volume | PIER Journals

Abstract

This paper presents an overview and review of the fundamental implicit finite-difference time-domain (FDTD) schemes for computational electromagnetics (CEM) and educational mobile apps. The fundamental implicit FDTD schemes are unconditionally stable and feature the most concise update procedures with matrix-operator-free right-hand sides (RHS). We review the developments of fundamental implicit schemes, which are simpler and more efficient than all previous implicit schemes having RHS matrix operators. They constitute the basis of unification for many implicit schemes including classical ones, providing insights into their inter-relations along with simplifications, concise updates and efficient implementations. Based on the fundamental implicit schemes, further developments can be carried out more conveniently. Being the core CEM on mobile apps, the multiple one-dimensional (M1-D) FDTD methods are also reviewed. To simulate multiple transmission lines, stubs and coupled transmission lines efficiently, the M1-D explicit FDTD method as well as the unconditionally stable M1-D fundamental alternating direction implicit (FADI) FDTD and coupled line (CL) FDTD methods are discussed. With the unconditional stability of FADI methods, the simulations are fast-forwardable with enhanced efficiency. This is very useful for quick concept illustrations or phenomena demonstrations during interactive teaching and learning. Besides time domain, many frequency-domain methods are well-suited for further developments of useful mobile apps as well.

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134. Tan, E. L., "Enhanced R-matrix algorithms for multilayered diffraction gratings," Appl. Opt., Vol. 45, No. 20, 4803-4809, 2006. Google Scholar

135. Tan, E. L., "Hybrid-matrix algorithm for rigorous coupled-wave analysis of multilayered diffraction gratings," J. Mod. Opt., Vol. 53, No. 4, 417-428, 2006. Google Scholar

136. Ning, J. and E. L. Tan, "Generalized eigenproblem of hybrid matrix for Bloch-Floquet waves in one-dimensional photonic crystals," J. Opt. Soc. Am. B, Vol. 26, No. 4, 676-683, 2009. Google Scholar

137. Tan, E. L. and Y. W. M. Chia, "Green's function and network analysis of quasi-2D SAW ID-tags," IEEE Ultrasonics Symp., 55-58, San Juan, Puerto Rico, 2000. Google Scholar

138. Tan, E. L., "A robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies," IEEE Trans. Ultrason., Ferroelec., Freq. Contr., Vol. 49, No. 7, 929-936, 2002. Google Scholar

139. Tan, E. L., "A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids," Ultrasonics, Vol. 41, No. 3, 229-236, 2003. Google Scholar

140. Tan, E. L., "Stiffness matrix method with improved efficiency for elastic wave propagation in layered anisotropic media," J. Acoust. Soc. Am., Vol. 118, No. 6, 3400-3403, 2005. Google Scholar

141. Tan, E. L., "Hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media," J. Acoust. Soc. Am., Vol. 119, No. 1, 45-53, 2006. Google Scholar

142. Tan, E. L., "Generalized eigenproblem for acoustic wave propagation in periodically layered anisotropic media," J. Comput. Acoustics, Vol. 16, No. 1, 1-10, 2008. Google Scholar

143. Tan, E. L., "Generalized eigenproblem of hybrid matrix for Floquet wave propagation in one- dimensional phononic crystals with solids and fluids," Ultrasonics, Vol. 50, No. 1, 91-98, 2010. Google Scholar

144. Tan, E. L., "Recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media," Open J. Acoustics, Vol. 1, 27-33, 2011. Google Scholar

145. Tan, E. L., "Simple derivation and proof of geometrical stability criteria for linear two-ports," Microwave Opt. Technol. Lett., Vol. 40, No. 1, 81-83, 2004. Google Scholar

146. Tan, E. L., "Simplified graphical analysis of linear three-port stability," IEE Proc. Microw. Antennas Propag., Vol. 152, No. 4, 209-213, 2005. Google Scholar

147. Tan, E. L., J. Ning, and K. S. Ang, "Geometrical stability criteria for two-port networks in invariant immittance parameters representation," Asia-Pacific Microwave Conf., Hong Kong, 2008. Google Scholar

148. Tan, E. L., "Comments on `Distance from unconditional stability boundary of a two-port network'," IET Microw. Antennas Propag., Vol. 8, No. 1, 64, 2014. Google Scholar

149. Tan, E. L., "Rollett-based single-parameter criteria for unconditional stability of linear two-ports," IEE Proc. Microw. Antennas Propag., Vol. 151, No. 4, 299-302, 2004. Google Scholar

150. Tan, E. L., X. Sun, and K. S. Ang, "Unconditional stability criteria for microwave networks," Progress In Electromagnetics Research Symposium, 1524-1528, Beijing, China, March 23-27, 2009. Google Scholar

151. Tan, E. L., "A Quasi-invariant single-parameter criterion for linear two-port unconditional stability," IEEE Microw. Wireless Compon. Lett., Vol. 14, No. 10, 487-489, 2004. Google Scholar

152. Tan, E. L., "Quasi-invariant single-parameter criterion for unconditional stability: Review and application," Asia-Pacific Microwave Conf., 429-432, Yokohama, 2006. Google Scholar

153. Tan, E. L. and S. Z. Fan, "Graphical analysis of stabilization loss and gains for three-port networks," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 6, 1635-1640, 2012. Google Scholar

154. Tan, E. L. and D. Y. Heh, "Application of Belevitch theorem for pole-zero analysis of microwave filters with transmission lines and lumped elements," IEEE Trans. Microw. Theory Tech., Vol. 66, No. 11, 4669-4676, 2018. Google Scholar

155. Tan, E. L. and D. Y. Heh, "Analysis and determination of microwave filter order," Asia-Pacific Microwave Conf., 1360-1362, Kyoto, 2018. Google Scholar

156. Tan, E. L. and D. Y. Heh, "Pole-zero analysis of microwave filters using contour integration method exploiting right-half plane," Progress In Electromagnetics Research M, Vol. 78, 59-68, 2019. Google Scholar

157. Smunyahirun, R. and E. L. Tan, "Derivation of the most energy-efficient source functions by using calculus of variations," IEEE Trans. Circuits Syst. I: Regul. Pap., Vol. 63, No. 4, 494-502, 2016. Google Scholar

158. Smunyahirun, R. and E. L. Tan, "Optimum lowest input energy for first-order circuits in transient state," Int. Conf. Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, 143-146, Phuket, 2017. Google Scholar

159. Smunyahirun, R. and E. L. Tan, "Most energy-efficient input voltage function for RC delay line," 2018 Joint IEEE Int. Symp. Electromag. Compat. and Asia-Pacific Symp. Electromag. Compat., 1022-1026, Singapore, 2018. Google Scholar

Dr. Eng Leong Tan