  When using black hole excision to numerically evolve a fully generic black
hole spacetime, most 3-D 3+1 codes use an $xyz$-topology (spatial) grid. In
such a grid, an $r = \constant$ excision surface must be approximated by an
irregular and non-smooth "staircase-shaped" excision grid boundary, which may
introduce numerical instabilities into the evolution. In this paper I describe
an alternate scheme, which uses multiple grid patches, each with topology $\{r
\times ({\rm angular coordinates})\}$, to cover the slice outside the $r =
\constant$ excision surface. The excision grid boundary is now smooth, so the
evolution should be less prone to instabilities. With 4th order finite
differencing, this code evolves Kerr initial data to ${\sim} 60M$ using the ADM
equations; I'm currently implementing the BSSN equations in it in the hope that
this will improve the stability.
