FDTD has proved to be a robust way for numerically solving Maxwell's equations since it was introduced by Kane Yee in 1966. Approximating non rectangular domains with rectangular meshes causes staircasing and as a consequence the accuracy of the numerical solution deteriorates. Madsen and Ziolkowski proposed a way to implement FDTD for general 3D domains that suffers from late time instability. We describe a potential way to repair this instability. For this purpose we employ the Piola transformation which allows us to map cells from the physical space to the reference cell in a manner that preserves fluxes and circulations, a useful property regarding Maxwell's equations.
