Mini-course on Geometric Numerical Integration
February 16-18, 2016 Fundação Getulio Vargas

Ordinary differential equations (ODEs) often appear in the dynamical description of systems in physics, chemistry, biology, engineering, etc. Many differential equations exhibit geometric properties that are preserved by the dynamics. Recently, there has been a trend towards the construction of geometric numerical integrators. Such numerical methods are of particular interest in the simulation of mechanical systems, where the preservation of invariants such as the energy, momentum or symplectic form is important, especially in long-term simulations (of the outer solar system for example). This mini-course offers a first introduction to the field of Geometric Numerical Integration (GNI). In short, we will be interested in the development and numerical analysis of structure-preserving numerical methods for differential equations.

Topics covered in this mini-course are:

  • Brief exposition of classical numerical methods for ODEs
  • Numerical methods that preserve properties of Hamiltonian systems
  • Problems with highly oscillatory solutions
  • GNI for partial differential equations and stochastic differential equations.

    These topics will be illustrated by applications from physics, molecular dynamics and astronomy.

    The mini-course will be complemented by theoretical and practical exercises in Matlab.

    Schedule:
    Lectures (Auditório 1333): Tuesday 16.02.16, 9:20-12:00. Wednesday 17.02.16, 9:20-12:00. Thursday 18.02.16, 9:20-12:00.
    Computer Labs (Laboratório 422): Wednesday 17.02.16, 14:00-17:00. Thursday 18.02.16, 14:00-17:00.

    Lecture notes of the mini-course (18.02.2016).
    Assignments (14.02.2016).
    Solutions to the assignments (18.02.2016).

    Link to the lecture Introduction to PDE Constrained Optimization by Eddie Wadbro (15.02.2016)

    Sponsors

    This mini-course is organised by Hugo de la Cruz and David Cohen within the framework Initiation Grants of the Swedish Foundation for International Cooperation in Research and Higher Education STINT, we gratefully acknowledge its financial support.

    We thank Fundação Getulio Vargas for the hospitality.

    Contacts

    David Cohen

    Department of Mathematics and Mathematical Statistics
    Umeå universitet
    SE-90187 Umeå

    Hugo de la Cruz

    Escola de Matemática Aplicada
    Fundação Getulio Vargas
    B-22250900 Rio de Janeiro


    last modifications: 18.02.16