Numerical performance of the parabolized ADM (PADM) formulation of General Relativity

Understand

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.