Institute for Numerical Simulation
Rheinische Friedrich-Wilhelms-Universität Bonn
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Lecture in winter semester 2017/18:

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:Tuesday10:15 – 11:45
Thursday08:30 – 10:00
Location: Wegelerstraße 6 - Seminarraum 6.020
6th floor, last room on right, heading southwest

Tutorials

Registration for tutorials in the first lecture on Tuesday. 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.

Admittance for oral exam based on homework assignments requiring

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++.


Exam