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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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.

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

Dr. Eng Leong Tan