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Exponential Integrators (Winter Semester 2021/22)

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.

The course is meant for advanced Master students who are familiar with the basics of finite element methods and numerical methods for differential equations. Some knowledge on functional analysis is also helpful.

All relevant information are provided in the Ilias course of the lecture.

Lecture: Monday 8:00-9:30 20.30 SR 3.61
Thursday 8:00-9:30 (every 2nd week) 20.30 SR 3.69
Problem class: Thursday 8:00-9:30 (every 2nd week) 20.30 SR 3.69
Lecturer, Problem classes Dr. Benjamin Dörich
Office hours: by appointment
Room 3.057 Kollegiengebäude Mathematik (20.30)
Email: benjamin.doerich@kit.edu
Lecturer, Problem classes Dr. Jan Leibold
Office hours: by appointment
Room 3.007 Kollegiengebäude Mathematik (20.30)
Email: jan.leibold@kit.edu