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We develop a method for numerical time-domain wave propagation based on themodel order reduction approach. The method is built with high-performancecomputing (HPC) implementation in mind that implies a high level of parallelismand greatly reduced communication requirements compared to the traditionalhigh-order finite-difference time-domain (FDTD) methods. The approach isinherently multiscale, with a reference fine grid model being split intosubdomains. For each subdomain the coarse scale reduced order models (ROMs) areprecomputed off-line in a parallel manner. The ROMs approximate theNeumann-to-Dirichlet (NtD) maps with high (spectral) accuracy and are used tocouple the adjacent subdomains on the shared boundaries. The on-line part ofthe method is an explicit time stepping with the coupled ROMs. To lower theon-line computation cost the reduced order spatial operator is sparsified bytransforming to a matrix Stieltjes continued fraction (S-fraction) form. Theon-line communication costs are also reduced due to the ROM NtD mapapproximation properties. Another source of performance improvement is the timestep length. Properly chosen ROMs substantially improve theCourant-Friedrichs-Lewy (CFL) condition. This allows the CFL time step toapproach the Nyquist limit, which is typically unattainable with traditionalschemes that have the CFL time step much smaller than the Nyquist samplingrate.

S-fraction multiscale finite-volume method for spectrally accurate wave propagation