2003/04/04 by David R. Fiske
Mathematics · Physics and Astronomy · #Applied mathematics #Astrophysical Phenomena and Observations #Attractor #Black Holes and Theoretical Physics #Classical mechanics #Constraint (computer-aided design) #Einstein #Geometry #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Numerical relativity #Partial differential equation #Physics #Pulsars and Gravitational Waves Research #Theory of relativity #Time evolution #gr-qc #physics.comp-ph
paper · pdf · doi:10.1103/physrevd.69.047501
published as Phys.Rev. D69 (2004) 047501 · 6 pages, 3 figures, 1 table. Uses REVTeX4
arxiv created 2003/04/04 · openalex publication_date 2004/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
When constructing numerical solutions to systems of evolution equations subject to a constraint, one must decide what role the constraint equations will play in the evolution system. In one popular choice, known as free evolution, a simulation is treated as a Cauchy problem, with the initial data constructed to satisfy the constraint equations. This initial data are then evolved via the evolution equations with no further enforcement of the constraint equations. The evolution, however, via the discretized evolution equations introduce constraint violating modes at the level of truncation error, and these constraint violating modes will behave in a formalism dependent way. This paper presents a generic method for incorporating the constraint equations into the evolution equations so that the off-constraint dynamics are biased toward the constraint satisfying solutions.