  This paper addresses the overwhelming computational resources needed with
standard numerical approaches to simulate architected materials. Those
multiscale heterogeneous lattice structures gain intensive interest in
conjunction with the improvement of additive manufacturing as they offer, among
many others, excellent stiffness-to-weight ratios. We develop here a dedicated
HPC solver that benefits from the specific nature of the underlying problem in
order to drastically reduce the computational costs (memory and time) for the
full fine-scale analysis of lattice structures. Our purpose is to take
advantage of the natural domain decomposition into cells and, even more
importantly, of the geometrical and mechanical similarities among cells. Our
solver consists in a so-called inexact FETI-DP method where the local,
cell-wise operators and solutions are approximated with reduced order modeling
techniques. Instead of considering independently every cell, we end up with
only few principal local problems to solve and make use of the corresponding
principal cell-wise operators to approximate all the others. It results in a
scalable algorithm that saves numerous local factorizations. Our solver is
applied for the isogeometric analysis of lattices built by spline composition,
which offers the opportunity to compute the reduced basis with macro-scale
data, thereby making our method also multiscale and matrix-free. The solver is
tested against various 2D and 3D analyses. It shows major gains with respect to
black-box solvers; in particular, problems of several millions of degrees of
freedom can be solved with a simple computer within few minutes.
