Celephais: efficient spectral initial data code for precessing compact binaries

Abstract

Large numerical-relativity surveys require compact-binary initial data that are both spectrally accurate and inexpensive to construct, including for systems with unequal masses and misaligned spins. We present \celephais, a compact-object initial-data code built on the \texttt{Kadath} spectral library, that constructs binary-neutron-star and black-hole--neutron-star initial data without imposing equatorial symmetry. The method exploits the sparse structure of the globally coupled multi-domain Jacobian and the approximate parity separation of fields. The assembled matrix is factored with \texttt{MUMPS} and reused as a refreshed right preconditioner in a Jacobian-free Newton--Krylov iteration, thereby avoiding dense storage. An adaptive $hp$--refinement scheme then concentrates resolution where the spectral tails are not yet resolved. For a mass-ratio-$20$ black-hole--neutron-star benchmark, the adaptive schemes recover the uniform-grid constraint accuracy with about three times fewer unknowns. We also extend the post-Newtonian force-balance estimate to arbitrary spin orientations and use it to initialise eccentricity reduction. Validation comprises binding-energy comparisons with post-Newtonian sequences, a precessing binary-neutron-star eccentricity-reduction test, and a full evolution whose waveform-reconstructed precession axis follows a post-Newtonian simple-precession model. These results establish an efficient route to spectrally resolved binary-neutron-star and black-hole--neutron-star initial data with arbitrary spin orientations.