Fundamental Implicit FDTD Schemes for Computational Electromagnetics and Educational Mobile Apps (Invited Review)

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 interrelations 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.

Bandpass Unconditionally Stable Ce-Bor-PML Scheme With CNDG Algorithm for Rotational Symmetric Simulation

“…Until now, many implementations have been proposed to improve the efficiency of the ADI algorithm including the leapfrog ADI, the fundamental ADI, etc. [42][43][44]. Within these algorithms, the complex manipulations can be simplified to make the ADI scheme more efficient.…”

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

“…By substituting Equation (8) into Equation (7) after taking the curl, the Helmholtz equation of the double curl of the electric field E can be obtained…”

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Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

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“…This reformulation avoids applications of the discrete operators on the right-hand side leading to an even more efficient scheme. One can directly apply these ideas to the scheme considered here and in [22], since it exhibits the exact same structures exploited in [41,42].…”