Christian Reisswig et al 2007 Class. Quantum Grav. 24 S327 doi:10.1088/0264-9381/24/12/S21
Christian Reisswig1, Nigel T Bishop2, Chi Wai Lai2, Jonathan Thornburg1 and Bela Szilagyi1
Show affiliationsThe 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.
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 12 (21 June 2007)
Received 5 October 2006, in final form 11 December 2006
Published 4 June 2007
Christian Reisswig et al 2007 Class. Quantum Grav. 24 S327
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