Analysis of GPR Wave Propagation in Complex Underground Structures Using CUDA-Implemented Conformal FDTD Method

In this paper, we summrize the new development of hardware-acceleration techniques and a parallel conformal Finite-Difference Time-Domain (FDTD) method in computational electromagnetics engineering. We investigate the performance of a parallel conformal FDTD method on different hardware platforms, such as Intel and AMD processors, with vector-arithmetic logic unit (VALU) acceleration, a regular PC cluster, a high-performance server cluster, the use of a graphics-processing unit (GPU), and an IBM CELL processor. The FDTD method, which is parallel in nature, is one of the best candidate numerical methods for using multiple-core processors and computer clusters to efficiently simulate various electromagnetic problems. Several representative examples, such as a UWB (ultra-wideband) antenna array and reflector antennas, are employed to demonstrate the engineering applications of the parallel conformal FDTD method.

A finite-difference time-domain method (FDTD) has become an essential tool in the modern engineering and scientific research from RF through THz technology up to optical spectrum. Among many other reasons, it follows from great flexibility as well as competitive computational requirements of the FDTD method when compared to other numerical modeling methods. Nevertheless, market demands are always well ahead of the current computational horizons of the classic FDTD method, prompting development of semi-analytical numerical methods that enable modeling of the most challenging electromagnetic (EM) applications. As an example of those continuing trends, we will recall semi-analytical FDTD solutions for axisymmetrical and periodic structures, both widely addressed in the literature and solvable by the commercial EM simulation tools. It will be shown that a tremendous cut of required computational resources is achievable when the FDTD method is supported by appropriate analytical solutions. Several application examples, like cylindrical corrugated horn antenna, Cassegrain reflectors, photonic crystals and micro-structured telecommunications fibers, will be presented.

In this paper, we present an analysis of electromagnetic environments in indoor offices using Finite Difference Time Domain (FDTD) method with MATLABMPI. The FDTD method is implemented by using MATLAB from The Mathworks, Inc. [3] and a parallel computation algorithm is realized by MATLABMPI [4].

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.

The numerical dispersion is one of the main factors to affect the accuracy of the finite-difference time-domain (FDTD) method. It can be easy to be taken for granted that a smaller time step leads to smaller simulation errors. This paper reveals that smaller time steps do not always make more accurate results in FDTD simulations. We analytically investigated how time steps affect the numerical dispersion of two FDTD methods: the leapfrog FDTD(2,2) method and the FDTD(2,4) method. The investigations in this paper show that in the FDTD(2,2) method, a larger time step limited by the Courant-Friedrichs-Lewy (CFL) condition is more helpful to reduce the numerical dispersion error. However, in the FDTD(2,4) method, as the time step grows, the numerical dispersion error decreases at the beginning and then increases. Several numerical examples are carried out to verify our analysis.

Summary form only given. Modeling an electromagnetic (EM) structure with curved boundaries using a conformal finite-difference time-domain (CFDTD) method retains a second order accuracy while using a staircased FDTD one only gives a first order accuracy. In spite of the advantages to use the CFDTD method in EM simulations, the calculation of surface electric fields is performed by interpolation methods but usually gives unsatisfied results. In this work, a new algorithm being able to accurately determine surface electric fields near a curved surface has been developed and tested. The preliminary benchmark results show convergence that the surface electric fields can be calculated as accurately as higher than 99% using a 160 by 160 grid in 2D. Since the algorithm has been validated in 2D, a 3D counterpart is under development. Accurate determination of surface electric fields in CFDTD simulations is important for a lot of research studies such as surface breakdown, field emission, plasma wall interaction, etc. Detailed algorithm and benchmark results will be presented.

Ground Penetrating Radar (GPR) is a non-destructive tool with a wide varitey applications. Stratigraphy in shallow depth is one of the geotechnical applications of GPR tool. Model has been simulated according to magnetic permeability, dielectric coefficient and resistivity of the medium. The finite difference time domain method (FDTD) has been used to model a stratigraphic section. A hyperbola and its characteristic can be imaged and recognized better by using simulating. The codes for the algorithm used are instructed in MATLAB. A case study is operated and primary processing such as Time zero correction, Dewow and topography applied are discussed. Other processing such as band-pass filtering is applied to decrease random noise and other noises like ringing noise which is caused by antenna coupling effects. The main aim is to derive a final section with higher resolution. Finally a simple time to depth conversion has been conducted at velocity of 0.12 m/ns. The stratigraphic layer in the final section presents distinct electromagnetic properties.

In this book, analysis of electromagnetic (EM) field inside microwave cavities (e.g., oven, autoclave) is presented using finite difference time domain method (FDTD). In this regard, a domestic microwave oven is considered where EM field distribution inside its cavity is determined using FDTD method. Further, the leakage of RF field from the oven door is also estimated at different plane of the door.

We present a time domain hybrid method to realize the fast coupling analysis of transmission lines excited by space electromagnetic fields, in which parallel finite-difference time-domain (FDTD) method, interpolation scheme, and Agrawal model-based transmission line (TL) equations are organically integrated together. Specifically, the Agrawal model is employed to establish the TL equations to describe the coupling effects of space electromagnetic fields on transmission lines. Then, the excitation fields functioning as distribution sources in TL equations are calculated by the parallel FDTD method through using the message passing interface (MPI) library scheme and interpolation scheme. Finally, the TL equations are discretized by the central difference scheme of FDTD and assigned to multiple processors to obtain the transient responses on the terminal loads of these lines. The significant feature of the presented method is embodied in its parallel and synchronous calculations of the space electromagnetic fields and transient responses on the lines. Numerical simulations of ambient wave acting on multi-conductor transmission lines (MTLs), which are located on the PEC ground and in the shielded cavity respectively, are implemented to verify the accuracy and efficiency of the presented method.

To get a better understanding of the Ground penetrating radar (GPR) response, a two dimensional (2-D) finite difference time-domain (FDTD) computational model for underground detection of subsurface layers (concrete and clay) and buried objects (metal bar/strip, water/oil pipe, crack) is presented. For the model, the electromagnetic differential Gaussian pulse is used as the GPR source, the uniaxial perfectly matched layer (UPML) medium is adopted for truncation of the FDTD lattices. The FDTD simulation result of GPR B-scan response is obtain, and the influence of some parameters including buried depth, conductivity and geometry of the object on the characteristic of the back wave the object scattered is discussed.

Maritime communication has been considered as a core issue in the marine activities. However, insufficient knowledge of radio channel characteristics over the sea limits the development of wide-band wireless communication systems for maritime applications. In order to increase understanding of the radio channel over the sea, the modeling of wireless between the UAV and vessels is studied. In this work, a channel-modeling effort using the finite-difference time domain method (FDTD) is conducted to assess the effects of sea surface conditions on the marine communications. Data analysis conducted on the receiving waveform of many receiving points over the sea has produced the path loss characteristic.

There is a very strong link between the behavior of ground penetrating radar (GPR) wave propagation in zinc-contaminated soil and the dielectric properties of soil. This relationship can be of significant use in the practices of quick detecting the degree of pollution in zinc-contaminated soil. In this research, measurements were conducted on the zinc-contaminated soil samples with different soil index properties (i.e., zinc ion concentration, wet density and moisture content). The radar reflection wave data of the common midpoint and common-offset sounding mode were obtained by using the 600 MHz antenna, and the relative permittivity was measured using the vector network analyzer. The attribute analysis of radar reflection wave shows that the wave velocity is affected by wet density and moisture content, but independent of zinc ion concentration. Both the amplitude and the peak frequency decrease with the increase in zinc ion concentration, wet density and moisture content. For the soil dielectric properties, the metal ions can change the conductivity of solution in soil, affecting the imaginary part of relative permittivity, but with little effect on the real part. The positive correlations between the relative permittivity with density and moisture content are caused by the variation of three-phase composition of soil. Besides, the measured soil dielectric properties and the radar reflected wave attributes confirm each other, which can well explain the change rules of electromagnetic wave velocity, amplitude and central frequency. The presented results can increase understanding and confidence on GPR for quantitative monitoring and detecting of zinc-contaminated soil.

Numerical modeling and simulation of ground-penetrating radar (GPR) systems have been recognized as the preferred means of obtaining an understanding of subsurface-scattering mechanisms. Among the techniques used, the finite-difference time-domain (FDTD) method has been distinctly popular due to its versatility in solving problems involving arbitrarily complicated inhomogeneities. In this paper, realistic three-dimensional GPR scenarios are simulated using the FDTD method and the perfectly-matched layer (PML) absorbing boundary conditions. The radar unit, which contains the transmitting and receiving antennas, moves over the ground-air interface on a predetermined path.

The Lorentz–Drude model incorporated Maxwell equations are simulated by using the three-dimensional finite difference time domain (FDTD) method and the method is parallelized on multiple graphics processing units (GPUs) for plasmonics applications. The compute unified device architecture (CUDA) is used for GPU parallelization. The Lorentz–Drude (LD) model is used to simulate the dispersive nature of materials in plasmonics domain and the auxiliary differential equation (ADE) approach is used to make it consistent with time domain Maxwell equations. Different aspects of multiple GPUs for the FDTD method are presented such as comparison of different numbers of GPUs, transfer time in between them, synchronous, and asynchronous passing. It is shown that by using multiple GPUs in parallel fashion, significant reduction in the simulation time can be achieved as compared to the single GPU.

Since the invention of sound diffusers three decades ago a substantial effort has been made to predict the acoustic behaviour of these structures. BEM methods are well established for this purpose after a systematic comparison between simulations and experimental data. Volumetric methods such as finite element methods (FEM) or the finite difference time domain method (FDTD) are not often used, due to their large computational cost. However, near to far field transformations (NFFT) can overcome that problem. Recently some of the authors have shown that the FDTD method is a useful technique to analyse the time domain signature of sound diffusers. In this paper a careful analysis of the performance of diffusers in the time domain (“time spreading”) are reported, opening a new field of research.