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Binary black hole simulations become increasingly more computationallyexpensive with smaller mass ratios, partly because of the longer evolutiontime, and partly because the lengthscale disparity dictates smaller time steps.The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method foralleviating the scale disparity in simulations with mass ratios in theintermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), wherepurely perturbative methods may not be adequate. A region ("worldtube") muchlarger than the small black hole is excised from the numerical domain, andreplaced with an analytical model approximating a tidally deformed black hole.Here we apply this idea to a toy model of a scalar charge in a fixed circulargeodesic orbit around a Schwarzschild black hole, solving for the masslessKlein-Gordon field. This is a first implementation of the worldtube excisionmethod in full 3+1 dimensions. We demonstrate the accuracy and efficiency ofthe method, and discuss the steps towards applying it for evolving orbits and,ultimately, in the binary black-hole scenario. Our implementation is publiclyaccessible in the SpECTRE numerical relativity code.

Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions