Physics-aware hyper-reduction for full-vector photonic waveguide mode solvers
Photonic waveguide design often requires repeated full-vector Maxwell eigenmode solves over wavelength and geometry, where the subpixel smoothing needed at dielectric interfaces makes operator assembly a substantial part of the cost. We present a physics-aware hyper-reduction framework for accelerating this assembly. The method exploits an exact affine dependence of the discrete operators on the locally sampled inverse-permittivity tensor, and chooses its strategy from how a parameter acts on the interface cells. We demonstrate two regimes. In wavelength sweeps at fixed geometry, tensor values change on a fixed set of cells, and proper orthogonal decomposition with matrix discrete empirical interpolation reproduces the operators from few snapshots. In moving-boundary sweeps, interface information relocates across the grid, and event-driven dynamic local sampling updates only the coefficients a geometric step changes, reproducing full assembly exactly. These results show that operator assembly can be reduced by more than an order of magnitude without approximating the moving boundary, shifting the cost of a photonic mode sweep to the eigensolver.