Derivation of 3D space-time Maxwell grid equation using finite integration method

A geometrical formulation of a space-time finite integration (FI) method is studied for effcient computations of electromagnetic wave propagation. A space-time dual grid is constructed based on the Hodge duality and Lorentzian metric. A relation between the incidence matrices of space-time primal and dual grids is compared with the geometrical relation in the Euclidean space. 3D space-time Maxwell grid equations are systematically derived using the incidence matrices and an impedance matrix.