How do we model gravitational waves from extreme mass-ratio mergers?

LISA will detect gravitational waves from small objects spiraling into massive black holes, but modeling those signals requires second-order perturbation calculations nobody has cracked for spinning (Kerr) black holes. Using numerical relativity tools — discontinuous Galerkin elements, adaptive mesh refinement, multigrid solvers — this method solves 20 frequency modes in parallel in seconds, reaching exponential convergence even for near-maximally spinning black holes at the innermost stable orbit. The open-source code lays groundwork for the full gravitational case needed to extract physics from LISA data.