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Numerical Algorithms for Visual Computing

Summer Term 2019

Numerical Algorithms for Visual Computing

Dr. Matthias Augustin
Office hour: Wednesday, 14:30 - 15:30.

Summer Term 2019

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

Lectures:
Monday, 16:00-18:00, Building E1.3, Lecture Hall 001
Thursday, 12:00-14:00, Building E1.3, Lecture Hall 001

First lecture: Thursday, April 11, 2019

Onetime alternates:

  • Friday, April 26, 2019, 12:00-14:00, Building E1.3, Lecture Hall 003 as substitute for Monday, April 22, 2019
  • Friday, May 31, 2019, 12:00-14:00, Building E1.3, Lecture Hall 003 as substitute for Thursday, May 30, 2019
  • Friday, June 14, 2019, 12:00-14:00, Building E1.3, Lecture Hall 003 as substitute for Monday, June 10, 2019

First tutorial: Thursday, April 25, 2019; see also below.

Onetime alternate:
Friday, June 21, 2019, 12:00-14:00, Building E1.3, Lecture Hall 003 as substitute for Thursday, June 20, 2019



AnnouncementsDescriptionPrerequisitesTutorialsRegistrationExamContents Assignments Literature



  • 2019-07-19: Lecture notes updated; corrected some typos in Chapters 4 and 5, added proof to Corollary 4.26, changed some things in Chapter 6 to improve the introduction and discussion of characteristics and the CFL condition.
    Sample solution to Assignment 07 is online and the assignment is updated to account for the fact that asking for a CFL condition without having in mind a particular scheme does not make sense.


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 PDEs of potential and diffusion type,
  • properties of PDEs which transfer to FD schemes,
  • iterative solvers for linear systems of equations,
  • 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

  • 2019-04-25,
  • 2019-05-09,
  • 2019-05-23,
  • 2019-06-06,
  • 2019-06-20, (will be given at 2019-06-21 due to a holiday)
  • 2019-07-04, and
  • 2019-07-18.

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 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.


Registration is closed since the submitting date of the first assignment passed (2019-04-23).

According to the regulations concerning storage and processing of personal data (Art. 6 (1) Datenschutzgrundverordnung (DSGVO)) we store and process your personal data for the purpose of lecture and tutorial organisation only. I.e. we may use them to contact you, to inform you about your grade, and to transmit your grades to the examination office.


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 two exams, one at the beginning and one at the end of the semester break. In case of qualification, you are allowed to take part in both exams. The better grade counts, but each exam will count as an attempt individually. Please remember that you have to register online for the exam in the HISPOS system of the Saarland University for each attempt separately.

The first exam takes place on
Monday, July 29, 2019.

The second exam takes place on
Friday, October 11, 2019.

Exams will be oral or written, depending on the number of participants.
Further information about the exam will become available here as the semester proceeds.



Lecture notes in one file

Slides with organizational issues from the first lecture


No. Title Date Submit until
Assignment 04 Laplace Equation in 1D 05/27 [download] 06/03
Assignment 05 Iterative Solvers -- Splitting Methods 06/09 [download] 06/16
Assignment 06 Parabolic Schemes 06/24 [download] 07/01


No. Title Date Submit until
Assignment 01 Classification, Definiteness 04/15 [download] 04/23
Assignment 02 Finite Differences, Consistency, Stability 04/29 [download] 05/06
Assignment 03 Finite Difference for simple ODE, More on Stability and Consistency 05/13 [download] 05/20
Assignment 04 2D Stencils, Higher Order Consistency, Numerics for Laplace's Equation 05/27 [download] 06/03
Assignment 05 Iterative Solvers -- Splitting Methods 06/09 [download] 06/16
Assignment 06 Conjugate Gradient Method, Parabolic Schemes 06/24 [download] 07/01
Assignment 07 Hyperbolic Schemes 07/19 [download] 07/15


No. Title Date
Assignment 01 Classification, Conic Sections 04/25 [download]
Assignment 02 Finite Differences, Consistency, Stability 05/09 [download]
Assignment 03 Finite Difference for simple ODE, More on Stability and Consistency 05/27 [download]
Assignment 04 2D Stencils, Higher Order Consistency 06/09 [download]
Assignment 04 Numerics for Laplace's Equation 06/09 [download]
Assignment 05 Iterative Solvers -- Splitting Methods 06/24 [download]
Assignment 05 Sample Programme: Iterative Solvers 06/24 [download]
Assignment 06 Conjugate Gradient Method, Parabolic Schemes 07/08 [download]
Assignment 06 Sample Programme: Explicit Euler, Implicit Euler, Theta-schemes 07/08 [download]
Assignment 07 Hyperbolic Schemes 07/19 [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.
  • Numerical Methods for Conservation Laws
    R. J. LeVeque, Birkhäuser, 1992.
  • Numerical Solution of Partial Differential Equations
    K. W. Morton, D. Mayers, Cambridge University Press, 2005.
  • 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 as needed.


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