A time-domain method with isotropic dispersion and increased stability on an overlapped lattice

A time-domain method on an overlapped lattice is presented for the accurate and efficient simulation of electromagnetic wave propagation through inhomogeneous media. The method comprises a superposition of complementary approximations to electromagnetic theory on a lattice. The discrete space-time (DST) method, is set on a pair of dual lattices whose field components are collocated on their respective lattice sites. The other, the time-domain element (TDE) method, is set on overlapping dual lattices whose field components are noncollocated. The TDE method is shown to be a generalization and reinterpretation of the Yee algorithm. The benefits of the combined algorithm over comparable methods include: (1) increased accuracy over larger bandwidths; (2) increased stability allowing larger time steps; (3) local stencil-satisfying boundary conditions on interfaces; (4) self-contained mathematical framework; (5) it is physically intuitive.