preserving

A novel structure preserving scheme for Schrondiger-Poisson systems.

Dr. Th. Katsaounis

Feb 28, 16:00 - 17:00

B2 L5 R5220

Novel structure preserving Schrondiger Poisson Systems

In this talk I will present a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrodinger-Poisson system. We use the Crank-Nicolson scheme as a time-stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system’s mass conservation and energy balance laws for constant discretization parameters.