  We develop a method for numerical time-domain wave propagation based on the
model order reduction approach. The method is built with high-performance
computing (HPC) implementation in mind that implies a high level of parallelism
and greatly reduced communication requirements compared to the traditional
high-order finite-difference time-domain (FDTD) methods. The approach is
inherently multiscale, with a reference fine grid model being split into
subdomains. For each subdomain the coarse scale reduced order models (ROMs) are
precomputed off-line in a parallel manner. The ROMs approximate the
Neumann-to-Dirichlet (NtD) maps with high (spectral) accuracy and are used to
couple the adjacent subdomains on the shared boundaries. The on-line part of
the method is an explicit time stepping with the coupled ROMs. To lower the
on-line computation cost the reduced order spatial operator is sparsified by
transforming to a matrix Stieltjes continued fraction (S-fraction) form. The
on-line communication costs are also reduced due to the ROM NtD map
approximation properties. Another source of performance improvement is the time
step length. Properly chosen ROMs substantially improve the
Courant-Friedrichs-Lewy (CFL) condition. This allows the CFL time step to
approach the Nyquist limit, which is typically unattainable with traditional
schemes that have the CFL time step much smaller than the Nyquist sampling
rate.
