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> AUG 17: NA Seminars
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AUG 17: NA Seminars
Event date: Tuesday, August 17, 2010, from 2:10 PM to 3:10 PM
Location: Bahen Centre Rm. 5256
Speaker: Elena Celledoni
Mathematics Department
Norwegian University of Science and Technology Trondheim, Norway
Title: Energy-preserving integrators and B-series
Abstract: This talk will be concerned with numerical integrators that preserve
first integrals of differential equations exactly, in particular
energy-preserving integrators. The preferred method to preserve first
integrals of differential equations is the Discrete Gradient Method.
This method relies on the construction of a so-called discrete
gradient of the first integral, and requires the user to know and
input the first integral to be preserved. The average vector field
method is an integration method which belongs to this class but also
to the class of so-called B-series methods. These are methods which
have an associated Lie algebra of energy-preserving linear
combinations of elementary differentials, much like symplectic B-
series methods have an associated Lie algebra of Hamiltonian linear
combinations of elementary differentials. We have characterized the
linear subspaces of energy-preserving (EP) and Hamiltonian modified
vector fields which admit a B-series, their finite-dimensional
truncations, and their annihilators. We have also studied the
manifolds of B-series conjugate to Hamiltonian and conjugate to energy-
preserving.