  The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be
solved accurately in the coordinate space with the recently developed solvers
HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of
superfluid Fermi systems with complicated topologies and significant spatial
extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the
neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX
solver based on B-spline techniques uses a hybrid MPI and OpenMP programming
model for parallel computation for distributed parallel computation, within a
node multi-threaded LAPACK and BLAS libraries are used to further enable
parallel calculations of large eigensystems. The MADNESS-HFB solver uses a
novel multi-resolution analysis based adaptive pseudo-spectral techniques to
enable fully parallel 3D calculations of very large systems. In this work we
present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped
fermions.
