Journal
GENERAL RELATIVITY AND GRAVITATION
Volume 45, Issue 5, Pages 1069-1094Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10714-013-1513-1
Keywords
Numerical studies of black holes and black-hole binaries; Wave generation and sources; Gravitational-wave astrophysics; Wave propagation and interactions; Characteristic evolutions
Funding
- National Science Foundation [AST-0855535, OCI-0905046]
- NASA [PF2-130099]
- Smithsonian Astrophysical Observatory for NASA [NAS8-03060]
- National Research Foundation, South Africa
- NSF MRI [PHY-0960291]
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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. Consequently the scheme offers more accuracy at a given computational cost compared to previous methods which are second-order accurate. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.
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