Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-12-08
Phys.Rev.D78:064048,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 two column pages, 20 figures, submitted to PRD, two typos corrected
Scientific paper
10.1103/PhysRevD.78.064048
In a recent paper the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a mixed hyperbolic - second-order parabolic, well-posed system. The surface of constraints of PADM becomes a local attractor for all solutions and all possible well-posed gauge conditions. This paper describes a numerical implementation of PADM and studies its accuracy and stability in a series of standard numerical tests. Numerical properties of PADM are compared with those of standard ADM and its hyperbolic Kidder, Scheel, Teukolsky (KST) extension. The PADM scheme is numerically stable, convergent and second-order accurate. The new formulation has better control of the constraint-violating modes than ADM and KST.
Hansen Jakob
Khokhlov Alexei
Paschalidis Vasileios
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