Welcome to the homepage of the lecture Numerical Algorithms for Visual Computing Summer Term 2021 |
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Lectures (3h) with exercises (1h);
First tutorial:
Announcements – Description – Prerequisites – Tutorials – Registration – Exam – Contents – Assignments – Literature
**2021-07-21**: Sample solution to Assignment 06 online. Lecture notes updated: Corrected a sign error in the last line of Eq.(7.1.39).**2021-07-19**: Lecture notes updated: Changed a formulation on page 82 (reference version) which wrongly stated that, for the conjugate gradient scheme, the correction is given by the residual.**2021-07-13**: Assignment 06 is online. You can submit this assignment until 2021-07-20, 14:00 via e-mail to Matthias Augustin. Lecture notes updated (all numbers are with respect to the reference version of the lecture notes):- Corrected index in Eq. (5.2.19), first line, in the expression directly before the equality sign with the ! above.
- Corrected parentheses on left-hand side of Eq. (6.3.6).
- Corrected a sign in (6.3.11) and cancelled out the \tau on the right-most side.
- Added parentheses around the k+1 on the left-hand side of Eq. (6.3.20).
- Extended Definition 6.5 and Remark 6.6 slightly to clarify the kinds of limits that need to be considered.
- Changed Eq. (6.4.2) such that k is an upper index to the finite difference operator, not an argument.
- Added missing index to norm of matrix in Eq. (6.4.13).
- Added missing index j to t on right-hand side of Eq. (6.4.19).
- Changed n to k in Eqs. (6.4.20) and (6.4.22) as well as in the line before Eq. (6.4.24).
- Added a missing factor to Eq. (6.4.35) and added a line before that equation to explain where the factor comes from.
- Added missing factor h in the norms in Eq. (6.4.45), (6.4.46), and (6.4.47).
- 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. 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. A schedule detailing the amount of content that you need to prepare will be made available at the start of the lecturing period. Live sessions themselves are intended to follow a Q&A structures and might present further exercise material. There will be a total of 6 homework assignments which will be graded. Assignments will be published on the Teams file repository and this website. Students are expected to submit their solutions to these assignments 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. Registration is closed since the submitting date of the first assignment passed (2021-05-01).
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.
Further information about the exam can be found
here
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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