3:00 p.m., Monday (Jan. 28)
Math Annex 1100
Imperial College, London
Geometric Integration Methods for Materials and Fluids
Atomistic models of materials, i.e. molecular dynamics, result in
large systems of Newtonian equations of motion that evolve over
a wide range of time and length scales. Computational techniques
are required to reproduce the statistical mechanics of such systems
in a reliable and efficient manner. In that respect, the concept
of geometric integration, in particular symplectic integration,
has been proven to be a fundamental guiding principle.
In the first part of my talk, I will give an introduction to
symplectic integration and computational statistical mechanics.
This will be followed by a discussion of some of the challenges
arising from biomolecular modelling and the need for multi-scale
methods in space and time.
From a mathematical point of view Hamiltonian dynamics,
symplectic geometry and asymptotic expansions play a key role
in the design and analysis of numerical methods. I will discuss
this in the context of backward error analysis.
In the final part of my talk, these ideas will be extended
to PDEs and multi-symplectic geometry. In particular, the concept
of geometric integration has recently started to find its way
into geophysical fluid dynamics and numerical weather prediction.