Lecture notesDetailed lecture notes will be provided.
LiteratureSome textbooks related to the material covered in the course:
Stochastic Methods: A Handbook for the Natural and Social Sciences, Crispin Gardiner, Springer, 2010
The Fokker-Planck Equation: Methods of Solutions and Applications, Hannes Risken, Springer, 1996
Turbulent Flows, S.B. Pope, Cambridge University Press, 2000
Spectral Methods for Uncertainty Quantification, O.P. Le Maitre and O.M. Knio, Springer, 2010
151-0317-00LVisualization, Simulation and Interaction - Virtual Reality IIW4 credits3GA. Kunz
AbstractThis lecture provides deeper knowledge on the possible applications of virtual reality, its basic technolgy, and future research fields. The goal is to provide a strong knowledge on Virtual Reality for a possible future use in business processes.
ObjectiveVirtual Reality can not only be used for the visualization of 3D objects, but also offers a wide application field for small and medium enterprises (SME). This could be for instance an enabling technolgy for net-based collaboration, the transmission of images and other data, the interaction of the human user with the digital environment, or the use of augmented reality systems.
The goal of the lecture is to provide a deeper knowledge of today's VR environments that are used in business processes. The technical background, the algorithms, and the applied methods are explained more in detail. Finally, future tasks of VR will be discussed and an outlook on ongoing international research is given.
ContentIntroduction into Virtual Reality; basisc of augmented reality; interaction with digital data, tangible user interfaces (TUI); basics of simulation; compression procedures of image-, audio-, and video signals; new materials for force feedback devices; intorduction into data security; cryptography; definition of free-form surfaces; digital factory; new research fields of virtual reality
Lecture notesThe handout is available in German and English.
Prerequisites / NoticePrerequisites:
"Visualization, Simulation and Interaction - Virtual Reality I" is recommended.

Didactical concept:
The course consists of lectures and exercises.
151-0833-00LPrinciples of Nonlinear Finite-Element-Methods Information W5 credits2V + 2UB. Berisha, P. Hora, N. Manopulo
AbstractMost problems in engineering are of nonlinear nature. The nonlinearities are caused basically due to the nonlinear material behavior, contact conditions and instability of structures. The principles of the nonlinear Finite-Element-Method (FEM) will be introduced in the scope of this lecture for treating such problems.
ObjectiveThe goal of the lecture is to provide the students with the fundamentals of the non linear Finite Element Method (FEM). The lecture focuses on the principles of the nonlinear Finite-Element-Method based on explicit and implicit formulations. Typical applications of the nonlinear Finite-Element-Methods are simulations of:

- Crash
- Collapse of structures
- Materials in Biomechanics (soft materials)
- General forming processes

Special attention will be paid to the modeling of the nonlinear material behavior, thermo-mechanical processes and processes with large plastic deformations. The ability to independently create a virtual model which describes the complex non linear systems will be acquired through accompanying exercises. These will include the Matlab programming of important model components such as constitutive equations
Content- Fundamentals of continuum mechanics to characterize large plastic deformations
- Elasto-plastic material models
- Updated-Lagrange (UL), Euler and combined Euler-Lagrange (ALE) approaches
- FEM implementation of constitutive equations
- Element formulations
- Implicit and explicit FEM methods
- FEM formulations of coupled thermo-mechanical problems
- Modeling of tool contact and the influence of friction
- Solvers and convergence
- Modeling of crack propagation
- Introduction of advanced FE-Methods
Lecture notesyes
LiteratureBathe, K. J., Finite-Element-Procedures, Prentice-Hall, 1996
Prerequisites / NoticeIf we will have a large number of students, two dates for the exercises will be offered.
263-5001-00LIntroduction to Finite Elements and Sparse Linear System Solving Information W4 credits2V + 1UP. Arbenz, T. Kaman
AbstractThe finite element (FE) method is the method of choice for (approximately) solving partial differential equations on complicated domains. In the first third of the lecture, we give an introduction to the method. The rest of the lecture will be devoted to methods for solving the large sparse linear systems of equation that a typical for the FE method. We will consider direct and iterative methods.
ObjectiveStudents will know the most important direct and iterative solvers for sparse linear systems. They will be able to determine which solver to choose in particular situations.
ContentI. THE FINITE ELEMENT METHOD

(1) Introduction, model problems.

(2) 1D problems. Piecewise polynomials in 1D.

(3) 2D problems. Triangulations. Piecewise polynomials in 2D.

(4) Variational formulations. Galerkin finite element method.

(5) Implementation aspects.


II. DIRECT SOLUTION METHODS

(6) LU and Cholesky decomposition.

(7) Sparse matrices.

(8) Fill-reducing orderings.


III. ITERATIVE SOLUTION METHODS

(9) Stationary iterative methods, preconditioning.

(10) Preconditioned conjugate gradient method (PCG).

(11) Incomplete factorization preconditioning.

(12) Multigrid preconditioning.

(13) Nonsymmetric problems (GMRES, BiCGstab).

(14) Indefinite problems (SYMMLQ, MINRES).
Literature[1] M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications. Springer, Heidelberg, 2013.

[2] H. Elman, D. Sylvester, A. Wathen: Finite elements and fast iterative solvers. OUP, Oxford, 2005.

[3] Y. Saad: Iterative methods for sparse linear systems (2nd ed.). SIAM, Philadelphia, 2003.

[4] T. Davis: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006.

[5] H.R. Schwarz: Die Methode der finiten Elemente (3rd ed.). Teubner, Stuttgart, 1991.
Prerequisites / NoticePrerequisites: Linear Algebra, Analysis, Computational Science.
The exercises are made with Matlab.
263-5150-00LScientific Databases Information W4 credits2V + 1UG. H. Gonnet
AbstractScientific databases share many aspects with classical DBs, but have additional specific aspects. We will review Relational DBs, Object Oriented DBs, Knowledge DBs, textual DBs and the Semantic Web. All these topics will be studied from the point of view of the scientific applications (Bioinformatics, Physics, Chemistry, Health, Engineering) A toy SDB will be used for exercises.
ObjectiveThe goals of this course are to:
(a) Familiarize the students with how existing DBs can be used for
scientific applications.
(b) Recognize the areas where SciDBs differ and require additional
features compared to classical DBs.
(c) Be able to understand more easily SciDBs, improve existing ones
or design/create new ones.
(d) Familiarize the students with at least two examples of SciDBs.
Content1) - Introduction, Statement of the problem, course structure, exercises,
why Scientific DBs (SDBs) do not fit exactly the classical DB area.
Hierarchy: File systems, data bases, knowledge bases and variations.
Efficiency issues and how they differ from classical DB.

2) - Relational DB used for scientific data, pros/cons
Introduction to RDB, limitations of the model, basics of SQL,
handling of metadata, examples of scientific use of RDBs.

3) - Object Oriented DB. Rich/structured objects are very appealing
in SDB. OODB primitives and environments. OODB searching.
Space and access time efficiency of OODBs.

4) - Knowledge bases, key-value stores, ontologies, workflow-based
architectures. WASA.

5) - MapReduce / Hadoop

6) - Storing and sharing mathematical objects, Open Math, its relation
with OODB and Knowledge bases. Also the problem of chemical
formula representation.

7) - SGML and XML, human-readable databases, genomic databases.
Advantages of human-readable databases (the huge initial success
of genomic databases).

8) - Semantic web, Resource Description Framework (RDF) triples, SparQL.
An example of very flexible database for knowlege storage. Goals of
the Semantic Web, discussion about its future.

9) - An ideal scenario (and the design of a toy system with most of the
desired features for exploration and exercises).

10) - Automatic dependency management, (make and similar). The graph
theory problem. Critical paths.

11) - Functional testing, Verifiers, Consistency, Short-circuit testing,
Recovery and Automatic recovery, Backup (incremental) methods.

12) - Performance and space issues, various uses of compression,
concurrency control. Hardware issues, clusters, Cloud computing,
Crowd-sourcing.

13) - Guest speaker: Ioannis Xenarios (UniProtKB/Swiss-Prot).
LiteratureSeveral papers and online articles will be made available.
There is no single textbook for this course.
A significant amount of material will be delivered in the lectures making lecture attendance highly recommended.
263-3010-00LBig Data Information W6 credits3V + 1U + 1AT. Hofmann
AbstractOne of the key challenges of the information society is to turn data into information, information into knowledge, and knowledge into value. To turn data into value in this way involves collecting large volumes of data, possibly from many and diverse data sources, processing the data fast, and applying complex operations to the data.
ObjectiveOne of the key challenges of the information society is to turn data into information, information into knowledge, and knowledge into value. To turn data into value in this way involves collecting large volumes of data, possibly from many and diverse data sources, processing the data fast, and applying complex operations to the data. This combination of requirements is typically referred to as Big Data and it has led to a completely new way to do business (e.g., develop new products and business models) and do science (sometimes referred to as data-driven science or the "fourth paradigm"). Unfortunately, big data grows faster than our ability to process the data so that new architectures and approaches for processing Big Data are needed.
ContentThe goal of this course is to give an overview of Big Data technologies. All aspects are covered: data formats and models, programming languages, optimization techniques, systems, and applications.
LiteraturePapers from scientific conferences and journals. References will be given as part of the course material during the semester.
263-2800-00LDesign of Parallel and High-Performance Computing Information W7 credits3V + 2U + 1AT. Hoefler, M. Püschel
AbstractAdvanced topics in parallel / concurrent programming.
ObjectiveUnderstand concurrency paradigms and models from a higher perspective and acquire skills for designing, structuring and developing possibly large concurrent software systems. Become able to distinguish parallelism in problem space and in machine space. Become familiar with important technical concepts and with concurrency folklore.
227-0102-00LDiscrete Event Systems Information W6 credits4GR. Wattenhofer
AbstractIntroduction to discrete event systems. We start out by studying popular models of discrete event systems. In the second part of the course we analyze discrete event systems from an average-case and from a worst-case perspective. Topics include: Automata and Languages, Specification Models, Stochastic Discrete Event Systems, Worst-Case Event Systems, Verification, Network Calculus.
ObjectiveOver the past few decades the rapid evolution of computing, communication, and information technologies has brought about the proliferation of new dynamic systems. A significant part of activity in these systems is governed by operational rules designed by humans. The dynamics of these systems are characterized by asynchronous occurrences of discrete events, some controlled (e.g. hitting a keyboard key, sending a message), some not (e.g. spontaneous failure, packet loss).

The mathematical arsenal centered around differential equations that has been employed in systems engineering to model and study processes governed by the laws of nature is often inadequate or inappropriate for discrete event systems. The challenge is to develop new modeling frameworks, analysis techniques, design tools, testing methods, and optimization processes for this new generation of systems.

In this lecture we give an introduction to discrete event systems. We start out the course by studying popular models of discrete event systems, such as automata and Petri nets. In the second part of the course we analyze discrete event systems. We first examine discrete event systems from an average-case perspective: we model discrete events as stochastic processes, and then apply Markov chains and queuing theory for an understanding of the typical behavior of a system. In the last part of the course we analyze discrete event systems from a worst-case perspective using the theory of online algorithms and adversarial queuing.
Content1. Introduction
2. Automata and Languages
3. Smarter Automata
4. Specification Models
5. Stochastic Discrete Event Systems
6. Worst-Case Event Systems
7. Network Calculus
Lecture notesAvailable
Literature[bertsekas] Data Networks
Dimitri Bersekas, Robert Gallager
Prentice Hall, 1991, ISBN: 0132009161

[borodin] Online Computation and Competitive Analysis
Allan Borodin, Ran El-Yaniv.
Cambridge University Press, 1998

[boudec] Network Calculus
J.-Y. Le Boudec, P. Thiran
Springer, 2001

[cassandras] Introduction to Discrete Event Systems
Christos Cassandras, Stéphane Lafortune.
Kluwer Academic Publishers, 1999, ISBN 0-7923-8609-4

[fiat] Online Algorithms: The State of the Art
A. Fiat and G. Woeginger

[hochbaum] Approximation Algorithms for NP-hard Problems (Chapter 13 by S. Irani, A. Karlin)
D. Hochbaum

[schickinger] Diskrete Strukturen (Band 2: Wahrscheinlichkeitstheorie und Statistik)
T. Schickinger, A. Steger
Springer, Berlin, 2001

[sipser] Introduction to the Theory of Computation
Michael Sipser.
PWS Publishing Company, 1996, ISBN 053494728X
227-0197-00LWearable Systems IW6 credits4GG. Tröster, U. Blanke
AbstractContext recognition in mobile communication systems like mobile phone and wearable computer will be studied using advanced methods from sensor data fusion, pattern recognition, statistics, data mining and machine learning.
Context comprises the behavior of individuals and of groups, their activites as well as the local and social environment.
ObjectiveFuture mobile systems will act as personal and cooperative assistant by providing the appropriate information and services. The systems consist of a smart phone which communicates with sensors on-body and in the environment. Context comprises user's behavior, his activities, his local and social environment.

In the data path from the sensor level to signal segmentation to the classification of the context, advanced methods of signal processing, pattern recognition and machine learning will be applied. Sensor data generated by crowdsouring methods are integrated. The validation using MATLAB is followed by implementation and testing on a smart phone.
Context recognition as the crucial function of mobile systems is the main focus of the course. Using MatLab the participants implement and verify the discussed methods also using a smart phone.
ContentThe next generation of mobile communication systems are integrated in our clothes and act as personal and cooperative assistant providing information we need just now (see Link). Context recognition - what is the situation of the user, his activity, his environment, how is he doing, what are his needs - as the central functionality of mobile systems constitutes the focus of the course.

The main topics of the course include
Sensor nets, sensor signal processing, data fusion, segmentation, Bayes Decision Theory, Decision Trees, Random Forest, kNN-Methods, Support Vector Machine, Hidden Markov Models, Adaboost, Crowdsourcing, SOM and clustering.

The exercises show concrete design problems like motion and gesture recognition using distributed sensors, detection of activity patterns and identification of the local environment.

Presentations of the PhD students and the visit at the Wearable Computing Lab introduce in current research topics and international research projects.

Language: german/english (depending on the participants)
Lecture notesLecture notes for all lessons, assignments and solutions.
Link
LiteratureLiterature will be announced during the lessons.
Prerequisites / NoticeNo special prerequisites
227-0417-00LInformation Theory IW6 credits4GA. Lapidoth
AbstractThis course covers the basic concepts of information theory and of communication theory. Topics covered include the entropy rate of a source, mutual information, typical sequences, the asymptotic equi-partition property, Huffman coding, channel capacity, the channel coding theorem, the source-channel separation theorem, and feedback capacity.
ObjectiveThe fundamentals of Information Theory including Shannon's source coding and channel coding theorems
ContentThe entropy rate of a source, Typical sequences, the asymptotic equi-partition property, the source coding theorem, Huffman coding, Arithmetic coding, channel capacity, the channel coding theorem, the source-channel separation theorem, feedback capacity
LiteratureT.M. Cover and J. Thomas, Elements of Information Theory (second edition)
227-0427-00LSignal and Information Processing: Modeling, Filtering, LearningW6 credits4GH.‑A. Loeliger
AbstractFundamentals in signal processing, detection/estimation, and machine learning.
I. Linear signal representation and approximation: Hilbert spaces, LMMSE estimation, regularization and sparseness.
II. Learning linear and nonlinear functions and filters: kernel methods, neural networks.
III. Structured statistical models: hidden Markov models, factor graphs, Kalman filter, parameter estimation.
ObjectiveThe course is an introduction to some basic topics in signal processing, detection/estimation theory, and machine learning.
ContentPart I - Linear Signal Representation and Approximation: Hilbert spaces, least squares and LMMSE estimation, projection and estimation by linear filtering, learning linear functions and filters, regularization and sparseness, singular-value decomposition and pseudo-inverse, principal-components analysis.
Part II - Learning Nonlinear Functions: fundamentals of learning, neural networks, kernel methods.
Part III - Structured Statistical Models and Message Passing Algorithms: hidden Markov models, factor graphs, Gaussian message passing, Kalman filter and recursive least squares, Monte Carlo methods, parameter estimation, expectation maximization.
Lecture notesLecture notes.
Prerequisites / NoticePrerequisites:
- local bachelors: course "Discrete-Time and Statistical Signal Processing" (5. Sem.)
- others: solid basics in linear algebra and probability theory
227-0627-00LApplied Computer ArchitectureW6 credits4GA. Gunzinger
AbstractThis lecture gives an overview of the requirements and the architecture of parallel computer systems, performance, reliability and costs.
ObjectiveUnderstand the function, the design and the performance modeling of parallel computer systems.
ContentThe lecture "Applied Computer Architecture" gives technical and corporate insights in the innovative Computer Systems/Architectures (CPU, GPU, FPGA, special processors) and their real implementations and applications. Often the designs have to deal with technical limits.
Which computer architecture allows the control of the over 1000 magnets at the Swiss Light Source (SLS)?
Which architecture is behind the alarm center of the Swiss Railway (SBB)?
Which computer architectures are applied for driver assistance systems?
Which computer architecture is hidden behind a professional digital audio mixing desk?
How can data volumes about 30 TB/s, produced by a protone accelerator, be processed in real time?
Can the weather forecast also be processed with GPUs?
How can a good computer architecture be found?
Which are the driving factors in succesful computer architecture design?
Lecture notesScript and exercices sheets.
Prerequisites / NoticePrerequisites:
Basics of computer architecture.
252-0237-00LConcepts of Object-Oriented ProgrammingW6 credits3V + 2UP. Müller
AbstractCourse that focuses on an in-depth understanding of object-oriented programming and compares designs of object-oriented programming languages. Topics include different flavors of type systems, inheritance models, encapsulation in the presence of aliasing, object and class initialization, program correctness, reflection
ObjectiveAfter this course, students will:
Have a deep understanding of advanced concepts of object-oriented programming and their support through various language features. Be able to understand language concepts on a semantic level and be able to compare and evaluate language designs.
Be able to learn new languages more rapidly.
Be aware of many subtle problems of object-oriented programming and know how to avoid them.
ContentThe main goal of this course is to convey a deep understanding of the key concepts of sequential object-oriented programming and their support in different programming languages. This is achieved by studying how important challenges are addressed through language features and programming idioms. In particular, the course discusses alternative language designs by contrasting solutions in languages such as C++, C#, Eiffel, Java, Python, and Scala. The course also introduces novel ideas from research languages that may influence the design of future mainstream languages.

The topics discussed in the course include among others:
The pros and cons of different flavors of type systems (for instance, static vs. dynamic typing, nominal vs. structural, syntactic vs. behavioral typing)
The key problems of single and multiple inheritance and how different languages address them
Generic type systems, in particular, Java generics, C# generics, and C++ templates
The situations in which object-oriented programming does not provide encapsulation, and how to avoid them
The pitfalls of object initialization, exemplified by a research type system that prevents null pointer dereferencing
How to maintain the consistency of data structures
LiteratureWill be announced in the lecture.
Prerequisites / NoticePrerequisites:
Mastering at least one object-oriented programming language (this course will NOT provide an introduction to object-oriented programming); programming experience
252-0417-00LRandomized Algorithms and Probabilistic MethodsW7 credits3V + 2U + 1AA. Steger, A. Ferber
AbstractLas Vegas & Monte Carlo algorithms; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks
ObjectiveAfter this course students will know fundamental techniques from probabilistic combinatorics for designing randomized algorithms and will be able to apply them to solve typical problems in these areas.
ContentRandomized Algorithms are algorithms that "flip coins" to take certain decisions. This concept extends the classical model of deterministic algorithms and has become very popular and useful within the last twenty years. In many cases, randomized algorithms are faster, simpler or just more elegant than deterministic ones. In the course, we will discuss basic principles and techniques and derive from them a number of randomized methods for problems in different areas.
Lecture notesYes.
Literature- Randomized Algorithms, Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press (1995)
- Probability and Computing, Michael Mitzenmacher and Eli Upfal, Cambridge University Press (2005)
252-0527-00LProbabilistic Graphical Models for Image Analysis Information W4 credits3GB. V. McWilliams
AbstractThis course will focus on the algorithms for inference and learning with statistical models. We use a framework called probabilistic graphical models which include Bayesian Networks and Markov Random Fields.

We will use examples from traditional vision problems such as image registration and image segmentation, as well as recent problems such as object recognition.
ObjectiveStudents will be introduced to probablistic graphical models and will learn how to apply them to problems in image analysis and understanding. The focus will be to study various algorithms for inference and parameter learning.
LiteratureWill be announced during the lecture.
252-0546-00LPhysically-Based Simulation in Computer Graphics Information W4 credits2V + 1UB. Solenthaler, B. Thomaszewski
AbstractThis lecture provides an introduction to physically-based animation in computer graphics and gives an overview of fundamental methods and algorithms. The practical exercises include three assignments which are to be solved in small groups. In an addtional course project, topics from the lecture will be implemented into a 3D game or a comparable application.
ObjectiveThis lecture provides an introduction to physically-based animation in computer graphics and gives an overview of fundamental methods and algorithms. The practical exercises include three assignments which are to be solved in small groups. In an addtional course project, topics from the lecture will be implemented into a 3D game or a comparable application.
ContentThe lecture covers topics in physically-based modeling,
such as particle systems, mass-spring models, finite difference and finite element methods. These approaches are used to represent and simulate deformable objects or fluids with applications in animated movies, 3D games and medical systems. Furthermore, the lecture covers topics such as rigid body dynamics, collision detection, and character animation.
Prerequisites / NoticeFundamentals of calculus and physics, basic concepts of algorithms and data structures, basic programming skills in C++. Knowledge on numerical mathematics as well as ordinary and partial differential equations is an asset, but not required.
327-5101-00LNonequilibrium SystemsW4 credits2V + 2UH. C. Öttinger
AbstractFoundations of nonequilbrium thermodynamics based on a unified approach, including hydrodynamics, linear irreversible thermodynamics and the theory of complex fluids
ObjectiveTo provide, illustrate, and practice the thermodynamic approach to describe time-evolving systems on a coarse-grained level in full accordance with the fundamental laws of thermodynamics
Content1. Introduction: Thermodynamics and Rigor, Formulating versus Deriving Irreversibility, Beyond Balance Equations, Framework, Equilibrium Thermodynamics of Stationary States, Fluctuations, Historical Context, Mechanics and Geometry, Functional Derivatives
2. Hydrodynamics: Balance Equations, Constructing Building Blocks
3. Linear Irreversible Thermodynamics: Forces and Fluxes, Transformation Behavior, Curie's Principle, Stationary States, Onsager-Casimir Relations, Thermoelectric Effects
4. Complex Fluids: Basic Rheological Properties, Linear Viscoelasticity, Nonlinear Material Behavior, Tensors and Scalars as Configurational Variables, Configurational Distribution Functions, Dumbbell Model of Polymer Solutions, Reptation Model of Polymer Melts
Lecture notesThe course is based on the book "Beyond Equilibrium Thermodynamics"
Literature1. H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, New York, 2005)
2. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamic (Dover Publications, New York, 1984)
3. H. J. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations (Oxford University Press, Oxford, 1981)
401-4647-64LFinite Element Methods for PDE-Constrained Optimal Control ProblemsW3 credits2VB. Vexler
AbstractIn this course we present theoretical and practical aspects of finite element methods applied to discretizations of PDE-constrained optimization problems.
Objective
ContentWe discuss different discretization concepts carefully taking
into account the difference between discretization of a single equation
and the discretization of an optimization problem. We derive a priori
error estimates for different situations including problems with
inequality constraints as well as problems governed by semilinear PDEs.
Moreover we discuss a posteriori error estimates and adaptive mesh
refinement algorithms for PDE-constrained optimization. Last but not
least, we give an overview of current research topics in this area.
Prerequisites / NoticeCompleted ETH BSc Mathematics, completed ETH BSc Computational Science and Engineering, or completed ETH MSc.
401-4655-64LNumerical Analysis of High-Dimensional ProblemsW6 credits3GC. Schwab
AbstractIn many applications of mathematics, efficient numerical methods for PDEs on high dimensional state and/or parameter spaces is required. This course provides succinct surveys of recently developed numerical methods, their computer implementation for model problems, and elements of their mathematical analysis for the efficient approximation of high- and infinite-dimensional PDE problems.
Objective
Content[not necessarily in order of appearance]

1. Infinite-Dimensional Analysis
Probability spaces and measures,
Tensor Products,
Measures on function spaces,
Covariance operators,
PCA and KL-expansions,
(generalized) polynomial chaos expansions,
Kolmogoroff N-widths

2. Examples.
Parametric Approximation Problems.
Parametric ODEs (biochemical reaction pathways).
Parametric PDEs (diffusion problems with random coefficients).
PDEs in Parametric Domains (Scattering from random obstacles).

3. Sparse Polynomial Chaos Approximations and Sparse Tensor Approximations of parametric PDEs.

4. Stochastic Galerkin Methods

5. Stochastic Collocation Methods
Smolyak's algorithm and its generalizations;
sparse, adaptive interpolation algorithms

6. Reduced Basis Methods

7. Monte Carlo Methods

8. Quasi-Monte Carlo Methods

9. Applications.
Bayesian Inverse Problems
Shape Sensitivity Analysis of PDEs.
Optimal Control of parametric ODEs and PDEs.
Optimization of Parametric ODEs and PDEs.
LiteratureBooks and Surveys:

1. A.T. Patera and G. Rozza:
Reduced Basis Approximation and A Posteriori Error Estimation
for Parametrized Partial Differential Equations,
MIT Press (2009)

2. F. Y. Kuo and Ch. Schwab and I. H. Sloan
Quasi-Monte Carlo methods for high dimensional integration -
the standard (weighted Hilbert space) setting and beyond,
ANZIAM Journal, 53/1 (2011), pp. 1-37.

3. A. Stuart: Bayesian Inverse Problems,
Acta Numerica, 19 (2010).

4. Ch. Schwab and C. J. Gittelson
Sparse tensor discretizations of
high-dimensional parametric and stochastic PDEs,
Acta Numerica, 20 (2011), pp. 291-467.
Prerequisites / NoticeETH BSc Math or equivalent

and

Num. elliptic and Parabolic PDE
or
Num. hyperbolic PDE

or

ETH Doctoral Studies in applied mathematics or CSE.

Programming:
MATLAB (for MSc MATH)
or
Python and C/C++/MPI programming (MSc CSE).
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