Lecture during the winter term 2015/16:

V4E1 – Numerical Algorithms

Prof. Dr. Carsten Burstedde

Assistant: Jose A. Fonseca

Requirements: Numerische Mathematik (V2E1, V2E2), Wissenschaftliches Rechnen I (V3E1/F4E1)

In this lecture we consider partial differential equations that formalize the conservation of physical quantities, namely mass, momentum, and energy. Such equations arise from the physics of fluids, including gases. This course covers two classes of numerical methods that can be used to simulate such fluids: the finite volume and the discontinuous Galerkin method. The goal of the lecture is to lead the students to a basic understanding of essential modern, high-performance computational methods.

Date & time

Lectures:	Tue,	10:15–11:45 am,	Wegelerstraße 6, Room 6.020
	Thu,	8:30–10:00 am,	Wegelerstraße 6, Room 6.020
First lecture:	Tue,	27.10.2015
Tutorial:	Thu,	10:15–11:45 am,	Wegelerstraße 6, Room 6.020
First Tutorial:	Thu,	5.11.2015

 Notice: Lecture on Thursday,  22.10.15 is cancelled due to the conference "Panorama of Mathematics"

Exercise sheets

Exercises are handed out on Tuesdays, and are to be handed in one week later.

• Sheet 0
• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4 and sample code for animation
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8 and expected output sample
• Sheet 9
• Sheet 10
• Sheet 11, incomplete code and expected output sample

Theoretical exercises will be complemented with programming problems. The goal is to implement some of the classical methods covered during the lecture using the Scientific Computing Tools for Python (SciPy).

Requirements for the exam

Students need to achieve 50% of all points, separately for theory and programming exercises.

Examinations date: Thu, 11.02.16 and Fri, 12.02.16

Literature

• Hesthaven, J.S. & Warburton, T., Nodal Discontinuous Galerkin Methods. Algorithms, Analysis and Applications. Springer-Verlag New York, 2008.
• Deville, M.O., Fischer, P.F. Mund, E.H., High-order methods for incompressible fluid flow. Cambridge Univ. Press, 2002 .
• Leveque, Randall J., Finite volume methods for hyperbolic problems. Cambridge Univ. Press, 2011.
• Kopriva, D.A., Implementing spectral methods for partial differential equations. Springer 2009.

Some of these books are also available as ebook in the library.

Programming resources

• Official SciPy documentation
• The Scipy Lecture Notes provides a step-by-step introduction on the scientific Python central tools.