Research Group of Prof. Dr. J. Schweitzer
Institute for Numerical Simulation
maximize

Lecture in winter semester 2016/17:

Numerical Algorithms (V4E1)

Prof. Dr. Marc Alexander Schweitzer


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Content

Learning targets

Broad overview and understanding of propositions, relations and methods from the area of numerical algorithms. Competence to evaluate the scope, utility, and limits of the methods and techniques and to independently apply abstract mathematical results to concrete problems. Competence to place the results in a more general mathematical context. Overview of connections to other areas and ability to arrive at rigorous mathematical proofs starting from heuristic considerations. The selection of topics is based on the module handbook for the Master programme in mathematics. In particular, we will introduce and discuss the h-,p- and hp-versions of the finite element method (FEM) and its application to conservation equations.

Topics

  1. From smooth/regular problems and solutions
  2. to general/irregular/non-smooth/singular/discontinuous solutions

Literature

Some of these books are also available in German/English, as ebook or in another edition in the library.

Prerequisites

Prerequisites for this lecture are the topics and exercises of the preceding lectures
Algorithmische Mathematik I (V1G5), Algorithmische Mathematik II (V1G6), V2E1 Einführung die Grundlagen der Numerik (V2E1)
These prerequisite topics include:

Lecture times

Dates:Tuesday1015 – 1145
Thursday0830 – 1000
Location: Wegelerstraße 6 - Seminarraum 6.020
6th floor, last room on right, heading southwest

BASIS


Tutorials

Registration for tutorials in the first lecture Tuesday, 2016-10-18. Only one tutorial in either the morning or late afternoon timeslot will be given. Please, be present in the first lecture for poll and choice of timeslot. Tutorials start on Wednesday, 2015-10-26.

The contact person for tutorials is Sa Wu.

Admittance for oral exam based on homework assignments requiring

Time and Room

DayTimeRoom
Wednesday0830 – 10005.002, Wegelerstr. 6

Homework assignments

Worksheets with homework assignments are distributed and put on the website Thursdays. Please, submit your homework assignments Thursdays right before and at the beginning of the lecture one week after handout. Submit programming assignments as plain text Python files.

Programming exercises will be based mainly in Python/NumPy/matplotlib. Please send in your solutions to programming exercises via mail to your tutorial's teaching assistant.

This combination is a very useful for quick implementation. Algorithms can be put into code fast. Plots can be produced with little effort. Much of what is needed for the lecture can be found in the following examples.

Some Documentation and Tutorials can be found at the following links.

One easy way to obtain all necessary Python packages is Anaconda.

More installation alternatives, suggestions and instructions can be found on the websites for NumPy and matplotlib.

Model solutions are base on Python in version 2.7.8. For editing and writing Python code, any good editor will do. We recommend Vim or Notepad++.

Exercise sheets

NumberLinkDueRemarks and errata

0exercise_sheet_00.pdfRevision and warm up sheet, no submission, not graded

1exercise_sheet_01.pdf2016-11-03

2exercise_sheet_02.pdf2016-11-10Exercise 7, in generalized Céa lemma, $\inf$ instead of $\int$
Exercise 9d), $r_1=(1,0),r_2=(0,1)$, $K_T = \frac{1}{2} \abs{\det{\ldots}}$

3exercise_sheet_03.pdf2016-11-17Abridged solution from programming exercise 3 as template
Programming exercise 4: For [0,1]^2, Dirichlet boundary values left and right, Neumann top and bottom, see template
Programming exercise 4: For solution, remove only Dirichlet nodes
No lecture on 2016-11-17, please submit in my office or via scan/email

4exercise_sheet_04.pdf2016-11-24

5exercise_sheet_05.pdf2016-12-01proposal for solution (Python3)

6exercise_sheet_06.pdf2016-12-08Some typos in Exercise 21
Programming exercise 6: $f=1+x^2+2y^2$

7exercise_sheet_07.pdf2016-12-15

8exercise_sheet_08.pdf2016-12-22

9exercise_sheet_09.pdf2016-01-19proposal for solution

10exercise_sheet_10.pdf2016-01-26

11exercise_sheet_11.pdf2016-02-02glyphs.py

Exam