Constraint-preserving boundary treatment for a harmonic formulation of   the Einstein equations
  We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions. 
Jennifer Seiler, Bela Szilagyi, Denis Pollney, and Luciano Rezzolla