Three dimensional finite-difference time-domain slotline analysis on a limited memory personal computer

Ground penetrating radar (GPR) forward is one of the geophysical research directions.Through the forward of geological model,the database of radar model can be enriched and the characteristics of typical geological radar echo images can be understood,which in turn can guide the data interpretation of GPR measured profile,thereby improving the GPR data interpretation level.In this article,the interpolating wavelet scale function by using iterative interpolation method is presented,and the derivative of scale function is used in spatial differentiation of discrete Maxwell equations. The forward modeling formula of GPR based on the interpolation wavelet scale method is derived by using fourth-order Runge-Kutta method (RK4) for calculating the higher time derivative.Compared with the conventional finite difference time domain (FDTD) algorithm based on the central difference method,the interpolation wavelet scale algorithm improves the accuracy of GPR wave equation in both space and time discretization.Firstly,the FDTD algorithm and the interpolation wavelet scale method are applied to the forward modeling of a layered model with analytic solution. Single channel radar data and analytical solution fitting indicate that the interpolation wavelet scale method has higher accuracy than FDTD,with the same mesh generation used.Therefore,auxiliary differential equation perfectly matching layer (ADE-PML) boundary condition is used on an interpolation wavelet scale,and the comparisons between reflection errors obtained using CPML (FDTD),RK4ADE-PML (FDTD),and RK4ADE-PML (interpolating wavelet scales) in a homogeneous medium model show that the absorption effect of RK4ADE-PML (interpolating wavelet scales) is better than the other two absorbing boundaries.Finally,interpolation wavelet scale method,with both UPML,FDTD and RK4ADE-PML loaded,is used for two-dimensional GPR forward modeling,showing good absorption effect for evanescent wave.From all the experimental results,the following conclusions are obtained.1) Using the derivative of the interpolating wavelet scale function instead of central difference schemes for the spatial derivative discretization of Maxwell equations and time derivative calculated using the fourth-order Runge Kutta algorithm,the interpolating wavelet scale algorithm has higher accuracy than regular FDTD algorithm due to the improvement in the spatial and time accuracy of GPR wave equation.2) The best absorption layer parameters of interpolating wavelet scale RK4ADE-PML are selected, when the maximum value of the reflection error is the minimum.The maximum reflection error can reach-93 dB,which increases 20 dB compared with that of UMPL boundary in FDTD algorithm.And the higher simulation accuracy of interpolating wavelet scale algorithm than FDTD algorithm is confirmed after calculating single channel radar data.3) Comparing wave field snapshots of GPR forward modeling,radar pictures from wide-angle method and section method indicates that interpolating wavelet scale RK4ADE-PML reduces reflection error of absorption boundary,improves both spatial and time accuracy,is more effective than UPML boundary in eliminating false reflection of large angle incidence, and has better absorption effect for evanescent wave and low-frequency wave.

Recently, there has been a growing interest in the use of cylindrical transmission lines in a variety of applications. In this paper, the finite difference time domain (FDTD) method is used to calculate the propagation characteristics of cylindrical transmission lines. An efficient two-dimensional (2D) FDTD algorithm is developed by projecting the three-dimensional FDTD cell in the cylindrical coordinates on to the r−φ plane. An effective absorbing boundary condition is employed to truncate the mesh at its outer radial boundary. In addition to a detailed description of the developed 2D-FDTD algorithm, extensive numerical results are derived for different cylindrical transmission lines and compared with data available in the literature. Specifically, the newly proposed cylindrical coplanar waveguide is studied both theoretically and experimentally.

Discusses a computational procedure, based on the finite difference time domain (FDTD) algorithm, for extremely low-frequency (1 Hz) modeling of electromagnetic scattering by buried objects in lossy sedimentary layers under sea water. The FDTD algorithm is found to be accurate for modeling such objects tens of meters away from a constant current dipole source of 1 A in sea water. For validation of the extremely low-frequency and lossy FDTD modeling, the computed FDTD results are compared with those calculated by using integral equation techniques.

In this paper we discuss a low-frequency computational procedure based on the Finite Difference Time Domain (FDTD) algorithm, for numerical modeling of electromagnetic scattering by buried objects in sediment layers under sea water. The FDTD algorithm is found to be accurate for modeling buried objects in sediment layers tens of meters away from a constant current dipole source of 1A in sea water. For validation of the low-frequency FDTD modeling, the computed FDTD results are compared with those calculated by using analytic expressions and integral,equation techniques. In this paper we also present a technique for detecting conductivity anomalies in sediments, e.g., a buried object in sedimentary layers under sea water, by using the neural network approach. The electric field values are used as the inputs to the neural network and the associated conductivities are used as the targets. The neural network is then trained to associate these conductivities and field values. It is shown in this paper...

Cylindrical microwave applicators have been proven to be advantageous in industrial microwave heating applications where heating uniformity is highly desired. When the traditional Cartesian Finite Difference Time Domain (FD-TD) approach is used to analyze a cylindrical structure, staircase boundaries are introduced during the discretization of the outer cylindrical boundaries of the applicator. Computational errors, computational time, and computer memory requirements are increased accordingly. In this paper, a new formulation employing a hybrid Cartesian-cylindrical FD-TD scheme is developed to analyze the performance of cylindrical applicators with rectangular waveguide feeding structures. Numerical results show excellent agreement with those calculated by the traditional staircase FD-TD model with very fine meshes and the commercial software package MAFIA (MAxwell equation solution by Finite Integration Algorithm). Compared with the staircase FD-TD model, the hybrid FD-TD model achieved better computational accuracy with much less computational time and computer memory.

In order to study the parameters of cable coupling characteristics, we calculated the voltage and current distribution at each point of the transmission line numerically. An iterative solution method based on Theory of Multiconductor Transmission Line (MTL) and finite difference time domain (FDTD) is used. Firstly, the appropriate FDTD parameters are selected, and in each iteration step, the voltage and current along the line are calculated using the Finite Difference Time Domain (FDTD) algorithm, and the voltage and current distribution is updated accordingly. When the convergence condition is satisfied, the solution of the transmission line equation is obtained. The main advantage of this method is that the inherent parallel algorithm can reduce the computation time and obtain more detailed numerical values within the line.

A proper dielectric coating can reduce the electromagnetic scattering of the conducting object significantly so that it cannot be detected by the radar. However, when the object contains a thin coating, fine grid size is needed to discretize the thin coating in the conventional finite-difference time-domain (FDTD) algorithm, which increases the amount of memory and computational time significantly. To overcome this dilemma, we present a transformation optics-based FDTD (TO-FDTD) algorithm to accelerate the solution of electromagnetic scattering from objects with thin dielectric coatings. Two kinds of novel TO-FDTD models are proposed in this paper for a coated cylinder and a coated arbitrary polygonal cylinder, respectively. Through coordinate transformation, the size of the object remains unchanged while its thin coating is enlarged to a thicker one, meaning that it can be simulated by the FDTD algorithm with uniform coarse grids instead of fine grids. The transformed material parameters become inhomogeneous and anisotropic in the transformed region, which can be obtained by solving a Jacobian transformation matrix. We then develop a stable FDTD algorithm for solving anisotropic Maxwell’s equations. Bistatic scatterings of coated cylinders and a coated polygonal cylinder are solved by the TO-FDTD algorithm proposed in this paper, respectively. The result of the TO-FDTD algorithm matches well with the exact value and the result of the commercial software Comsol. The computational efficiency and accuracy of the proposed TO-FDTD algorithm are validated by numerical experiments. Numerical results show that the TO-FDTD algorithm has higher computational accuracy than the conventional FDTD algorithm that fails to simulate the absorbing property of the coating, when the same coarse grid size is used in the simulation. Under the same level of accuracy, the proposed TO-FDTD method can improve the computational efficiency by 62-63 times than the conventional FDTD method with fine grids in the simulations in the paper.

In this paper a new compact type of nanosecond high voltage pulse generator, developed for innovative medical treatments, which combines microstrip line technology and microchip laser triggered photoconductive semiconductor switches (PCSS), has been numerically characterized. Two different modeling methodologies have been considered. The first is based on a full wave finite difference time domain (FDTD) analysis. The second approach proposes a circuit model of the generator solved through SPICE simulations. Further, considering the FDTD analysis an appropriate model for the PCSS has been developed. The presented results show a good agreement between the two modeling methodologies and first experimental measurements performed on a generator prototype. Therefore, these outcomes suggest the presented approaches as suitable modeling tools for the development of such kind of innovative devices.

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

As with the number of cancer increases year by year, so it is important to be found and treated earlier. With biological cells and tissues are sensitive to infrared and visible light, cell morphology and physical structure of the optical properties can easily obtain, we can provide theoretical basis for the early diagnosis of cancer by observing the difference of optical properties between normal and cancerous cells. Compared with Mie scattering theory, finite difference time domain (FDTD) algorithm can analyze any complex structure model. In this paper we use mathematical modeling method to establish the single cell mathematical model and with finite difference time domain algorithm to simulate the propagation and scattering of light in the biological cells, you can calculate the scattering of electromagnetic field distribution at anytime and anywhere. With radar cross section (RCS) to measure the results of the scattering characteristics. Due to the difference between normal cells and cancerous cells are embodied in cell shape, size and the refractive index, through the simulation we can get different cell parameters of light scattering information, Find out the cell parameters change the changing rule of the influence on the scattering characteristics and find out change regularity of scattering characteristics. These data can judge very accurate of the cells is normal or cancerous cells.

The general expressions of the finite difference method (FDM) and the finite difference time domain (FDTD) method are obtained for the quasi-static and full wave analysis, respectively. Maxwell's equations are replaced by a set of finite difference equations which are eigenvalue problems in FDTD. The even and odd mode capacitances are presented for various ratios of the widths of microstrip line in the first layer to the thickness of the first layer in two-layer three-coupled microstrip lines on anisotropic substrates in the quasi-static analysis. The effective dielectric constants are obtained for frequency in the full wave analysis and are compared with those of spectral domain method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, the finite difference time domain (FDTD) method is applied to solve the Gross-Pitaevskii (GP) equation. A simple procedure to include the non-linear term of the GP equation in the FDTD algorithm is given and discussed. For validation of the FDTD method, ground state, excited state wavefunctions and energies are computed for various trap potentials and compared to results from other numerical methods. The FDTD method is shown to be suitable and accurate for solving the GP equation.

The Finite-Difference Time-Domain (FDTD) code available at the University of Utah has been used to simulate sintering of ceramics in single and multimode cavities, and many useful results have been reported in literature [1–4]. More detailed and accurate results, specifically around and including the ceramic sample, are often desired to help evaluate the adequacy of the heating procedure. In electrically large multimode cavities, however, computer memory requirements limit the number of the mathematical cells, and the desired resolution is impractical to achieve due to limited computer resources. Therefore, an FDTD algorithm which incorporates multiple-grid regions with variable-grid sizes is required to adequately perform the desired simulations. In this paper we describe the development of a three-dimensional multi-grid FDTD code to help focus a large number of cells around the desired region. Test geometries were solved using a uniform-grid and the developed multi-grid code to help validate the results from the developed code. Results from these comparisons, as well as the results of comparisons between the developed FDTD code and other available variable-grid codes are presented. In addition, results from the simulation of realistic microwave sintering experiments showed improved resolution in critical sites inside the three-dimensional sintering cavity. With the validation of the FDTD code, simulations were performed for electrically large, multimode, microwave sintering cavities to fully demonstrate the advantages of the developed multi-grid FDTD code.

This paper presents an efficient hybrid method consisting of finite-difference time-domain (FDTD) method, transmission line (TL) equations, and a novel time-domain S -parameter cascade (TD-SC) technique, which can be directly applied in time domain for the EMI analysis of transmission line network (TLN) in shielded electronic device excited by ambient electromagnetic wave. The FDTD method combined with an auto mesh generator is utilized to model the shielded structure of an arbitrary electronic device rapidly, and obtain the excitation fields of the TLN exactly. Then, the TD-SC technique based on TL equations, FDTD method, and S parameter of circuits is proposed for the further EMI analysis of the TLN consisting of multistage TLs and circuits. It has the advantage of without modeling the fine structures of TLs and circuits directly. Numerous examinations exhibit that this hybrid method is an efficient method for the EMI analysis of TLN by comparing with a three-dimensional FDTD method. The computation time and memory cost by this hybrid method is much less than that of the FDTD method, because the hybrid method provides a fast way to compute the transient responses on TLN in which the TLs and circuits do not need to be meshed.

본 논문은 유한 차분 시간 영역(FDTD: Finite-Difference Time-Domain)법을 이용하여 낙뢰에 노출된 항공기와 같이 높은 도전성 물질로 구성된 구조체의 간접적 영향 분석을 위한 전자파 해석기법 연구를 수행하였다. 간접적 영향 분석을 위해 사용되는 낙뢰 파형은 매우 낮은 주파수 특성을 가지며, 알루미늄과 탄소섬유복합물질과 같이 높은 도전성 물질들로 구성된 구조체는 매우 짧은 표피 깊이를 가지고 있기 때문에 일반적인 3차원 FDTD법을 이용하여 해석을 수행할 경우, 매우 많은 메모리와 해석시간이 요구된다. 본 연구팀에서는 낙뢰 특성과 높은 도전율을 갖는 구조에 적합한 전자파 해석기법을 개발하였다. 개발된 해석 기법은 2차원 FDTD와 INBC(Impedance Network Boundary Condition) 알고리즘을 적용하였으며, 개발된 해석기법을 이용하여 낙뢰에 노출된 구조체의 간접적 영향을 분석하였다. We perform a electromagnetic analysis method for indirect effects of a high-conductive structure such as an aircraft exposed by lightning, by using the finite-difference time-domain(FDTD) method. The lightning waveform used to analyze indirect effects has low frequency spectrum and high-conductive materials such as aluminum and carbon fiber composite materials have very short skin depths, and thus, it requires large memory and long computation time using conventional three dimensional FDTD analysis method. We develop an efficient electromagnetic analysis method suitable for lightning and high-conductive structures. The developed analysis method is based on two dimensional FDTD and impedance network boundary condition(INBC) algorithms and we investigate the indirect effects on the structures exposed to lightning.