A compact higher‐order ADI‐FDTD method

A compact fourth order locally one-dimensional FDTD Method

“…A fourth order ADI-FDTD method involves solution of hepta-diagonal matrix equations. Recently a compact high order scheme was used in split-step and ADI FDTD which only needed to solve penta-diagonal matrix equations and led to higher computation efficiency [13][14]. The numerical dispersion in this fourth order ADI-FDTD method based on a compact scheme is proved to be similar to that in the original (2,4) ADI-FDTD [14].…”

“…x y [ Substituting (12) into (13), one can derive 1 n X / n X (14) in which 2 1 / / / . With the help of MATLAB software, the eigenvalues of amplification matrix can be solved, and the result is To analyze the numerical dispersion characteristic, let's consider a monochromatic wave with frequency , field components in (11) can be represented as…”

“…The numerical dispersion characteristics of this new compact fourth order LOD-FDTD method will be studied in comparison with the original second order LOD-FDTD method [6] as well as the ADI-FDTD counterpart [14]. The normalized numerical phase velocities of these three methods are computed, whose numerical result will be labeled in the illustrative figures herein as "2nd LOD", "4th ADI", "4th LOD", respectively, for simplicity.…”

“…So LOD-FDTD method is simpler and less CPU time consumed than ADI-FDTD counterpart. For the spatial derivative of field components in (1a)-(1c) and (2a)-(2c), a compact fourth order finite difference scheme [14] is used to approximate the spatial difference operator. For example, for spatial derivative in x-direction, the compact fourth order finite difference scheme can be presented as…”

Analysis of iterated ADI-FDTD schemes for Maxwell curl equations

“…This effect becomes less pronounced as the grid is refined, or if higherorder spatial stencils are used, e.g. fourth-order explicit differentiation ðf ð/Þ ¼ sin / / ð1 þ 1 6 sin 2 /Þ [17,22]) or implicit differentiation ðf ð/Þ ¼ sin / / 12 11þcos 2/ , [7,23]), see also [13] for a collection of schemes and references.…”