Numerical relativity: combining the Cauchy and characteristic initial value problems

Numerical relativity can be performed within the context of the Cauchy problem or the characteristic initial value problem (CIVP). These two approaches are reviewed in the case of axial symmetry without rotation. It is shown how to compactify CIVP coordinates so that a finite grid extends to future null infinity. Many physical situations have matter in a central region and vacuum outside. It is shown how to interface Cauchy algorithms in the central region with CIVP algorithms in the external vacuum.