Comparative study of grids based on the cubic crystal system for the FDTD solution of the wave equation

In this paper, a scalar wave is solved in the fully explicit finite difference time domain scheme for different stencils based on the cubic crystal system. In particular, we study four systems: the simple cubic, the body-centered cubic, the face-centered cubic and the compact packing cubic. In many papers that are focused on the artificial anisotropy induced by these grids in the propagated wave, one candidate is often better than all the others. In this manuscript, we study the stability, the physical phase velocity error and the anisotropy under two views. Firstly, we consider the same burdens or density of nodes per cubic wavelength and secondly we look at the asymptotic case. We also investigate the computational complexity based on several considerations: burdens, asymptotic time and implementation difficulties. Therefore, we pointed out how each problem or application, due to its different characteristics, has an appropriate grid in order to be treated properly.