Tuesday, August 21, 2012

1208.3891 (Christian Reisswig et al.)

General relativistic null-cone evolutions with a high-order scheme    [PDF]

Christian Reisswig, Nigel T. Bishop, Denis Pollney
We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.
View original: http://arxiv.org/abs/1208.3891

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