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A geometrical formulation of a space-time finite-integration (FI) method is studied for application in electromagnetic-wave propagation calculations. Based on the Hodge duality and Lorentzian metric, a modified relation is derived between the incidence matrices of space-time primal and dual grids. A systematic method to construct the Maxwell grid equations on the space-time primal and dual grids is developed. The geometrical formulation is implemented on a simple space-time grid, which is proven equivalent to an explicit time-marching scheme of the space-time FI method. [ABSTRACT FROM AUTHOR]

A simple and stable sub-grid scheme is derived from the space-time finite integration method, where staircase-shaped edges can be used to construct a rectangle-based grid. Comparison with classical sub-grid methods shows that the proposed method suppresses unphysical wave reflection without interpolation of field values for the sub-grid connection. No numerical instability was observed even after 10^\mathrm \mathbf 6 time steps. The proposed method was applied to the computation of a photonic band gap. [ABSTRACT FROM PUBLISHER]