Excision and avoiding the use of boundary conditions in numerical relativity

A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in Bieri et al (2019 (arXiv:1905.08657 [gr-qc])). In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike or tangent to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry. (note)