A New Generalized Harmonic Evolution System
  A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented. 
Lee Lindblom, Mark A. Scheel, Lawrence E. Kidder, Robert Owen, and   Oliver Rinne