A time-domain discretisation of Maxwell's equations in nontrivial media using collocated fields

In this paper we present an unconditionally stable time-domain discretisation of Maxwell's equations where the discretized fields are collocated. This allows us to combine Maxwell's equations, which are usually discretized on a staggered grid, with constitutive differential equations which may not be well-suited for staggered grids. This approach guarantees that the numerical dispersion relation always closely mimics the exact one.