  The efficient compression of kernel matrices, for instance the off-diagonal
blocks of discretized integral equations, is a crucial step in many algorithms.
In this paper, we study the application of Skeletonized Interpolation to
construct such factorizations. In particular, we study four different
strategies for selecting the initial candidate pivots of the algorithm:
Chebyshev grids, points on a sphere, maximally-dispersed and random vertices.
Among them, the first two introduce new interpolation points (exo-vertices)
while the last two are subsets of the given clusters (endo- vertices). We
perform experiments using three real-world problems coming from the
multiphysics code LS-DYNA. The pivot selection strategies are compared in term
of quality (final rank) and efficiency (size of the initial grid). These
benchmarks demonstrate that overall, maximally-dispersed vertices provide an
accurate and efficient sets of pivots for most applications. It allows to reach
near-optimal ranks while starting with relatively small sets of vertices,
compared to other strategies.
