Geometric Numerical Integration II W16/17
-- H. G. Forder, Auckland 1973
Applied mathematics is not engineering.
-- Paul Halmos, Mathematics Tomorrow 1981
Dates | Description | Prerequisites | Lecture Notes | Exercises | References
12月22日（木）4-5限 ５１－０８０５室 (exercises)
In this second part of the course on geometric numerical integration, we will cover advanced topics from the integration of ODEs as well as methods for PDEs. We will discuss how to deal with constrained systems and external forcing. We will see how to construct integrators for noncanonical Hamiltonian and degenerate Lagrangian systems, for which no standard methods exist. Then we will move on to PDEs, first covering the continuous theory, that is Lagrangian and Hamiltonian field theory. We will discuss multisymplectic methods for canonical Hamiltonian systems and variational integrators for Lagrangian systems. Lastly, we will discuss discrete differential forms and the discrete deRham complex as means for constructing stable discretisations.
See Part I.
Script (Chapter 1-12, modified 09.01.2017)
- Constraints and Forces (modified 16.12.2016)
- Lagrangian Field Theory (modified 07.01.2017)
- Variational Integrators for Partial Differential Equations (modified 07.01.2017)
- Hamiltonian Field Theory (modified 09.01.2017)
- Multisymplectic Integrators
- Discrete Poisson Brackets
The exercise sheets 5 and 6 will be discussed on 12月22日.
- Discrete Mechanics with Forces
- Discrete Mechanics with Constraints
- Ernst Hairer, Christian Lubich and Gerhard Wanner. Geometric Numerical Integration. Springer, 2006. (eBook)
- Jerrold E. Marsden and Matthew West. Discrete Mechanics and Variational Integrators. Acta Numerica Volume 10, 357-514, 2001. (Journal)
- Thomas J. Bridges and Sebastian Reich. Numerical Methods for Hamiltonian PDEs. Journal of Physics A General Physics 39, 5287, 2006. (Journal)