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Numerical Algorithms for Visual Computing

Summer Term 2018

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, 8:30-10:00, Building E1.3, Lecture Hall 003
Thursday, 12:30-14:00, 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

• 2018-09-26: 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.
• 2018-07-19: 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.
• 2018-07-19: 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.
• 2018-06-25: Updated exam information.
• 2018-04-19: 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 12:15-13:45.

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),
• 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

• 2018-04-26,
• 2018-05-10 (will be given at 2018-05-11),
• 2018-05-24,
• 2018-06-07,
• 2018-06-21,
• 2018-07-05, and
• 2018-07-19.

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 (2018-04-24).

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 ball-pen that has no function other than writing, and
  • a so-called 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	“Big-Oh”-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	“Big-Oh”-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, Theta-schemes	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.

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