Numerical Algorithms for Visual Computing
Dr. Matthias Augustin
Office hour: Wednesday, 14:30  15:30.
Summer Term 2018
Lectures (3h) with exercises (1h);
(6 ETCS points)
Lectures:
Tuesday, 8:3010:00, Building E1.3, Lecture Hall 003
Thursday, 12:3014:00, Building E1.3, Lecture Hall 001
First lecture: Tuesday, April 10, 2018
First tutorial: Thursday, April 26, 2018; see also below.
Announcements –
Description –
Prerequisites –
Tutorials –
Registration –
Exam –
Contents –
Assignments –
Literature
 20180926: The results
of the second written exam are now online.
You have the opportunity to inspect your graded solutions on
Friday, September 18, 2018 from 12:30 to 14:30
in room 4.10 in Building E1.7.
 20180719: The results
of the first written exam are now online.
You have the opportunity to inspect your graded solutions on
Monday, August 06, 2018 from 9:30 a.m. to 11:30 a.m
in room 4.10 in Building E1.7.
 20180719: Example solution to assignment 07 is online. As there
were some typos, the assignment itself was also updated.
Lecture notes updated, corrected some typos in chapter 06.
 20180625: Updated exam information.
 20180419:
Shift in times: As requested by students today, from now on
lectures on Thursdays and Fridays will start at 12:30 and end at
14:00 sharp instead of 12:1513:45.
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),
 finitedifference (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
(multidimensional) calculus and linear algebra as covered in introductory
maths course (such as Mathematik für Informatiker IIII). 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
 20180426,
 20180510 (will be given at 20180511),
 20180524,
 20180607,
 20180621,
 20180705, and
 20180719.
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
(20180424).
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 written 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 written exam takes place on
Wednesday, August 01, 2018 from 10:00 to 12:00, in
Lecture Hall 001, Building E1 3.
The second written exam takes place on
Monday, September 24, 2018 from 10:00 to 12:00, in
Lecture Hall 001, Building E1 3.
Please note that the actual exam takes 90 minutes.
Both exams will be closed book exams.
You will have to follow these rules:

You are allowed and obliged to bring three things
to your desk only:
 Your student ID card (Studierendenausweis),
 a ballpen that has no function other than writing, and
 a socalled cheat sheet.
This cheat sheet is a A4 page with formulas or important equations
from the lecture. Please note that the cheat sheet has to be
handwritten by yourself. You may use both sides. It will be collected
at the end of the exam, and you can get it back at the exam inspection.

The following things are not allowed at your desk:
 lecture notes, homework and classroom work solutions,
 any additional handwritten notes,
 books, dictionaries,
 sheets of paper, or
 any electronic devices, including, but not limited to pocket calculators,
mobile phones, PDAs, laptops, tablets, and smart watches. Turn them off
and store them somewhere safe.

Please keep your student ID card ready for an attendance check during
the exam.
 Do not use pencils or pens that are erasable with a normal rubber.
 You are not allowed to take anything with you that contains
information about the exam.
A violation of this rule means failing the
course.
 You must stay until the exam is completely over.
If you cannot attend the exam, contact Matthias Augustin as early as possible.
In case you have proof that you cannot take part for medical reasons or you
have another exam on the same day, we can probably find a solution. Note that
we need written proof (e.g. a certificate from a physician/Krankenschein) for
the exact date of the exam.
The results of the first written exam can be found
here, and the corresponding
distribution of points and grades
here.
Each student who has participated in the first written exam has the
opportunity to inspect his/her graded solutions in room 4.10 in Building E1.7
on Monday, August 06, 2018 from 9:30 a.m. to 11:30 a.m.
The results of the second written exam can be found
here, and the corresponding
distribution of points and grades
here.
Each student who has participated in the second written exam has the
opportunity to inspect his/her graded solutions in room 4.10 in Building E1.7
on Friday, September 28, 2018 from 12:30 to 14:30.
Lecture notes in one file
Slides with
organizational issues from the first lecture
No. 
Title 
Date 

Submit until 
Assignment 03 
Laplace Equation in 1d 
05/15 
[download] 
05/22 
Assignment 05 
Iterative Solvers  Splitting Methods 
06/12 
[download] 
06/19 
Assignment 06 
Parabolic Schemes 
06/27 
[download] 
07/03 
No. 
Title 
Date 

Submit until 
Assignment 01 
Classification, Conic Sections 
04/17 
[download] 
04/24 
Tutorial 
How to Sketch Conic Sections 
04/17 
[download] 
 
Assignment 02 
“BigOh”notation, Finite Differences 
05/02 
[download] 
07/11 
Assignment 03 
Elliptic PDEs, Finite Differences, First Numerical Solutions 
05/15 
[download] 
05/22 
Assignment 04 
Poisson Equation, Norms 
05/29 
[download] 
06/05 
Assignment 05 
Iterative Solvers  Splitting Methods 
06/12 
[download] 
06/19 
Assignment 06 
Conjugate Gradient Method, Parabolic Schemes 
06/26 
[download] 
07/03 
Assignment 07 
Hyperbolic Schemes 
07/10 
[download] 
07/17 
No. 
Title 
Date 

Assignment 01 
Classification, Conic Sections 
04/26 
[download] 
Assignment 02 
“BigOh”notation, finite differences 
05/15 
[download] 
Assignment 03 
Elliptic PDEs, Finite Differences, First Numerical Solutions 
05/29 
[download] 
Assignment 03 
Sample Programme: Laplace Equation in 1d 
05/29 
[download] 
Assignment 04 
Poisson Equation, Norms 
06/21 
[download] 
Assignment 05 
Iterative Solvers  Splitting Methods 
06/21 
[download] 
Assignment 05 
Sample Programme: Iterative Solvers 
06/21 
[download] 
Assignment 06 
Conjugate Gradient Method, Parabolic Schemes 
07/05 
[download] 
Assignment 06 
Sample Programme: Explicit Euler, Implicit Euler, Thetaschemes 
07/05 
[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.

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.
