Anisotropic-media extension of the body-centered tetragonal FDTD method

We extend the body-centered tetragonal (BCT) finite-difference time-domain (FDTD) method to anisotropic dielectrics with a full real-symmetric positive-definite permittivity tensor. Because the BCT grid collocates the three electric-field components at every node, the tensor constitutive relation becomes an interpolation-free pointwise 3×3 product-the staggered Yee grid must instead interpolate its off-diagonal terms-and the time step is guaranteed by a CFL bound set solely by the tensor's smallest eigenvalue. The scheme reproduces uniaxial Christoffel dispersion, converges at second order for a fully rotated biaxial crystal, and reproduces double refraction with the walk-off angle within 1% of theory. At equal grid-point density, the BCT grid resolves a rotated crystal with a 2-2.4× smaller index error and, in our eager PyTorch implementation, completes the anisotropic run in approximately 57% of the wall-clock time of the interpolated Yee reference.