Surface Impedance Boundary Condition Research Articles

Advanced Numerical Methods for Graphene Simulation with Equivalent Boundary Conditions: A Review

Since the discovery of graphene, due to its excellent optical, thermal, mechanical and electrical properties, it has a broad application prospect in energy, materials, biomedicine, electromagnetism and other fields. A great quantity of researches on the physical mechanism of graphene has been applied to engineering in electromagnetism and optics. To study the properties of graphene, different kinds of numerical methods such as the mixed finite element method (Mixed FEM), the mixed spectral element method (Mixed SEM), Method of Auxiliary Sources (MAS), discontinuous Galerkin time-domain method (DGTD) and interior penalty discontinuous Galerkin time domain (IPDG) have been developed for simulating the electromagnetic field effects of graphene and equivalent boundary conditions such as impedance transmission boundary condition (ITBC), surface current boundary condition (SCBC), impedance matrix boundary condition (IMBC) and surface impedance boundary condition (SIBC) have been employed to replace graphene in the computational domain. In this work, the numerical methods with equivalent boundary conditions are reviewed, and some examples are provided to illustrate their applicability.

Electromagnetic field computation of multilayer vacuum chambers with physics-informed neural networks

The electromagnetic interaction of a charged particle beam with multilayer vacuum chambers is of particular interest in accelerator physics. This paper presents a deep learning-based approach for calculating electromagnetic fields generated by the beam in infinitely long multilayer vacuum chambers with arbitrary cross section. The presented approach is based on physics-informed neural networks and the surface impedance boundary condition of a multilayer structure derived from the transmission line theory. Deep neural networks (DNNs) are utilized to approximate the solution of partial differential equations (PDEs) describing the physics of electromagnetic fields self-generated by a charged particle beam traveling in a particle accelerator. A residual network is constructed from the output of DNNs, the PDEs and boundary conditions are embedded into the loss function and differential operators are calculated using the automatic differentiation. As a result, the presented approach is regarded to be mesh-free. The approach is applied to circular and elliptical vacuum chambers with a three-layer structure. It is verified in comparison with the recently proposed boundary element method. The effects of chamber geometries and multilayer structure on the beam coupling impedance are demonstrated.

Impedance computation of cryogenic vacuum chambers using boundary element method

A two-dimensional boundary element method for calculating the impedance of infinitely long cryogenic vacuum chambers of general cross section is presented. The formulation is based on combining Kirchhoff's boundary integral representation of an electromagnetic field with the surface impedance boundary condition for the anomalous skin effect, which can occur in metals at cryogenic temperature. As a result, the electromagnetic field in the chamber is expressed as a superposition of the direct and indirect space charge fields and resistive-wall wakefield. This feature allows us to compute the corresponding three impedance contributions separately. This method does not assume a specific transverse charge density such as uniform and Gaussian distributions as well as the ultrarelativistic approximation. A technique for computing the impedances and the form factors in the method is also described. The presented method is applied to circular, rectangular, elliptical, and racetrack-type vacuum chambers. The geometric effect of the cryogenic vacuum chamber cross section on the resistive-wall impedance is shown. The effect of beam velocity is demonstrated for the racetrack-type cryogenic vacuum chamber.

FDTD Simulations of Modulated Metasurfaces with Arbitrarily Shaped Meta-atoms by Surface Impedance Boundary Condition

In this paper, we propose a reduced-complexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells. The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 ××10 wavelengths, using a standard PC with 64GB RAM.

Mode Theory and Propagation of ELF Radio Wave in a Multilayered Oceanic Lithosphere Waveguide

Extremely low-frequency (ELF: below 30 Hz) wave penetration theory in the layered oceanic lithosphere is essential for studying submarine communications. In this article, we investigate the mode theory of ELF wave propagation in a layered oceanic lithosphere waveguide. Based on the real situation of the oceanic lithosphere approximated by the stratified prototype, in which a low-conductivity layer lies between two overlying and underlying high-conductivity regions, a theoretically sound physical model of oceanic lithosphere waveguide is built. The modal equations for transverse magnetic (TM) and transverse electric (TE) polarized guided modes are delivered using surface impedance boundary conditions. By evaluating the reflection coefficients of the upper and lower waveguide boundaries, formulas for the modal equation's roots are derived. Analytical expressions for propagable mode parameters, such as the phase velocity, attenuation rate, excitation factor, and the field strength for different components, are obtained, and the cutoff frequency for high-order modes is given. Computations show that the field component curves exhibit typical peaks and nulls associated with multiple-mode propagation in the waveguide region, with each mode traveling at different phase velocities and attenuation rates. Moreover, it is found that all the high-order modes are evanescent below the cutoff frequency.

Boundary Element Formulation Enforcing High-Order Surface Impedance Boundary Conditions for Axisymmetric Eddy Current Problems

This article presents a boundary element method (BEM) formulation coupled with high-order surface impedance boundary conditions (SIBCs) for axisymmetric eddy current problems. The formulation is based on the perturbation theory (PT) and the reduced magnetic scalar potential. A big advantage of the proposed approach is that if the solution is sought at different frequencies, the boundary integral equations can be solved only once and, then, the fields are easily computed at any frequency using a series expansion according to PT. Three test problems are solved, for which the reference solution is given by the standard finite-element method (FEM). The convergence of BEM-SIBC results toward FEM solution with respect to frequency is verified. The proposed approach requires reduced memory and computational times compared to the standard FEM and can be applied with linear, isotropic, and homogeneous materials.

Research on Fast Algorithm of Radio Wave Propagation in Low-Lossy Obstacles Environment

To predict the propagation of radio waves in the environment of dielectric ground and dielectric obstacles, a new two-way parabolic equation (2W-PE) method based on the domain decomposition principle and surface impedance boundary conditions (SIBC) is proposed. First, we decompose the obstacle area into different subdomains and derive the SIBC in each subdomain in detail; then, the discrete hybrid Fourier transform (DMFT) in the upper subdomain and finite difference (FD) algorithm in the lower subdomain is used to solve 2W-PE combined with SIBC, respectively. After that, we explain the algorithm steps in the process of calculating the total field, compared with the traditional 2W-PE, and then finally introduce the method of moments (MoM) combined with the enhanced discrete complex image (E-DCIM) method for accuracy verification of the new 2W-PE algorithm. The simulation results show that no matter how the obstacle medium parameters change, the results of 2W-PE method proposed in this paper and MoM are always in good agreement, which proves the accuracy of 2W-PE and its superiority in speed. Therefore, this paper provides a reliable and efficient method for solving the problem of radio wave propagation in the presence of obstacles, especially in the case of low-lossy obstacles.

BEM Computation of the Internal Impedance of Air-Core Inductors Enforcing High-Order Surface Impedance Boundary Conditions

The internal impedance of an axisymmetric air-core inductor is computed by the boundary element method (BEM) coupled with high-order surface impedance boundary conditions (SIBCs), which considers the curvature of the cross sections of the conductors. The proposed method is based on the perturbation technique (PT) and provides accurate results in a wide frequency range by solving only once the BEM formulation. A flat spiral air-core inductor is considered as a test case and the finite element method (FEM) without SIBC is used to obtain the reference results.

Chassis Influence on the Exposure Assessment of a Compact EV during WPT Recharging Operations

In this study, the external magnetic field emitted by a wireless power transfer (WPT) system and the internal electric field induced in human body models during recharging operations of a compact electric vehicle (EV) are evaluated. The magneticfield is calculated with a hybrid scheme coupling the boundary element method with the surface impedance boundary conditions in order to fit the multiscale open-boundary characteristics of the problem. A commercial software is then used to perform numerical dosimetry. Specifically, two realistic anatomical models, both in a driving position and in a standing posture, are considered, and the chassis of the EV is modeled either as a currently employed aluminum alloy and as a futuristic carbon fiber composite panel. Aligned and misaligned coil configurations of the WPT system are considered as well. The analysis of the obtained results shows that the International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference levels are exceeded in the driving position, especially for the carbon fiber chassis, whereas the system is compliant with the basic restrictions, at least for the considered scenarios.

Numerical Analysis of a Single-Stage Fast Linear Transformer Driver Using Field-Circuit Coupled Time-Domain Finite Integration Theory

The focus of this paper is numerical analysis on the performance of a newly designed mega-ampere (MA) class single-stage fast linear transformer driver (FLTD) with 24 separate columns in the China Z-pinch driver CZ34. However, the internal structure and media distribution of the FLTD induction cavity is very complicated and the short rise time of the bricks’ discharge current will make spatial discretization much denser, resulting in a dramatic increase in the computational complexity of a 3-D model. In this paper, the electromagnetic (EM) characteristics of the single-stage FLTD with 24-separate columns are investigated based on the time-domain finite integration theory (TD-FIT). The discharge currents of brick capacitors in the circuit model are coupled to the field model as excitations. The grid size of the key components in FLTD cavity are refined by nonuniform grids. To further reduce the number of degrees of freedom (DoFs), the surface impedance boundary condition (SIBC) is used to model good conductors. Measurements and simulation results demonstrate that TD-FIT is effective and accurate in analyzing the EM transients of FLTD. Equivalent inductance of the discharging brick will increase by ~35 nH due to the mutual flux linkage among neighboring bricks when all the 23-bricks are triggered synchronously.

Simulation of induction thermography NDT technique using SIBC

PurposeThis paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing (NDT) technique to reduce the computation time.Design/methodology/approachThe time harmonic electromagnetic problem is expressed in A – ϕ formulation and lightened by using the surface impedance boundary condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved by using surface electromagnetic power density as thermal source.FindingsThe accuracy and the usefulness of the method for the design of the induction thermography NDT technique have been shown with acceptable deviation compared with a full FEM model. It is also observed that at high frequency, when the ratio between the local radius of the conductor and the skin depth is high, a very good accuracy can be obtained with the SIBC methods. At lower frequency, the effect of the curvature of the surface becomes significant. In this case, the use of the Mitzner’s impedance can help to correct the error.Originality/valueThe SIBC can be used for both massive coil and workpieces with open cracks to alleviate 3D FEMs of the coupled electrothermal model. The implementation in matrix form of the coupled electrothermal formulation is given in details. The comparisons with reference analytical solution and full 3D FEM show the accuracy and performance of the method. In the test case presented, the computation time is 6.6 times lower than the classical model.

Efficient analysis of coated object using fast algorithm with surface impedance boundary condition

An effective solution method is proposed to analyze the electromagnetic scattering problem of coated targets, which is based on a novel form of multilevel matrix decomposition algorithm (NFMLMDA). It uses an efficient directional grouping scheme to s

Unstructured PEEC method with the use of surface impedance boundary condition

PurposeThis paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.Design/methodology/approachBecause of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.FindingsThe new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.Research limitations/implicationsThe propagation effects are not taken into account in the proposed formulation.Originality/valueThe formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

Harmonic analysis and reduction of the scattered field from electrically large cloaked metallic cylinders.

In this paper, an analysis of the spectral composition of the scattered field from coated metallic cylinders is performed, focusing particularly on the cloaking of electrically large structures. An expression of the scattering coefficients is derived, considering both a dielectric and a metasurface coating. Modeling the metasurface as a surface impedance boundary condition, the surface impedance, which annuls one harmonic of the scattered field, is formulated in a closed and compact form. Moreover, in the case of cylinders with radius comparable with the wavelength of interest, it is demonstrated that a reduction of the scattering is possible by using a homogeneous metasurface coating, which presents a positive surface reactance. In particular, a reduction of the scattering width of 4 dB is achieved for a cylinder radius of $ a = 0.917{\lambda _0} $a=0.917λ0.

Dispersive FDTD Scheme and Surface Impedance Boundary Condition for Modeling Pulse Propagation in Very Lossy Medium

A dispersive surface impedance boundary condition (SIBC) is implemented in a dispersive finite-difference time-domain (FDTD) scheme to model pulse propagation and scattering from an aquifer, which has high permittivity and high conductivity. A quadratic complex rational function (QCRF) is adopted to model the dispersive media over a wide frequency band for implementing the dispersive FDTD scheme. The proposed method is demonstrated by simulating the operation of ground-penetrating radar (GPR) in detecting water table. Group delay and pulse-broadening parameter (PBP) are defined to analyze the deformation of pulses propagating in a dispersive lossy medium.

Effects of frequency-dependent surface impedance on the vacuum electronic terahertz sources

When the working frequency of vacuum electronic device reaches the terahertz frequency, the ohmic loss has a significant impact on the vacuum electronic device. To study the effect of the ohmic loss on the working characteristic of the vacuum electronic terahertz devices, this paper implements the frequency-dependent surface impedance boundary condition (SIBC) in the 3 dimensional particle in cell code UNIPIC-3D. Conformal mesh is adopted in the code to overcome the staircase error in traditional particle in cell method. By using the surface impedance boundary, we eliminate the need to study the field inside the lossy dielectric objects which require extremely small grid cells for numerical stability. In comparison with constant parameter SIBC, the dispersive SIBC is applicable over a very large frequency bandwidth and over a large range of conductivities. The correctness of the implementation is verified by simulating the lossy resonant cavity and circular waveguide, the simulated power loss is comparable with the theoretical predication. High power vacuum electronic devices of terahertz regime are attracting extensive interests due to their potential applications in science and technologies. The impulse-wave relativistic surface wave oscillator (SWO) and low-voltage continuous-wave planar grating backward wave oscillator (BWO) both made of copper are numerically studied by using UNIPIC-3D and dispersive surface impedance boundary condition. Numerical results show that the strongest field is very close to the slow wave structure where the beam-wave interaction occurs and that terahertz wave generates both in these two devices. The distributed wall loss has a considerable effect on the devices: the output power has a significant decrease and the startup time becomes longer, but the working frequencies of the two devices keep unchanged. To improve the efficiency of relativistic SWO, a resonant reflector is proposed between the diode and the slow wave structure. Numerical results show that the working frequency of the device with a resonant reflector keeps unchanged as the original one, but the output power increases to 60 MW from 41 MW of the original one when the ohmic loss is considered.

FEM and BEM Implementations of a High Order Surface Impedance Boundary Condition for Three-Dimensional Eddy Current Problems

We implement a three-dimensional formulation for eddy current problems based on the reduced magnetic scalar potential enforcing a high order surface impedance boundary condition (SIBC) which takes into account the curvatures of the conductor surface. Based on perturbation theory, the formulation reduces to three Laplace boundary value problems with Neumann boundary conditions and hence can be easily implemented in any existing Finite Element Method (FEM) or Boundary Element Method (BEM) code for the Laplace equation. The appropriate choice of the small parameter in the perturbation approach correctly represents the order of accuracy of the SIBC. The validation is carried out by comparison with full FEM solutions of a canonical test problem and of a more realistic example of a non-destructive testing probe. The validity of the extension of a high order SIBC to lower frequencies is verified and the fields can be obtained at any frequency in the range of interest once the formulation is solved only once.

Analysis of Thin Truncated Cylinder Scatterers Using Incomplete Hankel Functions and Surface Impedance Boundary Conditions

The incomplete Hankel functions (IHFs) are employed to evaluate the scattered field from thin truncated cylinders excited by uniform plane waves or by arbitrarily oriented elemental current sources. Metallic and dielectric lossy structures are modeled by means of impedance boundary conditions (IBCs) including surface curvature effects. The scattering currents, expanded in triangular basis functions, are determined upon solving electrical field integral equations (EFIEs) by means of the point-matching method of moments (MoM). The scattered field is then expressed in closed analytical form in terms of IHFs, thus yielding highly accurate numerical results. Furthermore, accurate IHFs approximants are also derived to reduce the computational burden in the analysis of large electrical structures. The proposed approach is demonstrated in practical applications involving cylindrical dielectric structures used in planar lenses, lossy dielectric cylinders suitable to model cane-like vegetation, as well as polarization rotators featuring multiple stages composed of thin metallic wire arrays.

FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Frequency-Dependent Lossy Multi-Conductor Transmission Lines

A finite-difference time-domain (FDTD) formulation for a uniform frequency-dependent lossy multi-conductor transmission line (MTL) is presented. It is based on a distributed parameter MTL model using partial resistances and partial inductances. In order to consider both skin and proximity effects, the partial internal impedances are computed with a boundary element method (BEM) formulation, enforcing a high-order surface impedance boundary condition (SIBC). The proposed FDTD formulation is numerically validated with two test cases.

Dispersive Contour-Path MNL-FDTD Scheme for Fast Analysis of Waveguide Metamaterials

A semi-implicit dispersive thin-wire finite-difference time-domain (FDTD) scheme is proposed for fast analysis of waveguide metamaterials. The proposed scheme is based on combining the Newmark-beta method with Makinen’s improved thin-wire FDTD model based on the contour-path integral of Maxwell’s equations around a wire corrected with scaling factors and Wait’s surface-impedance boundary condition for thin wires of finite conductivity. Its stability condition is determined by only the two meshes in the transverse plane to the wire axis. This feature allows using larger mesh steps than a wire radius without time step reducing. In order to verify the scheme, we demonstrate four device applications: plasmonic parallel-plate waveguide filled with only positive dielectrics, edge Fabry–Perot resonator, waveguide metatronic high-pass filter, and coaxial-to-waveguide matching with an epsilon-near-zero narrow channel. Its stability, accuracy, and computational efficiency are assessed in comparison with the standard FDTD explicit scheme, analytical solutions, and existing experimental data.