Extremely high-order convergence in simulations of relativistic stars

We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. demonstrate proof-of-principle 1+1-dimensional numerical implementation that exhibits up to 7th-order convergence highly dynamic barotropic stars in curved spacetime, and errors 6 orders of magnitude smaller than standard method. Aside high-order interpolation (Runge's phenomenon), there are no obvious fundamental obstacles even higher order. The uses novel surface-tracking method, where the surface is evolved accurate boundary conditions imposed there. Computational memory does not need be allocated fluid variables vacuum region spacetime. anticipate application this new method full $3\! +\! 1$-dimensional simulations inspiral phase compact binary systems at least one body. additional challenge deformable must addressed multiple spatial dimensions, but it also opportunity input more precise tension physics.