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.|
|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.|
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.
Mornings 9:15-10, 10:15-11, 11:30-12:15
Afternoons 14:00 -17:00
- Notes of the course
- Geometric Numerical Integration
Hairer, Lubich and Wanner, Springer
- 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.
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.
- 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.