Search result: Catalogue data in Autumn Semester 2018

Computational Science and Engineering Master Information
Core Courses
Two core courses out of three must be attended and examinations must be taken in both.

252-0543-01L Computer Graphics won't be offered as a core course after HS 2018.
NumberTitleTypeECTSHoursLecturers
401-4671-00LAdvanced Numerical Methods for CSEW9 credits4V + 2U + 1PR. Hiptmair, C. Jerez Hanckes
AbstractThis course discusses modern numerical methods involving complex algorithms and intricate data structures that render an efficient implementation non-trivial. The focus will be on boundary element methods, hierarchical matrix techniques, convolution quadrature, and algebraic multigrid methods.
Objective- Appreciation of the interplay of functional analysis, advanced calculus, numerical linear algebra, and sophisticated data structures in modern computer simulation technology.
- Knowledge about the main ideas and mathematical foundations underlying boundary element methods, hierarchical matrix techniques, convolution quadrature, and reduced basis methods.
- Familiarity with the algorithmic challenges arising with these methods and the main ways on how to tackle them.
- Knowledge about the algorithms' complexity and suitable data structures.
- Ability to understand details of given implementations.
- Skills concerning the implementation of algorithms and data structures in C++.
Content1 Boundary Element Methods (BEM)
1.1 Elliptic Model Boundary Value Problem: Electrostatics . . . . . . . .
1.2 Boundary Representation Formulas . . . . . . . . . . . . . . . . . .
1.3 Boundary Integral Equations (BIEs) . . . . . . . . . . . . . . . . . .
1.4 Boundary Element Methods in Two Dimensions . . . . . . . . . . . . . . . . . . .
1.5 Boundary Element Methods on Closed Surfaces . . . . . . . . . . . . . . . . . . .
1.6 BEM: Various Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Local Low-Rank Compression of Non-Local Operators
2.1 Examples: Non-Local Operators . . . . . . . . . . . . . . . . . . . . .
2.2 Approximation of Kernel Collocation Matrices . . . . . . . . . . . . . . .
2.3 Clustering Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Hierarchical Matrices . . . . . . . . . . . . . . . . . . .
3 Convolution Quadrature
3.1 Basic Concepts and Tools
3.2 Convolution Equations: Examples . . . . . . . . . . . . . .
3.3 Implicit-Euler Convolution Quadrature . . . . . . . . . . . .
3.5 Runge-Kutta Convolution Quadrature . . . . . . . . . . . .
3.6 Fast Oblivious Convolution Quadrature . . . . . . . .
4 Algebraic Multigrid Methods
Lecture notesLecture material will be created during the course and will be made available online and in chapters.
LiteratureS. Sauter and Ch. Schwab, Boundary Element Methods, Springer 2010
O. Steinbach, Numerical approximation methods for elliptic boundary value problems, Springer 2008
M. Bebendorf, Hierarchical matrices: A means to efficiently solve elliptic boundary value problems, Springer 2008
W. Hackbusch, Hierarchical Matrices, Springer 2015
S. Boerm, Efficient Numerical Methods for Non-Local Operators: H2-Matrix Compression, Algorithms and Analysis, EMS 2010
S. Boerm, Numerical Methods for Non-Local Operators, Lecture Notes Univ. Kiel 2017
M. Hassell and F.-J. Sayas, Convolution Quadrature for Wave Simulations
J.-C. Xu and L. Zikatanov, Algebraic Multirgrid Methods, Acta Numerica, 2017
Ch. Wagner, Introduction to Algebraic Multigrid, Lecture notes IWR Heidelberg, 1999, Link
Prerequisites / Notice- Familiarity with basic numerical methods
(as taught in the course "Numerical Methods for CSE").
- Knowledge about the finite element method for elliptic partial differential equations (as covered in the course "Numerical Methods for Partial Differential Equations").
252-0543-01LComputer Graphics Information W6 credits3V + 2UM. Gross, J. Novak
AbstractThis course covers some of the fundamental concepts of computer graphics, namely 3D object representations and generation of photorealistic images from digital representations of 3D scenes.
ObjectiveAt the end of the course the students will be able to build a rendering system. The students will study the basic principles of rendering and image synthesis. In addition, the course is intended to stimulate the students' curiosity to explore the field of computer graphics in subsequent courses or on their own.
ContentThis course covers fundamental concepts of modern computer graphics. Students will learn about 3D object representations and the details of how to generate photorealistic images from digital representations of 3D scenes. Starting with an introduction to 3D shape modeling and representation, texture mapping and ray-tracing, we will move on to acceleration structures, the physics of light transport, appearance modeling and global illumination principles and algorithms. We will end with an overview of modern image-based image synthesis techniques, covering topics such as lightfields and depth-image based rendering.
Lecture notesno
Prerequisites / NoticePrerequisites:
Fundamentals of calculus and linear algebra, basic concepts of algorithms and data structures, programming skills in C++, Visual Computing course recommended.
The programming assignments will be in C++. This will not be taught in the class.
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