Speaker
Damiano Lombardi
(INRIA)
Description
In this work we present a variational structure preserving discretisation method for metriplectic systems. These are composed of two parts: a Hamiltonian flow and a dissipation. The dissipation is built based on the Casimirs of the Hamiltonian system. A weak formulation of the Hamiltonian flow is defined. Based on this, a variational semi-discretisation in space is performed, leading to a finite dimensional Hamiltonian system. We discuss the possibility of introducing a dynamical variational discretisation by leveraging the geometrical description of the weak Hamiltonian flow, in the spirit of the Dynamical Low Rank method.
Work in collaboration with Cecilia Pagliantini.
