Piecewise linear recursive convolution for dispersive media using FDTD

Abstract

Introduced a new method for computing dispersive media using finite difference time domain method by employing the recursive convolution approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function. The RC approach results in a fast and computationally efficient algorithm; however, the accuracy achieved is not generally as good as that obtained with other methods. A new piecewise linear recursive convolution (PLRC) method is described here that has greatly improved accuracy over the original RC approach but retains its speed and efficiency advantages.

Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

“…During the past two decades, there have been numerous investigations of FDTD dispersive media formulations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. These include the recursive convolution FDTD (RC-FDTD) method [2], the piecewiselinear recursive convolution FDTD (PLRC-FDTD) method [3,4], the Z transform FDTD (ZT-FDTD) method [5,6], the piecewiselinear current density recursive convolution FDTD (PLCDRC-FDTD) method [7], the trapezoidal recursive convolution finite-difference timedomain (TRC-FDTD) method [8,9], the FDTD method based on locally one-dimensional scheme [6,10,11], the current-density-Laplacetransfer FDTD (CLT-FDTD) method [12] and the shift-operator finitedifference time-domain (SO-FDTD) method [13][14][15], and so on. The above FDTD methods have been mainly used to analyze EM problems for magnetized plasma where the external magnetic field direction is parallel to the direction of EM-wave propagation, which is a serious limitation.…”

PLRC and Ade Implementations of Drude-Critical Point Dispersive Model for the FDTD Method

“…Substituting Eq. (6) into the definition of χ m and ξ m shown in Kelley and Luebbers [11], we obtain the following equations…”

“…The PLRC method uses a linear approximation to evaluate the electric field E(t) over each time-stepping interval [11] and has better accuracy compared to the RC method which assumes a constant electric field over the time-stepping interval. The equation for updating the electric field E n at time-step t = n∆t is…”

“…For example, Kelley and Luebbers [11] proposed a piecewise-linear recursive-convolution (PLRC) method to implement the Debye and Lorentz dispersive media and the results were compared to that of Luebbers et al [12] which used the recursive-convolution (RC) method. Vial [13] implemented the DCP model by using RC method while Sullivan [14], Weedon and Rappaport [15] used the Z-transform technique to implement dispersive media into the FDTD algorithm.…”

An Optimized PLRC-FDTD Model of Wave Propagation in Anisotropic Magnetized Plasma

“…The recursive convolution (RC) FDTD method [6] which has high numerical dispersion in most conditions is easy to be implemented and saves computational memory compared with current density J and electric field E (JE) convolution [7] method and auxiliary differential equation (ADE) [8] methods. The piecewise linear RC [9] method which has the advantage of high efficiency and small memory of RC-FDTD method is proposed to reduce the numerical dispersion of RC-FDTD method assuming that the field value of each grid has linear variation. The accuracy of the aforementioned efforts for expanding the FDTD method to frequency dependent materials is controlled by the choice of the second-order precision central difference format to achieve difference instead of differential.…”