Search result: Catalogue data in Spring Semester 2021

Computational Science and Engineering Master Information
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
252-0232-AALSoftware Engineering
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-6 credits13RF. Friedrich Wicker, M. Schwerhoff
AbstractThis course introduces both theoretical and applied aspects of software engineering. It covers:

- Software Architecture
- Informal and formal Modeling
- Design Patterns
- Software Engineering Principles
- Code Refactoring
- Program Testing
ObjectiveThe course has two main objectives:

- Obtain an end-to-end (both, theoretical and practical) understanding of the core techniques used for building quality software.
- Be able to apply these techniques in practice.
ContentWhile the lecture will provide the theoretical foundations for the various aspects of software engineering, the students will apply those techniques in project work that will span over the whole semester - involving all aspects of software engineering, from understanding requirements over design and implementation to deployment and change requests.
LiteratureWill be announced in the lecture
406-0353-AALAnalysis III
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RF. Da Lio
AbstractThe focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
Objective
LiteratureReference books and notes

Main books:

Giovanni Felder: "Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure" (Download PDF: Link ),
Erwin Kreyszig: "Advanced Engineering Mathematics", John Wiley & Sons, just chapters 11, 16.


Extra readings:

Norbert Hungerbühler: "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich,
Yehuda Pinchover, Jacob Rubinstein: "Partial Differential Equations", Cambridge University Press 2005.


For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis (Download PDF)
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-0603-AALStochastics (Probability and Statistics)
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RM. Kalisch
AbstractIntroduction to basic methods and fundamental concepts of statistics and
probability theory for non-mathematicians. The concepts are presented on
the basis of some descriptive examples. The course will be based on the
book "Statistics for research" by S. Dowdy et.al. and on the
book "Introductory Statistics with R" by P. Dalgaard.
ObjectiveThe objective of this course is to build a solid fundament in probability
and statistics. The student should understand some fundamental concepts and
be able to apply these concepts to applications in the real
world. Furthermore, the student should have a basic knowledge of the
statistical programming language "R". The main topics of the course are:
- Introduction to probability
- Common distributions
- Binomialtest
- z-Test, t-Test
- Regression
ContentFrom "Statistics for research":
Ch 1: The Role of Statistics
Ch 2: Populations, Samples, and Probability Distributions
Ch 3: Binomial Distributions
Ch 6: Sampling Distribution of Averages
Ch 7: Normal Distributions
Ch 8: Student's t Distribution
Ch 9: Distributions of Two Variables [Regression]

From "Introductory Statistics with R":
Ch 1: Basics
Ch 2: Probability and distributions
Ch 3: Descriptive statistics and tables
Ch 4: One- and two-sample tests
Ch 5: Regression and correlation
Literature"Statistics for research" by S. Dowdy et. al. (3rd
edition); Print ISBN: 9780471267355; Online ISBN: 9780471477433; DOI:
10.1002/0471477435;
From within the ETH, this book is freely available online under:
Link

"Introductory Statistics with R" by Peter Dalgaard; ISBN
978-0-387-79053-4; DOI: 10.1007/978-0-387-79054-1
From within the ETH, this book is freely available online under:
Link
406-0663-AALNumerical Methods for CSE
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-8 credits17RR. Hiptmair
AbstractIntroduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology.
Objective* Knowledge of the fundamental algorithms in numerical mathematics
* Knowledge of the essential terms in numerical mathematics and the
techniques used for the analysis of numerical algorithms
* Ability to choose the appropriate numerical method for concrete problems
* Ability to interpret numerical results
* Ability to implement numerical algorithms afficiently in C++
Content1. Computing with Matrices and Vectors
2. Direct Methods for Linear Systems of Equations
3. Direct Methods for Linear Least Squares Problems
4. Filtering Algorithms
5. Data Interpolation and Data Fitting in 1D
6. Approximation of Functions in 1D
7. Numerical Quadrature
8. Iterative Methods for Non-linear Systems of Equations
12. Numerical Integration - Single Step Methods
13. Single Step Methods for Stiff Initial Value Problems
Lecture notesLink
LiteratureW. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006.
M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002
P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002
U. Ascher and C. Greif "A first course in Numerical Methods"
Prerequisites / NoticeExamination will be conducted at the computer and will involve coding in C++/Eigen.
A course covering the material is taught in English every autumn term (course unit 401-0663-00L). Course documents, exercises and examinations are available online.
401-0674-AALNumerical Methods for Partial Differential Equations
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-10 credits21RR. Hiptmair
AbstractDerivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations,among them (convection)-diffusion and heat equations, wave equation, conservation laws. Implementation in C++ based on a finite element library.
ObjectiveMain skills to be acquired in this course:
* Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently.
* Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations.
* Ability to select and assess numerical methods in light of the predictions of theory
* Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm.
* Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations.
* Skills in the efficient implementation of finite element methods on unstructured meshes.

This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages.
Content1 Second-Order Scalar Elliptic Boundary Value Problems
1.2 Equilibrium Models: Examples
1.3 Sobolev spaces
1.4 Linear Variational Problems
1.5 Equilibrium Models: Boundary Value Problems
1.6 Diffusion Models (Stationary Heat Conduction)
1.7 Boundary Conditions
1.8 Second-Order Elliptic Variational Problems
1.9 Essential and Natural Boundary Conditions
2 Finite Element Methods (FEM)
2.2 Principles of Galerkin Discretization
2.3 Case Study: Linear FEM for Two-Point Boundary Value Problems
2.4 Case Study: Triangular Linear FEM in Two Dimensions
2.5 Building Blocks of General Finite Element Methods
2.6 Lagrangian Finite Element Methods
2.7 Implementation of Finite Element Methods
2.7.1 Mesh Generation and Mesh File Format
2.7.2 Mesh Information and Mesh Data Structures
2.7.2.1 L EHR FEM++ Mesh: Container Layer
2.7.2.2 L EHR FEM++ Mesh: Topology Layer
2.7.2.3 L EHR FEM++ Mesh: Geometry Layer
2.7.3 Vectors and Matrices
2.7.4 Assembly Algorithms
2.7.4.1 Assembly: Localization
2.7.4.2 Assembly: Index Mappings
2.7.4.3 Distribute Assembly Schemes
2.7.4.4 Assembly: Linear Algebra Perspective
2.7.5 Local Computations
2.7.5.1 Analytic Formulas for Entries of Element Matrices
2.7.5.2 Local Quadrature
2.7.6 Treatment of Essential Boundary Conditions
2.8 Parametric Finite Element Methods
3 FEM: Convergence and Accuracy
3.1 Abstract Galerkin Error Estimates
3.2 Empirical (Asymptotic) Convergence of Lagrangian FEM
3.3 A Priori (Asymptotic) Finite Element Error Estimates
3.4 Elliptic Regularity Theory
3.5 Variational Crimes
3.6 FEM: Duality Techniques for Error Estimation
3.7 Discrete Maximum Principle
3.8 Validation and Debugging of Finite Element Codes
4 Beyond FEM: Alternative Discretizations [dropped]
5 Non-Linear Elliptic Boundary Value Problems [dropped]
6 Second-Order Linear Evolution Problems
6.1 Time-Dependent Boundary Value Problems
6.2 Parabolic Initial-Boundary Value Problems
6.3 Linear Wave Equations
7 Convection-Diffusion Problems [dropped]
8 Numerical Methods for Conservation Laws
8.1 Conservation Laws: Examples
8.2 Scalar Conservation Laws in 1D
8.3 Conservative Finite Volume (FV) Discretization
8.4 Timestepping for Finite-Volume Methods
8.5 Higher-Order Conservative Finite-Volume Schemes
Lecture notesThe lecture will be taught in flipped classroom format:
- Video tutorials for all thematic units will be published online.
- Tablet notes accompanying the videos will be made available to the audience as PDF.
- A comprehensive PDF handout will cover all aspects of the lecture.
LiteratureChapters of the following books provide supplementary reading
(detailed references in course material):

* D. Braess: Finite Elemente,
Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online).
* S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online).
* A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004.
* Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007.
* W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992.
* P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003.
* S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003.
* R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002.

However, study of supplementary literature is not important for for following the course.
Prerequisites / NoticeMastery of basic calculus and linear algebra is taken for granted.
Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential.

Important: Coding skills and experience in C++ are essential.

Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks.
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