FDTD Method on a Lebedev Grid for Anisotropic Materials

The finite-difference time-domain method is derived on a Lebedev grid for lossy anisotropic media. The Lebedev grid uses collocated field components and supports spurious solutions but an intuitive method for removing the extra solutions is presented. Update equations at material discontinuities and metal planes are derived and shown to take the same form as updates in bulk media. Additionally, a dispersion relation and stability criteria are presented. A numerical comparison with the Yee grid shows that the Lebedev grid suffers from greater numerical dispersion but better represents material discontinuities when compared using equal memory requirements. Furthermore, the small stencil on the Lebedev grid decreases the required number of calls to memory and simplifies the programming structure.