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We describe a numerical method to construct Cauchy data extending tospace-like infinity based on Corvino's (2000) gluing method. Adopting thesetting of Giulini and Holzegel (2005), we restrict ourselves here to vacuumaxisymmetric spacetimes and glue a Schwarzschildean end to Brill-Lindquist datadescribing two non-rotating black holes. Our numerical implementation is basedon pseudo-spectral methods, and we carry out extensive convergence tests tocheck the validity of our numerical results. We also investigate the dependenceof the total ADM mass on the details of the gluing construction.

Numerical construction of initial data for Einstein's equations with static extension to space-like infinity