Johan Wärnegård: Numerical Methods for the Gross-Pitaevskii Equation
Time: Thu 2019-05-16 14.15 - 15.00
Lecturer: Johan Wärnegård, KTH
Location: Room F11, Lindstedtsvägen 22, våningsplan 2, F-huset, KTH Campus.
The Gross-Pitaevskii equation is a nonlinear Schrödinger equation with applications in several fields such as optics, fluid dynamics, in particular deep water waves and quantum physics. When selecting a suitable discretization for this problem, one needs to be aware of the rich geometric properties.
In this talk we compare various mass-conservative time-integrators for the Gross-Pitaevskii equation in physically relevant setups. The comparison contains methods that are purely mass-conservative, methods that are additionally symplectic and methods that preserve the energy exactly. A walkthrough of these properties will be given. Quite notably, the differences between symplectic and energy-conservative discretizations turn out to be stronger than expected if the regularity of the solution is low.