Currents induced in an anatomically based model of a human forexposure to vertically polarized electromagnetic pulses

The finite-difference time-domain (FDTD) technique is used to calculate the internal fields and the induced current densities in anatomically based models of a human using 5628 or 45024 cubical cells of dimensions 2.62 and 1.31 cm, respectively. A layer of dielectric constant of ε_r=4.2 and having a thickness of 2.62 cm is assumed under the feet to simulate a human wearing rubber-soled shoes. The total induced currents for the various sections of the body and the specific absorptions for several organs are given for two representative electromagnetic pulses. The calculated results for the induced currents are in excellent agreement with the data measured for a human subject. The FDTD method is ideally suited for exact representation of the pulse shapes and offers numerical efficiency to allow detailed modeling of the human body and the various organs     

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the "asymmetry" of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.     

PCB上微带线的电磁耦合时域建模分析方法

基于时域有限差分方法和传输线方程,结合高效网格建模技术,文中提出了一种高效的时域建模算 法,它能有效解决微带线的电磁耦合建模问题,实现空间电磁场与微带线瞬态响应的同步计算。首先,结合经验公 式,计算得到微带线的单位长度分布参数,构建适用于微带线电磁耦合分析的传输线方程。然后,采用时域有限差 分(Finite-Difference Time-Domain, FDTD)方法,结合非均匀网格技术和自动网格生成技术,仿真得到微带线激励场, 并在每个时间步进上引入传输线方程获得等效分布源项。最后,对传输线方程使用FDTD 的中心差分格式进行离 散,实现微带线及其端接电路上瞬态响应的迭代求解。为了验证时域建模算法的正确性和高效性,通过自由空间和 屏蔽腔内PCB 上微带线电磁耦合的数值模拟,从计算精度和耗时两方面与传统FDTD 方法的计算结果进行了对比。     

Development of a multigrid FDTD code for three-dimensionalapplications

Numerical modeling of realistic engineering problems using the finite-difference time-domain (FDTD) technique often requires more detail than is possible when using a uniform-grid FDTD code. We describe the development of a three-dimensional (3-D) multigrid FDTD code that focuses a large number of cells of small dimensions in the region of interest. The detailed solution procedure is described and some test geometries are solved using both a uniform-grid and the developed multigrid FDTD code to validate the results and check the accuracy of the solution. Results from these comparisons as well as comparisons between the new FDTD code and another available multigrid code are presented. In addition, results from the simulation of realistic microwave-sintering experiments in large multimode microwave cavities are given to illustrate the application of the developed method in modeling electrically large geometries. The obtained results show improved resolution in critical sites inside the 3-D multimode sintering cavity while keeping the required computational resources manageable. It is shown that it is possible to simulate the sintering of ceramic samples of 0.318-cm wall thickness in a cylindrical multimode microwave cavity with a diameter of 74 cm and a length of 112 cm using 2.24×10⁶ total FDTD cells. For comparison, a total of 102×10⁶ cells would have been required if a uniform-grid code with the same resolution had been used     

The theory of a singularity-enhanced FDTD method for diagonal metal edges

The complete theory of a singularity-enhanced finite-difference time-domain (FDTD) method for a sharp diagonal metal edge is presented. This method is very accurate and efficient for modeling printed microwave components with diagonal metal edges including some microstrip patch antennas, various other printed antennas, and printed transmission lines. Considering the singular nature of electromagnetic fields at a sharp metal edge, new FDTD equations are derived for all electric and magnetic nodes near the edge, using a contour-path subcell approach. The new FDTD equations for the affected nodes differ from the standard (Yee's) FDTD equations only by a few additional coefficients, for which complete mathematical expressions are given. Application of this method to several antenna and transmission-line problems demonstrated significantly improved accuracy over previous methods, without any noticeable computing overhead. A coarse grid can be used in conjunction with this method and hence the required computer memory and time can be reduced drastically. We have used the maximum allowed time step in all our applications and the method was always stable.     

An FDTD/MoM hybrid technique for modeling complex antennas in thepresence of heterogeneous grounds

Calculating the current distribution and radiation patterns for ground-penetrating radar antennas is a challenging problem because of the complex interaction between the antenna, the ground, and any buried scatterer. Typically, numerical techniques that are well suited for modeling the antennas themselves are not well suited for modeling the heterogeneous grounds, and visa versa. For example the finite-difference time-domain (FDTD) technique is well suited for modeling fields in heterogeneous media, whereas the method of moments (MoM) is well suited for modeling complex antennas in free space. This paper describes a hybrid technique, based upon the equivalence principle, for calculating an antenna's current distribution radiation pattern when the antenna is located near an air-ground interface. The original problem is decomposed into two coupled equivalent problems: one for the antenna geometry and the other for the ground geometry, with field information passing between them via a rapidly converging iterative procedure. The fields in each region may be modeled using numerical techniques best suited to them. Results for several test cases are presented, using FDTD to model the ground problem and MoM for the antenna problem, that demonstrate the accuracy of this hybrid technique     

FDTD calculation of radiation patterns, impedance, and gain for amonopole antenna on a conducting box

The ability of the finite-difference-time-domain (FDTD) method to calculate radiation patterns, input impedance, and gain for a monopole antenna on a conducting box is demonstrated. Results are given for the bare box and with the box coated with a dielectric layer. Radiation patterns are compared with measurements and with the method of moments for the bare box. Radiation patterns for the dielectric-covered box and all impedance and gain results are compared with measurements only. Good agreement is obtained in all cases. The FDTD approach includes a dielectric covering quite easily, while this would be quite difficult for a method of moments approach. The FDTD method requires similar computer time as the method of moments for a single-frequency result, but produces wide-bandwidth impedance and gain results with much less computer time     

FDTD中微带线激励源设置的新方法

ＦＤＴＤ已广泛应用于微带问题的计算中,本文提出了一种新的微带线馈电激励设置方式,同以往的激励设置方法不同,它不仅能计算Ｇａｕｓｓｉａｎ脉冲激励也能计算正弦波激励,计算过程中,源平面无需切换成吸收边界,场区的划分使反射场自然从总场区分离出来。     

A locally conformed finite-difference time-domain algorithm ofmodeling arbitrary shape planar metal strips

A general algorithm for modeling arbitrary shape planar metal strips by the finite-difference-time-domain (FDTD) method is presented. With this method, fields in the entire computation domain are computed by the regular FDTD algorithm except near metal strips, where special techniques proposed herein are applied. Unlike the case for globally conformed finite-difference algorithms, the computation efficiency of the regular FDTD method is maintained while high space-resolution is obtained by this locally conformed finite-difference method. Numerical tests have verified that a higher computation accuracy is achieved by this scheme than by the conventional staircase approximation. The modeling of electrical characteristics of two crossed strip lines is provided as an example     

Modeling good conductors using the finite-difference, time-domaintechnique

Finite-difference, time-domain (FDTD) is based upon the assumption that field behavior between sample points (i.e., cell nodes) is linear; for propagation in lossless or low-loss materials, the assumption of linearity will be valid as long as the number of cells per wavelength is kept above some minimum value. For good conductors, where the wavelength decreases many orders of magnitude from its free-space size, and the fields are decaying exponentially, it becomes impractical to shrink the cell size so as to maintain linearity between cells. When the number of cells per wavelength criterion is violated at a boundary, FDTD will not yield correct estimates of reflection from, or transmission into, that boundary. The work presented details and provides validation for two approaches that can be used to achieve realistic results when modeling good conductors with FDTD using practical cell sizes. These approaches do not require modifications to the FDTD algorithms, and do not affect program execution times. Achieving accurate loss estimates will be of particular interest to those modeling resonant structures using FDTD     

Computation of Electromagnetic Fields in Assemblages of Biological Cells Using a Modified Finite-Difference Time-Domain Scheme

When modeling objects that are small compared with the wavelength, e.g., biological cells at radio frequencies, the standard finite-difference time-domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating a generic lumped-element membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900,1800, and 2450 MHz. This method will facilitate deeper investigation of the phenomena in the interaction between electromagnetic fields and biological systems.     

用时域有限差分法对缝隙渐变天线的瞬态电磁场分析

本文用时域有限差分（ＦＤＴＤ）法分析缝隙渐变天线，分析中对天线缝隙边缘场和薄天线衬底采取了特殊的处理方法，求天线的远区辐射场采用了ＦＤＴＤ中近场到远场的变换方法。本文计算出的缝隙渐变天线的辐射方向图和远区辐射场与实验结果比较一致。本文给出了超短电磁脉冲在天线上传播和辐射过程的瞬态直观图象，同时还研究了这种天线衬底厚度、几何尺寸及介电常数对其辐射特性及频带的影响。     

Experimental and FDTD-computed radiation patterns of cellulartelephones held in slanted operational conditions

The objective of this paper is to investigate, numerically and experimentally, the radiation patterns of various commercial cellular telephones held in a realistically slanted position relative to the head, to understand the performance of such devices for normal use conditions. The investigation has been performed with and without the human head model at an angle of 30° with respect to the vertical. To avoid the stair-step modeling of the cellular telephone for the finite-difference time-domain (FDTD) formulation, the head has instead been tilted forward by 30° and a transformation of coordinates in the FDTD calculation has been used to obtain the desired vertical and horizontal polarizations. We show that the FDTD method gives results that are in good agreement with measurements, both for shape and gain of the radiation patterns, for all of the considered mobile telephones that use several types of antennas. Generally, a decrease of the cellular telephone gain for the vertical component of the field has been observed as compared to the vertical configuration of the telephone and also a decrease in gain is obtained when the phone is held against the human head. Furthermore, it is shown that the FDTD method is capable of providing fairly accurate results even for radiation patterns at a slanted angle and modeling of realistic cellular telephones     

Hybrid FDTD-MPIE method for the simulation of locally inhomogeneous multilayer LTCC structure

A new hybrid finite-difference time-domain (FDTD) and mixed potential integral equation (MPIE) method is proposed for the modeling of multilayer planar circuits with locally inhomogeneous objects. By using equivalence principle, the original problem can be decomposed into two kinds of regions. The FDTD method is employed to model the locally inhomogeneous objects and construct an interaction matrix to be used in the subsequent model coupling procedure. The MPIE method with less singular kernels is applied to model the layered structure with possible perfect electric conductors. The FDTD model and the MPIE model are coupled together by enforcing the continuity of the tangential electric and magnetic fields on the equivalent surface using a Galerkin testing procedure. Numerical results are presented to validate the proposed hybrid FDTD-MPIE method.     

Performance analysis of antennas for hand-held transceivers usingFDTD

The design of antennas for hand-held communications devices depends on the implementation of simulation tools that can accurately model general topologies. The paper presents the analysis of small antennas mounted on hand-held transceivers using the finite-difference time-domain (FDTD) method. The key features of the FDTD implementation are discussed, with particular emphasis placed upon modeling of the source region. The technique is used to predict the gain patterns and broadband input impedance behavior of monopole, planar inverted F, and loop antenna elements mounted on the handset. Effects of the conducting handset chassis, the plastic casing around the device, and lumped elements integrated into the antenna design are illustrated. Experimental results are provided to verify the accuracy of the computational methodology. The concept of antenna diversity is discussed, and key assumptions and expressions are provided that characterize the multipath fading fields. Several computational examples demonstrate the diversity performance of two receiving antennas on a single handset     

Generation of FDTD subcell equations by means of reduced order modeling

Adapted finite-difference time-domain (FDTD) update equations exist for a number of objects that are smaller than the grid step, such as wires and thin slots. We provide a technique that automatically generates new FDTD update equations for small objects. Our presentation focusses on 2D-FDTD. We start from the FDTD equations in a fine grid where the time derivative is not discretised. This yields a large state-space model that is drastically reduced with a reduced order modeling technique. The reduced state-space model is then translated into new FDTD update equations that can be used in an FDTD simulation in the same way as the existing update equations for wires and thin slots. This technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method.     

FDTD Maxwell's equations models for nonlinear electrodynamics andoptics

This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches     

Analysis of the open-ended image NRD guide using FDTD

Simulation is an indispensable means of designing antennas, especially when the evaluation of the antenna characteristics using theoretical analysis is complex or not very accurate. This work proposes an open-ended image nonradiative dielectric (NRD) guide antenna and presents its characteristics obtained using the finite-difference time-domain (FDTD) method. The key features of the FDTD implementation are discussed, particularly the simple and convenient approximate three dimensional modeling of the coaxial feed cable and the excitation probe that were used. The characteristics of the antenna that were determined are the return loss and absolute gain frequency characteristics and the E- and H-plane radiation patterns. Experimental results are used to verify the characteristics obtained using FDTD and are found to be in good agreement.     

Three-dimensional electromagnetic power deposition in tumors usinginterstitial antenna arrays

Interstitial arrays of insulated antennas have shown promise for microwave hyperthermia treatment of deep-seated tumors. Available analytical techniques for predicting the electromagnetic (EM) power deposition of these antennas have been limited to the case of a homogeneous conductive medium surrounding the array. Since tumors and host tissue may differ in their electrical characteristics, it is necessary to consider the impact of this variation in electrical properties and the geometry of the tumor in the calculation of the EM field distribution and power deposition pattern when modeling interstitial antennas. In this paper a three-dimensional model of a tumor of arbitrary shape subjected to the fields of an interstitial antenna array is developed to predict the EM power deposition in an inhomogeneous tumor-tissue medium. The volume integral equation for the imbedded tumor is developed and solved by method of moments. The incident fields are calculated based on the available formulation of interstitial antennas in homogeneous media. The accuracy of the developed computer code was checked by comparing the results from the volume integral approach with the Mie solution for the special case of spherical tumors. Good comparison was obtained for tumors with properties approximately 25 percent different from those of the surrounding tissue. Comparisons of results from models of antenna arrays with and without imbedded tumors show significant differences in their predictions of the EM power deposition in the tumor. Hyperthermia protocols generally specify uniform temperature distribution within the tumor. The developed inhomogeneous model was used to examine the feasibility of controlling the uniformity of the power deposition pattern in large tumors by adjusting the amplitude or relative phase between the array elements. Results are presented to show that a phase lead of +90 degrees or relative amplitude of 4.0 on one antenna in a square array of four antennas could be used to shift the power deposition pattern to sequentially heat outer portions of a 2 cm diameter tumor, thereby achieving a more uniform time-averaged temperature distribution in the tumor.     

网络并行FDTD方法分析电大目标电磁散射

本文应用基于消息传递(Message Passing)模式的网络并行计算系统来实现并行FDTD方法.通过区域分割技术将FDTD计算区域分割成多个子域进行分别计算,各个子区域在边界处与其相邻的子区域进行切向场值的数据交换以使整个迭代进行下去,从而实现FDTD并行计算.我们采用PVM并行平台来实现并行FDTD算法.计算结果表明了本方法的正确性和有效性.