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Numerical performance of the parabolized ADM (PADM) formulation of General Relativity | | Vasileios Paschalidis
; Jakob Hansen
; Alexei Khokhlov
; | | Date: |
8 Dec 2007 | | Abstract: | 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. | | Source: | arXiv, 0712.1258 | | Services: | Forum | Review | PDF | Favorites | |
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