Boundary Conditions for the Einstein Evolution System
  New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D non-linear numerical evolutions of dynamical black-hole spacetimes. 
Lawrence E. Kidder, Lee Lindblom, Mark A. Scheel, Luisa T. Buchman,   Harald P. Pfeiffer