Spectral XCTS initial data for precessing compact binaries — on a laptop.
Celephais is a numerical-relativity initial-data code built on the
Kadath spectral library — a sibling of FUKa, not a branch or fork of it.
It solves the XCTS system for binary neutron stars and black-hole–neutron-star systems
without imposing equatorial symmetry, so spins may take arbitrary
orientations. The globally coupled multi-domain Jacobian is assembled in sparse form, factored
with MUMPS, and reused as a refreshed right preconditioner inside a
Jacobian-free Newton–Krylov iteration; dense storage never appears.
A converged precessing-BNS solve on a survey grid completes in
≈26 s on four cores — about
140 solutions per hour from one laptop, with no cluster allocation.
Complete production-resolution job — fits in laptop memory
3×
Fewer unknowns for the same constraint accuracy with hp-AMR (q = 20)
Absolute cost — strong scaling
Sparse-Jacobian construction plus MUMPS analysis and factorisation for an
equal-mass 1.35 + 1.35 M☉ precessing BNS (DD2 EOS, coordinate separation
35 M☉, one star at χ = 0.3 tilted 81° to the orbital angular
momentum), at resolution N = 9. All timings are on a single MacBook Pro with an
Apple M4 Max processor.
Assembly speedup reaches 4.85× on eight ranks (60.7% parallel efficiency). Extra ranks
accelerate assembly but not the sparse factorisation, so the wall time flattens first —
adding ranks past this knee buys little.
Why adaptive refinement
Uniform spectral order is the expensive way to buy accuracy: stored nonzeros and
factorisation cost grow much faster than the unknown count. The same precessing BNS on two
ranks, swept in resolution:
A 4.6× increase in unknowns costs 19.5× in assembly alone and exhausts laptop memory at
N = 15, where the factorisation did not complete. Anisotropic
hp-refinement answers this: domain-local spectral tails decide where order is
added, so resolution is not spent on directions that are already resolved.
For a mass-ratio-20 BHNS, one h move reduces the Hamiltonian-constraint norm by about
a factor of 8 — roughly 2.4× better than the equal-cost p move — and subsequent
p moves match the finest uniform-grid accuracy with about
three times fewer unknowns. At mass ratio 10 the saving is 1.6×.
Solver coverage
Isolated black hole — BH (3D), BH2d
Isolated neutron star — NS, NS_nosym, NS2d, NS2d_xcts
Binary neutron star — BNS, BNS_nosym
Black hole – neutron star — BHNS, BHNS_nosym
Scalar–tensor (DEF) — NS_def, BNS_def
Scalar–Gauss–Bonnet — NS_sGB, BNS_sGB
_nosym variants drop orbital-plane symmetry for spinning and tilted
configurations; binary black holes are built on the BH formalism. MUMPS 5.9.0 and METIS 5.1.0
are vendored and built automatically — no separate installation.
Validation
Generated BNS initial data has been evolved with the SACRA code —
many thanks to Yong and Mingzhe for
their support in validating the codebase.
The accompanying code paper adds binding-energy comparisons against post-Newtonian sequences,
a precessing-BNS eccentricity-reduction test, and a full evolution whose
waveform-reconstructed precession axis follows a post-Newtonian simple-precession model.
Celephais is ready for production initial-data runs.
Navigate to a solver output directory, e.g. Celephais/apps/BNS/sbatch_outputs.
3
Launch locally or submit through sub_Celephais.sh — the same script runs under mpirun or sbatch.
Benchmark provenance: all figures are medians of three runs on one MacBook Pro with an Apple
M4 Max processor. Scaling and resolution data are from Table I of the Celephais code paper
(in preparation); the 26 s figure is an end-to-end converged solve of the canonical
BNS_nosym configuration at N = 7 on four MPI ranks, measured 4 August 2026, and
covers boost and binary stages to a final Newton error of 3 × 10−9.
Throughput is that solve run back to back on the same four ranks. At N = 15 the
factorisation did not complete within available memory.