3:00 p.m., Monday (Jan. 28)

Math Annex 1100

Sebastian Reich

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.

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