A numerical method that excises the outer computational boundary along the ingoing light cone makes boundary conditions unnecessary, at the cost of limiting evolution to about one light-crossing time of the initial grid.
Frauendiener, Living Reviews in Relativity 7, 1 (2004)
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Excision and avoiding the use of boundary conditions in numerical relativity
A numerical method that excises the outer computational boundary along the ingoing light cone makes boundary conditions unnecessary, at the cost of limiting evolution to about one light-crossing time of the initial grid.