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
|Problem class:||Thursday 15:45-17:15||Z 1|
|Lecturer, Problem classes||Prof. Dr. Marlis Hochbruck|
|Office hours: nach Vereinbarung|
|Room 3.001 Kollegiengebäude Mathematik (20.30)|
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.
- M. Hochbruck and A. Ostermann, Exponential Integrators, Acta Numerica, vol. 19, pp. 209-286 (2010)
- M. Hochbruck, A. Ostermann and J. Schweitzer, Exponential Rosenbrock-type methods, SIAM J. Numer. Anal., vol. 47, no. 1, pp. 786—803 (2009)
- M. Hochbruck and A. Ostermann, Exponential multistep methods of Adams type, Preprint 2010
- M. Hochbruck, Ch. Lubich, On Magnus integrators for time-dependent Schrödinger equations, SIAM J. Numer. Anal., vol. 41, no. 3, pp. 945—963 (2003)