This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einsteins equations for gravitation. This approach incorporates the best features of the two leading approaches to computational gravitation, carving up spacetime via Cauchy hypersurfaces within a central worldtube, and using characteristic hypersurfaces in its exterior to connect this region with null infinity and study gravitational radiation. It has worked well in simplified test problems, and is currently being used to build computer codes to simulate black hole collisions in 3-D.
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