Matter and Electromagnetic Fields in Strong Gravity
CSIC Building (#406),
Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions

Numerical Techniques for Simulating EM and GR Fields in the 21st Century
David Meier
NASA Jet Propulsion Laboratory

Abstract:
A new selfconsistent set of numerical techniques is
presented for the purpose of simulating the full set of Einsteins
field equations, with attendant conservation laws of the matter
sources, simultaneously with the full set of Maxwells field equations
in curved spacetime, plus their attendant conservation laws of charge
sources. It is suggested that such techniques would be applicable to
simulating the full black hole formation, plus gammaray burst,
problem, and they may be a model for additional highly complex
simulations in the coming decades. While the method is an outgrowth of
techniques used since the 1960s and 1980s in engineering and
astrophysics, it is, in fact, an implementation of Discreet Exterior
Calculus on a 4dimensional manifold. Tensors of orders 0 4 are
defined in a specific manner, which leads to a natural implementation
of duals, dual meshes, identity and LeviCivita density tensors,
etc. This also automatically ensures that field Bianchi identities
(boundary of a boundary is zero) are satisfied and that all field
constraints are automatically propagated throughout spacetime during
the evolution of one or more resident gauge fields. Although
unstructured mesh implementations should be possible, the author will
introduce this method using a structured mesh approach. And the latter
part of the talk will deal with efforts needed to treat properly the
conservation laws with shock capturing schemes and other techniques
related to information flow.

