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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.


AnnouncementsDescriptionPrerequisitesTutorialsRegistrationOral ExamContents 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

No. Title Date
Assignment 01 Classification, Conic Sections 05/04 [download]
Assignment 02 “Big-Oh”-notation, finite differences 05/22 [download]
Assignment 03 Elliptic PDEs, Grids, Stencils 06/01 [download]
Assignment 03 Sample Programme: Laplace Equation in 1d 06/01 [download]
Assignment 04 Poisson Equation, Norms, Fixpoint Iteration 06/31 [download]
Assignment 05 Iterative Solvers -- Splitting Methods 07/03 [download]
Assignment 05 Sample Programme: Iterative Solvers 07/03 [download]
Assignment 06 Conjugate Gradient Method, Parabolic Schemes 07/31 [download]
Assignment 06 Sample Programme: Explicit Euler, Implicit Euler, Theta-schemes 07/13 [download]
Assignment 07 Hyperbolic Schemes 07/27 [download]


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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