Authors: Zhizhang (David) Chen, Junfeng Wang, Jinyan Li
Source: FERMAT, Volume 25, Communication 7, Jan.-Feb., 2018
Abstract: Electromagnetics forms the foundation for electrical and computer engineering(ECE). Therefore, the first-principle solutions to ECE hardware-related problems and issues can be obtained by solving electromagnetic fields which are governed by Maxwell’s equations. Since only few analytical solutions are readily available for structures of regular shapes, numerical methods must be employed; many of them have been developed so far including the popular finite-different time-domain method (FDTD) and finite-element method (FEM). In the past 30 years, thanks to the tremendous increase of computer power, many software packages, based on different numerical methods, have been developed and made available in markets. Still, the challenges in computational memory and efficiency remain, in particular for Multiscale and Multiphysics modeling and simulations.
In this presentation, we provide the summary of the three recent developments pertaining to the time-domain methods for electromagnetic modeling; they are the analytical FDTD solutions, a practical time-reversal method and a unifying nodebased computational platform. The first development gives an in-depth look of the FDTD solution structures in terms of numerical eigen-mode expansions; it presents the ways to achieve multi-scale and multi-grid modeling. The second development allows the effective source locating and possible structure synthesis that avoids false solutions and can be carried out in a large computational domain. The third development shows the possibility of having most of numerical methods under a single mathematical framework and then hybridizing them. These three developments present potential new horizons for efficient and effective numerical modeling of Multi-scale and Multiphysics problems. Numerical examples are given to illustrate the points.
Index Terms: finite-difference time-domain (FDTD) method, finite-element method (FEM), time-domain modeling, eigen modes, multiscale, Multiphysics, time reversal, source reconstructions, node-based meshless methods, unification, hybridization.
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