Symplectic time integrators for numerical general relativity

Details Symplectic time integrators for numerical general relativity Symplectic time integrators for numerical general relativity

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aipc.1122..376r&link_type=abstract

PHYSICS AND MATHEMATICS OF GRAVITATION: Proceedings of the Spanish Relativity Meeting 2008. AIP Conference Proceedings, Volume

Mathematics

Numerical Relativity, Supersymmetry, Theory Of Quantized Fields

Scientific paper

We describe how we use symplectic time integrators in numerical general relativity. Of particular interest is the free symplectic Störmer-Verlet method and its application to the dynamical part of ADM-like equations.
The behavior of this scheme is illustrated on an effectively 1+1-dimensional version of Einstein's equations that we apply to a perturbed Minkowski problem. We discuss differences between symplectic and non-symplectic integrators, showing favorable evolution properties of the symplectic Störmer-Verlet method in this example.
To handle the constraint part of the equations with a symplectic integrator one can use a partially constrained scheme that applies the RATTLE method, a modification of the Störmer-Verlet method for holonomic constraints.

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