Numerical performance of the parabolized ADM formulation of general relativity

Vasileios Paschalidis, Jakob Hansen, Alexei Khokhlov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In a recent paper, the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner (ADM) formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a well-posed system which resembles the structure of mixed hyperbolic-second-order parabolic partial differential equations. 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.

Original languageEnglish (US)
Article number064048
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
StatePublished - Sep 18 2008
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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