We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einsteins equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.
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