Olivier Verdier: The spherical midpoint method

Abstract:

Spin systems model spinning black holes binaries, ferromagnetic materials (Laudau–Lifshitz equation), or hurricanes on gas planets. Their phase spaces, products of spheres, have a natural symplectic structure for which those systems are Hamiltonian. Is there a method with no extra variable which preserves symplecticity? The answer is yes, and it is a remarkable modification of the classical midpoint method. I will explain what symplecticity means, why it is important in numerical integration, and where this new midpoint method comes from.

This is joint work with Robert McLachlan and Klas Modin.