Geometric Numerical Integration II W16/17

They throw geometry out the door, and it comes back through the window.
-- H. G. Forder, Auckland 1973

Applied mathematics is not engineering.
-- Paul Halmos, Mathematics Tomorrow 1981

Dates | Description | Prerequisites | Lecture Notes | Exercises | References

Dates

12月15日（木）4-5限 ５１－０８０５室
12月16日（金）4-5限 ５１－１００６室
12月22日（木）4-5限 ５１－０８０５室 (exercises)

1月12日（木）4-5限 ５１－０８０５室
1月13日（金）4-5限 ５１－１００６室
1月19日（木）4-5限 ５１－０８０５室
1月20日（金）4-5限 ５１－１００６室

Description

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.

Prerequisites

See Part I.

Lecture Notes

Script (Chapter 1-12, modified 09.01.2017)

  1. Constraints and Forces (modified 16.12.2016)
  2. Lagrangian Field Theory (modified 07.01.2017)
  3. Variational Integrators for Partial Differential Equations (modified 07.01.2017)
  4. Hamiltonian Field Theory (modified 09.01.2017)
  5. Multisymplectic Integrators
  6. Discrete Poisson Brackets

Exercises

The exercise sheets 5 and 6 will be discussed on 12月22日.

  1. Discrete Mechanics with Forces
  2. Discrete Mechanics with Constraints

References

Additional references