Both for studies of cosmic censorship and for practical purposes in gravitational wave astronomy, it is desirable to include future null-infinity in the computational domain. Extending formulations of general relativity known to behave well in the strong-field regime out to infinity with compactification is, however, a subtle game. In my presentation I will explain how the competition between decay of fields near infinity and growth of coefficients (due to compactification) plays out in dual-frame generalized harmonic gauge. I will discuss ongoing work towards the numerical implementation of the resulting PDEs.
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