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Numerical Algorithms for Visual Computing

Summer Term 2020

Numerical Algorithms for Visual Computing

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

Summer Term 2020

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

Lectures: Online Sessions with Q&A and Tutorial Sections
Tuesday, 12:00-14:00
Friday, 12:00-14:00

First online session: Tuesday, May 05th, 2020

AnnouncementsDescriptionPrerequisitesTutorialsRegistrationExamContents Assignments Literature

  • 2020-07-15 Sample solution for Assignment 04 online.
    Lecture notes updated, corrected some errors in Section 6.2 about the conservation of the average grey value and clarified some steps in the proof of consistency orders for the different discretizations of the diffusion equation.
  • 2020-06-09: Assignment 02 is online.
    You can submit this assignment until 2020-06-16, 14:00 via e-mail to Matthias Augustin.
    Lecture notes updated; corrected a typo in Eq. (5.2.7) where one needs to take the second derivative of sine and cosine, not the first one.
  • 2020-05-15 Lecture notes updated, corrected some typos and clarified some arguments.
    An older version of the lecture notes is still available as a reference, since numbers of sections, equations, and pages as given in the schedule are based on this older version.
    Incorporated links to additional exercises into the schedule.
  • 2020-05-11: Exam date corrected!
    I was made aware that the date for the first exam on the homepage and in the exam calendar differed. The correct date is August, 03.
    Lecture notes updated: corrected some typos and made notion more consistent in Section 2.1.
    Added a preliminary schedule for online sessions.
  • 2020-05-05: Following a vote of students present during the meeting today, there is now a team for this class in MS Teams. Students are added after there registration for the course via email.
  • 2020-04-23: Following the general recommendations for health protection, the lectures and tutorials will be fully digital during 2020's summer term . This website has been updated accordingly.
    To participate in all activities, it is essential for each interested student to register as soon as possible.

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

  • iterative solvers for linear systems of equations,
  • (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,
  • 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 notes. All material will be in English. Knowledge from image processing may be helpful, but is not required.

Due to the current sitation caused by SARS-Cov2, this lecture will be closer to an inverted classroom / blended learning setting. This means that for each live online sessions, students will be required to prepare using the available material (lecture notes and possibly video recordings). The amount of content that you need to prepare will be announced towards the end of each live session. Live sessions themselves are intended to follow a Q&A structures and might present further exercise material.

Due to a shorter lecture period, there will be a total of 4 homework assignments which will be graded. Assignments will be published on this website and are expected to be submitted via email to Matthias Augustin within one week after publications. 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. All exams will be oral.

In order to register for the lecture, write an e-mail to Matthias Augustin.
Registration is open until Friday, May 15, 12 am.
The subject line must begin with the tag [NAVC20].
Please use the following template for the e-mail:

First name: [myFirstName]
Last name: [myLastName]
Date of birth: [dd.mm.yyyy]
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.
Such information will include further regulations, information about the format, and information on how to join the live sessions.

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

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 oral 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, August 03, 2020.

The second exam takes place on
Friday, October 09, 2020.

Further information about the exam will become available here as the semester proceeds.

Organizational slides from the first online session

Lecture notes
reference version
newest version
The first chapter of these lecture notes is intended to be a summary of content from liner algebra, in particular concerning things needed in the context of systems of linear equations. It is intended to allow students to quickly refresh their knowledge in this particular field. The actual content of this lecture starts with Chapter 2.
Due to the shortened lecture period, it will not be possible to cover the content of these lecture notes completely in the course of this semester. Topics for online sessions are according to the following schedule.
Links to additional exercises will be added to the schedule after each live session.

Date Please prepare Pages
05/05 Organizational Issues --
05/08 Section 2.1 47-53
05/12 Section 2.2 53-59
05/15 Section 2.3 59-65
05/19 Section 2.4. up to Section 2.4.2 65-71
05/22 Sections 2.4.3 and 2.5 72-78
05/26 Section 3.1 to Section 3.2.2 81-87
05/29 Section 3.3. to Section 4.2 90-95
06/02 Sections 4.3 and 4.4 96-100
06/05 Assignment 01 --
06/09 Section 5.1 to Equation 5.2.14 106-113
06/12 Equation 5.2.15 to Equation 5.2.34 106-113
06/16 Equation 5.2.35 to Section 5.3.2 113-120
06/19 Assignment 02 --
06/23 Section 5.3.3 to Theorem 5.16 120-124
06/27 Equation 5.3.46 to Equation 5.4.6 124-128
06/30 Section 5.4.2 to Section 6.1 128-134
07/03 Assignment 03 --
07/07 Section 6.2 to Equation 6.3.11 135-141
07/10 Remark 6.4 to Section 6.4.2 141-145
07/14 Section 6.4.3 145-150
07/17 Assignment 04 --

No. Title Date Submit until
Assignment 01 Iterative Solvers -- Splitting Methods 05/26 [download] 06/02
Assignment 04 Laplace Equation in 1D and Parabolic Schemes 07/07 [download] 07/14

No. Title Date Submit until
Assignment 01 Iterative Solvers -- Splitting Methods 05/26 [download] 06/02
Assignment 02 Conjugate Gradient Method; Classification 06/09 [download] 06/16
Assignment 03 BVPs, Harmonic Function, Properties of Laplacian (continuous and discrete) 06/23 [download] 06/30
Assignment 04 Numerics for Elliptic and Parabolic PDEs 07/07 [download] 07/14

No. Title Date
Assignment 01 Iterative Solvers -- Splitting Methods 06/03 [download]
Assignment 01 Sample Programme: Iterative Solvers 06/03 [download]
Assignment 02 Conjugate Gradient Method; Classification 06/17 [download]
Assignment 03 BVPs, Harmonic Function, Properties of Laplacian (continuous and discrete) 07/01 [download]
Assignment 04 Numerics for Elliptic and Parabolic Schemes 07/15 [download]
Assignment 04 Algorithms for Elliptic and Parabolic Schemes 07/15 [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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