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Research Group 1: Numerical Analysis

Secretariat
Allianz-Gebäude (05.20)
Room 3C-09, Kaiserstr. 89-93 (3. OG)

Address
Institut für Angewandte und
Numerische Mathematik 1
Karlsruher Institut für Technologie (KIT)
D-76128 Karlsruhe

na-sek@math.kit.edu

Office hours:
Montag bis Freitag 10:00-11:00 Uhr

Tel.: +49 721 608 42061

Fax.: +49 721 608 43767

Exponential Integrators (Winter Semester 2010/11)

Lecturer: Prof. Dr. Marlis Hochbruck
Classes: Lecture (1102), Problem class (1103)
Weekly hours: 2+1


Extra Lecture: Wednesday, February 23, 11.30-13:00 in 1C-03

Schedule
Lecture: Wednesday 11:30-13:00 1C-03
Problem class: Thursday 15:45-17:15 Z 1
Lecturers
Lecturer, Problem classes Prof. Dr. Marlis Hochbruck
Office hours: nach Vereinbarung
Room 3C-12 Allianz-Gebäude (05.20)
Email: marlis.hochbruck@kit.edu

In this class we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems.

The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts. Parabolic partial differential equations and their spatial discretization are typical examples. The second class consists of highly oscillatory problems with purely imaginary eigenvalues of large modulus.

Apart from motivating the construction of exponential integrators for various classes of problems, our main intention in this class is to present the mathematics behind these methods. We will derive error bounds that are independent of stiffness or highest frequencies in the system.

Since the implementation of exponential integrators requires the evaluation of the product of a matrix function with a vector, we will briefly discuss some possible approaches as well.

References


Slides

(KIT password required for download)

Lecture of October 20, 2010
Lecture of December 1, 2010


Problems

(KIT password required for download)

Tutorial Nov 11, 2010
Tutorial Nov 12, 2010
Tutorial Dec 02, 2010
Tutorial Jan 13, 2011
Tutorial Jan 20, 2011
Tutorial Feb 7, 2011 (new date, Feb 7, 2011, 2pm in 3C-11)