Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-10-05
Class.Quant.Grav.24:S327-S340,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, 5 figures, submitted to CQG (special NFNR issue)
Scientific paper
10.1088/0264-9381/24/12/S21
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.
Bishop Nigel T.
Lai Chi Wai
Reisswig Christian
Szilagyi Bela
Thornburg Jonathan
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