[신간안내] Computational Electrodynamics (the finite difference time - domain method)

Based upon the approximate Crank–Nicolson (CN) algorithms and the higher order (HO) concept, unconditionally stable perfectly matched layer (PML) implementations are proposed for electromagnetic problems in the finite-difference time-domain (FDTD) lattice. The approximate CN algorithms include the CN direct-splitting (CNDS) and CN approximate-factorization-splitting (CNAFS). The proposed schemes take advantage of the approximate CN algorithms in terms of eliminating the Courant–Friedrichs–Levy stability condition and maintaining the computational accuracy. By introducing the HO concept to the PML formulation, the absorbing performance can be enhanced during the simulation. Furthermore, to cope with the existence of half-time-step problems in simulating the anisotropic magnetized plasma, a modified ADE method is proposed at the integer time step. Thus, the modified ADE method can be directly employed in the approximate CN algorithms. Numerical examples and experiments are carried out to demonstrate the effectiveness, efficiency, and performance. Through the results, it can be observed that the computational efficiency and absorbing performance can be significantly improved. Meanwhile, it can be concluded that the CNAFS-PML and CNDS-PML algorithms show higher accuracy and considerable efficiency, respectively, when the time step surpasses far beyond the CFL condition.

Performance Enhanced Crank-Nicolson Boundary Conditions for EM Problems

This paper presents a Monte Carlo model to investigate the single-surface multipactor discharge on a dielectric surface in the presence of RF and dc electric fields. By employing a novel method in the numerical implementation of the secondary-electron emission, the susceptibility diagram is constructed, and beam loading and its power absorption by the multipactor discharge are examined. Meanwhile, the temporal evolution of the multipactor is also studied. The simulation results show clearly that a steady-state multipactor discharge can be built up from a very low density initial electron distribution, and an oscillatory steady state can be achieved when the positive charge, which is left by the emission of secondary electrons, is capable to build a large-enough dc electric field. During the saturation state, the normal electric field and the number of electrons in flight oscillate at twice the RF frequency. The average power absorbed by the multipactor, strongly depending on material parameters, is on the order of 1 % incident power or less. Based on this model, several useful guidelines to prevent or extinguish the multipactor are presented.

Monte Carlo Study of the Single-Surface Multipactor Electron Discharge on a Dielectric

For bandpass simulation of nonreciprocal devices with fine and complex structures, hybrid implicit–explicit (HIE) perfectly matched layer (PML) which is incorporated with the higher order concept and complex envelope (CE) method is proposed in finite-difference time-domain (FDTD) lattice. The proposed implementation shows advantages in terms of efficiency, accuracy, and absorption. The effectiveness is demonstrated through the simulation and measurement of ferrite circulator. Through numerical results, the proposed scheme can obtain considerable efficiency and enhanced absorption. From the measurement results, it can be seen that the proposed scheme impacts entire performance in bandpass nonreciprocal simulation.

Complex Envelope Hybrid Implicit–Explicit Procedure With Enhanced Absorption for Bandpass Nonreciprocal Application

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

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From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

By incorporating the complex envelope (CE) method and the higher order concept, unconditionally stable perfectly matched layer (PML) is proposed based on the Crank–Nicolson approximate-factorization-splitting (CNAFS) algorithm to simulate the bandpass problems in finite-difference time-domain lattice. The proposed algorithm has the advantages of the CNAFS algorithm, higher order PML concept, and CE method in terms of improving efficiency, enhancing absorbing performance, and simulating bandpass problems. A patched antenna model is carried to investigate effectiveness and efficiency.

Complex Envelope Approximate CN-PML Algorithm With Improved Absorption

In order to analyze the scattering properties in multi-radiator problems, the active radar cross section (ARCS) concept is proposed under complex electromagnetic (EM) environments. The corresponding calculation methods and formulation are proposed by incorporating the monostatic radar cross section (RCS) concept with external disturbances. By introducing the phase characteristics into the ARCS concept, the coherent problems can be accurately solved. Through analyzing the external disturbance and the radar waves by employing the finite element method, the coherent and the incoherent characteristics of the external disturbance can be simulated in complex structures. Numerical examples and an experiment are carried out to further demonstrate the effectiveness of the proposed ARCS concept. The results demonstrate that the proposed ARCS concept obtains better universality compared with the existing incoherent multi-radiator formulation. Meanwhile, the ARCS can be identical with the solution which is obtained by the single radar wave. Compared with the existing incoherent methods for external disturbances calculations, the proposed ARCS concept is more rational. Through the experiment, the effectiveness of the calculation method and formulation is further demonstrated and validated.

https://www.mdpi.com/1424-8220/20/12/3371/pdf

ARCS: Active Radar Cross Section for Multi-Radiator Problems in Complex EM Environments

Based on the alternating direction implicit (ADI) procedure, the complex envelope (CE) method, and the higher order (HO) concept, an unconditionally stable performance-enhanced convolutional perfectly matched layer (CPML) is proposed to efficiently simulate bandpass electromagnetic (EM) devices and signals in the finite-difference time-domain (FDTD) lattice. Through the numerical example, the proposed scheme shows the advantages of the unconditionally stable ADI procedure, HO-CPML scheme, and CE method in terms of absorbing performance, computational efficiency, and bandpass EM simulation.

Yongjun Xie

Papers

Performance Enhanced Crank-Nicolson Boundary Conditions for EM Problems

Complex Envelope Approximate CN-PML Algorithm With Improved Absorption

ARCS: Active Radar Cross Section for Multi-Radiator Problems in Complex EM Environments

Performance-Enhanced Complex Envelope ADI-PML for Bandpass EM Simulation

Different implementations of material independent multi-order nearly perfectly matched layers for EM simulations