Geometric Integration and Lie group methods
| Place: Trondheim, Norway (Digital event) |
| Date: February 1 – February 9, 2021 |
| Starting Monday 1. at 8:45 and the other days at 9:15. |
| February 1, 2, 3 and 5, 8, 9: lectures 9:15 to 12:15 and exercises 14:00 to 17:00. |
| February 4, guest lectures: 10-12 and 13-15. |
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| Messages |
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| Welcome to nwt6 of THREAD. In this webpage we will post messages, lecture material and exercises sets for this course. Watch this space. |
| The lectures of this course will be given via zoom. The links to the lectures will be communicated in due time. |
Prerequisites
In this course we will assume familiarity with basic concepts of numerical analysis such as error sources, convergence and stability. Knowledge about numerical methods for ordinary differential equations such as Runge-Kutta and Linear multistep methods are a prerequisite for the course. The note about numerical integration of ordinary differential equations contains the main background concepts and theorems about the subject.
Learning activities
Lectures
Mornings 9:15-10, 10:15-11, 11:30-12:15
Lunch
12:15-14:00
Exercises
Afternoons 14:00 -17:00
Lecturers
Teaching material
- Notes of the course
- Geometric Numerical Integration
Hairer, Lubich and Wanner, Springer
Other sources:
- Solving Ordinary differential equations vol 1 and 2, Hairer, Nørsett and Wanner and Hairer and Wanner.
- Simulating Hamiltonian Dynamics, Vol. 14 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, first edition, 2004. B. Leimkuhler, S. Reich.
- An introduction to Lie group integrators – basics, new developments and applications, Celledoni, Marthinsen and Owren, Journal of Computational Physics, 257 (2014) 1040-1061.
Learning outcome
Knowledge:Strucure preserving and geometric numerical integration of differential equations . Lie group integrators.
- Symplectic integration
- Preservation of first integrals, preservation/dissipation of energy
- Preservation of two or more geometric properties.
Abilities:
- ability to choose a suitable geometric numerical method depending on the problem to be solved
- ability of analysing the effect of using structure preserving integrators
- ability to implement the methods and test their properties for some simple test problems.
General competence:Increased knowledge and experience in the field of numerical analysis of differential equations.