Generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods are presented. The fundamental schemes constitute a family of implicit schemes that feature similar fundamental updating structures, which are in simplest forms with most efficient right-hand sides. The formulations of fundamental schemes are presented in terms of generalized matrix operator equations pertaining to some classical splitting formulae, including those of alternating direction implicit, locally one-dimensional and split-step schemes. To provide further insights into the implications and significance of fundamental schemes, the analyses are also extended to many other schemes with distinctive splitting formulae. Detailed algorithms are described for new efficient implementations of the unconditionally stable implicit FDTD methods based on the fundamental schemes. A comparative study of various implicit schemes in their original and new implementations is carried out, which includes comparisons of their computation costs and efficiency gains.

This letter presents an unconditionally stable locally 1-D finite-difference time-domain (LOD-FDTD) method for 3-D Maxwell's equations. The method does not exhibit the second-order noncommutativity error and its second-order temporal accuracy is ascertained via numerical justification. The method also involves simpler updating procedures and facilitates exploitation of parallel and/or reduced output processing. This leads to its higher computation efficiency than the alternating direction implicit and split-step FDTD methods

A split-step FDTD method with higher-order spatial accuracy is presented, which is proved to be unconditionally stable. From the dispersion analysis, it is justified that the method achieves improved accuracy compared with lower-order cases and its dispersion error is comparable with the higher-order ADI-FDTD method.

This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.

This study investigates the impacts of solar activity on the performance of the latest release of International Reference Ionosphere (IRI) model version 2012 (IRI-2012) predictions during the ascending phase of solar activity from 2009 to 2013. The study is based on the data of total electron content (TEC) retrieved from the Global Positioning System (GPS) at Singapore (NTUS) (geographic latitude 01.34°N, longitude 103.67°E, geomagnetic latitude 8.4°S), Thailand (CUSV) (geographic latitude 13.73°N, longitude 100.54°E, geomagnetic latitude 3.96°N), China (KUNM) (geographic latitude 25.02°N, longitude 102.79°E, geomagnetic latitude 15.15°N), Mongolia (ULAB) (geographic latitude 47.67°N, longitude 107.05°E, geomagnetic latitude 37.73°S), and Russia (IRKM) (geographic latitude 52.21°N, 104.31°E, geomagnetic latitude 42.28°S). The GPS-TEC has been compared with the IRI-2012 model TEC for three different options, namely, IRI-NeQ, IRI01-corr, and IRI-2001, for topside Ne over all the above five stations lying at different latitudes from equatorial-equatorial ionization anomaly (EIA) to mid-latitude regions but at around the same longitude line (104° ± 3°E). The study showed that the IRI model predictions for different topside options are different and significant in low-latitude region but insignificant in mid-latitude regions (except during winter season of high solar activity year 2012). During the period from 2009 to 2013, upon moving from low to high solar activity, the prediction nature (overestimation/underestimation) of IRI-2012 model changes significantly at EIA station KUNM of low-latitude region. The discrepancy in IRI-2012 model TEC as compared to GPS-TEC in low-latitude region is found to be larger and significant than in mid-latitude region (Mongolia and Russia). The discrepancy in the IRI-2012 model TEC with IRI-2001 topside is found to be maximum at equatorial station CUSV (RMSD 99%) during the solar minimum year 2009 and decreases moving towards high solar activity year. This suggests that significant improvements to the IRI-2012 model (hmF2 model) are required particularly in the equatorial regions taking the impacts of solar minimum year into account.

This paper presents new efficient algorithms for implementing 3-D Crank-Nicolson-based finite-difference time-domain (FDTD) methods. Two recent methods are considered, namely, the Crank-Nicolson direct-splitting (CNDS) and Crank-Nicolson cycle-sweep-uniform (CNCSU) FDTD methods. The algorithms involve update equations whose right-hand sides are much simpler and more concise than the original ones. Analytical proof is provided to show the equivalence of original and present methods. Comparison of their implementations signifies substantial reductions of the floating-point operations count in the new algorithms. Other computational aspects are also optimized, particularly in regard to the for-looping overhead and the memory space requirement. Through numerical simulation and Fourier stability analysis, it is found that while the CNDS FDTD is unconditionally stable, the CNCSU FDTD may actually become unstable.