The field of geometric numerical integration(GNI) seeks to exploit the
underlying (geometric)structure of a dynamical system in order to
construct numerical methods that exhibit desirable properties of
stability and/or preservation of invariants of the flow. Variational
Integrators are built for Hamiltonian systems by discretizing the
generating function of the symplectic flow, rather than discretizing
the differential equations directly. Traditionally, the generating
function considered is a type I generating function.
In this talk we will discuss the properties and
advantages/disadvantages of discretizing the type II/III generating
function of the flow. After establishing error analysis and adjoint
results, we consider the possible numerical resonance properties
corresponding to the different types of generating functions.
Tuesday, October 25, 2016
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813