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Numerical Algorithms for Visual Computing

Summer Term 2017

Numerical Algorithms for Visual Computing

Dr. Matthias Augustin
Office hour: Wednesday, 14:00 - 15:00.

Summer Term 2017

Lectures (3h) with exercises (1h);
(6 ETCS points)

Lectures:
Tuesday, 8-10 c.t., Building E1.3, Lecture Hall 003
Thursday, 16-18 c.t., Building E1.3, Lecture Hall 003

First lecture: Thursday, April 20, 2017


First Tutorial: Thursday, May 04, 2017; see also below.

Announcements – Description – Prerequisites – Tutorials – Registration – Oral Exam – Contents – Assignments – Literature

• 2017-07-31: Solutions to assignments 04 and 06 updated, corrected some typos.
  
• 2017-07-27: Solution to assignment 07 is online.
  
• 2017-07-25: Exam: Due to the small number of participants, exams will be oral. Further information is given below.
  Please remember to register both in HISPOS and per eMail.
  Updated all chapters of the lecture notes and included a download for all in once.
• The registration for the lecture is now closed as the first tutorial passed.

Target group: Students in the Master Programme Visual Computing
Lecture aim: Provide some concepts which are useful for the numerical treatment of partial differential equations. This includes

• (short) introduction to partial differential equations (PDEs),
• finite-difference (FD) schemes,
• schemes for parabolic and elliptic PDEs,
• properties of PDEs which transfer to FD schemes,
• iterative solvers for linear systems of equations,
• diffusion problems,
• hyperbolic problems and upwinding.

This course is suitable for students of visual computing, mathematics, and computer science.
Students attending this course should be familiar with basic concepts of (multi-dimensional) calculus and linear algebra as covered in introductory maths course (such as Mathematik für Informatiker I-III). Mathematical prerequisites which exceed the basic mathematics courses are provided within the lecture. Lectures and tutorials will be in English. Knowledge from image processing may be helpful, but is not required.

There will be a total of 7 tutorials which will take place instead of regular lectures on

• 2017-05-04,
• 2017-05-18,
• 2017-06-01,
• 2017-06-15 (will be given at an alternative date),
• 2017-06-29,
• 2017-07-13, and
• 2017-07-27.

The tutorials include homework assignments which have to be submitted in the lecture break, or earlier and which will be graded. Working together in groups of up to 3 students is permitted and encouraged. Some assignments may contain programming exercises.

In order to qualify for the final exam, it is necessary to achieve 50% of the points of all assignment sheets in total. There will be either oral exams or a written exam, depending on the number of participants.

In order to register for the lecture, write an e-mail to Matthias Augustin.
Registration is open until Monday, April 24, 12 am.
The subject line must begin with the tag [NAVC17].
Please use the following template for the e-mail:

First name: [myFirstName]
Last name: [myLastName]
Date of birth: [yyyy-mm-dd]
Student ID number: [...]
Course of study: [Bachelor/Master/...]
Subject: [Computer Science/Visual Computing/Mathematics/...]

Note that the e-mail address from which you send this information will be used to provide you with urgent information concerning the lecture.

This registration is for internal purposes at our chair only and completely independent of any system like LSF/HISPOS. They require a separate registration.

In order to qualify for the final exam, it is necessary to achieve 50% of the points of all assignment sheets in total.
The exam will be oral.

First exam: August 08, 2017
Second exam: October 12, 2017

• You can attend both exams.
• Each exam counts as one try.
• Second exam can be taken to improve the grade.
• Exams can be taken in English (default) or German.

Registration: You have to register in

• HISPOS.
• Furthermore, for internal uses, register per eMail to Matthias Augustin.
  (Deadline first exam: July 25, 2017)
  (Deadline second exam: September 28, 2017)
  Subject: [NAVC17] exams
Content:
First name: [myFirstName]
Last name: [myLastName]
Date of birth: [dd.mm.yyyy]
Student ID number: [...]
Registration for: [first/second] exam
Prefered language: [English/German]


• I will arrange the time slots and let you know.

Lecture notes in one file

Slides with organizational issues from the first lecture

Lecture notes in separate chapters

No.	Title	Date
Chapter 1	Introduction to PDEs, Classification	07/25	[download]
Chapter 2	Introduction to Finite Difference Schemes	07/25	[download]
Chapter 3	Elliptic PDEs	07/25	[download]
Chapter 4	Iterative Solvers for Systems of Linear Equations	07/25	[download]
Chapter 5	Parabolic PDEs and Diffusion Problems	07/25	[download]
Chapter 6	Hyperbolic PDEs and Conservation Laws	07/25	[download]
Appendix A	Supplementary Material	07/25	[download]
Bibliography	Literature	07/25	[download]

No.	Title	Date		Submit until
Assignment 03	Laplace Equation in 1d	05/23	[download]	05/30
Assignment 05	Iterative Solvers -- Splitting Methods	06/20	[download]	06/27
Assignment 06	Conjugate Gradient Method, Parabolic Schemes	07/04	[download]	07/11

No.	Title	Date		Submit until
Assignment 01	Classification, Conic Sections	04/25	[download]	05/02
Tutorial	How to Sketch Conic Sections	04/25	[download]	--
Assignment 02	“Big-Oh”-notation, Finite Differences	05/09	[download]	05/16
Assignment 03	Elliptic PDEs, Grids, Stencils	05/23	[download]	05/30
Assignment 04	Poisson Equation, Norms, Fixpoint Iteration	06/06	[download]	06/13
Assignment 05	Iterative Solvers -- Splitting Methods	06/20	[download]	06/27
Assignment 06	Conjugate Gradient Method, Parabolic Schemes	07/04	[download]	07/11
Assignment 07	Hyperbolic Schemes	07/18	[download]	07/25

There is no specific text book for this class, but here is a selection of some books covering many of the topics in this course, giving background material and providing further reading:

• Numerical Solution of Partial Differential Equations in Science and Engineering
  L. Lapidus, G. F. Pinder, Wiley, 1999.
• Numerical Partial Differential Equations
  Volume I: Finite Difference Methods
  Volume II: Conservation Laws and Elliptic Equations
  J. W. Thomas, Springer, 1995 (Vol. I) / 1999 (Vol. II).
• Finite Difference Methods for Ordinary and Partial Differential Equations
  R. J. LeVeque, SIAM, 2007.
• The Finite Difference Method in Partial Differential Equations
  A. R. Mitchell, D. F. Griffiths, Wiley, 1985.
• Numerical Solution of Differential Equations
  W. E. Milne, Wiley, 1960.
• Introduction to Numerical Analysis
  J. Stoer, R. Bulirsch, Springer, 1993.
  English translation of the originally german version.

Most of these and further books can be found in the mathematics and computer science library.

Further references will be provided during the lecture.

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