2006/10/05 by Christian Reisswig, Nigel T. Bishop, Chi Wai Lai +3 · 4 citations
Mathematics · Physics and Astronomy · #Angular resolution (graph drawing) #Classical mechanics #Code (set theory) #Computer science #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Einstein #Galaxies: Formation, Evolution, Phenomena #General relativity #Geometry #Gravitation #Mathematics #Numerical relativity #Order (exchange) #Physics #Radio Astronomy Observations and Technology #Stereographic projection #Theoretical physics #Theory of relativity #gr-qc
paper · pdf · doi:10.1088/0264-9381/24/12/s21
published as Class.Quant.Grav.24:S327-S340,2007 · 12 pages, 5 figures, submitted to CQG (special NFNR issue)
arxiv created 2006/10/05 · openalex publication_date 2007/06/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.