Research Activities > Programs > Matter and Electromagnetic Fields in Strong Gravity

Matter and Electromagnetic Fields in Strong Gravity

CSIC Building (#406), Seminar Room 4122.

Numerical Techniques for Simulating EM and GR Fields in the 21st Century

David Meier

NASA Jet Propulsion Laboratory

Abstract:   A new self-consistent 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 gamma-ray 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 4-dimensional manifold. Tensors of orders 0 4 are defined in a specific manner, which leads to a natural implementation of duals, dual meshes, identity and Levi-Civita 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.

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