State-space FDTD implementation of anisotropic perfectly matched layer

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...

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.

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.

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.

The finite difference time domain (FDTD) algorithm has become a popular-technique with which to solve many different electromagnetic problems. However, for real problems the mesh size becomes large and as a result the computation time on a workstation is in the region of tens of hours. In fact, in some cases there will be insufficient memory available on a workstation to solve large problems. We describe a general method based on distributed computing to reduce both the memory requirements and the computation time of the FDTD algorithm. An implementation of the FDTD algorithm on a network of workstations is then evaluated. The implementation is shown to give a peak speed up of 7.5 on a network of 8 workstations over the sequential computation time. >

Graphene, which is considered to be an infinitely thin two-dimension material, is a very promising optoelectronic material and has received much attention due to its outstanding electrical and optical properties. This paper describes an efficient message-passing interface (MPI) parallel implementation of the finite difference time domain (FDTD) algorithm for modeling infinite Graphene sheet simulations. The algorithm, which is based on the domain decomposition approach, reduces the number of field components to be exchanged between the neighboring processors as compared with the conventional parallel MPI FDTD implementation. Numerical simulations are included to show the effectiveness of the proposed parallel algorithm.

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.

In this paper, the well known Finite Difference Time Domain (FDTD) algorithm is utilized to design and analyze a number of planar printed microwave integrated circuits (MICs). Such designs and analyses are based on a developed FDTD computer solver. Prior to the designs, the solver has been validated through comparisons of its computed results with the ones which came from some analyzed structures previously published in other literature, and a good agreement has been observed. The results synthesized by the proposed designs lead to a strong belief that the FDTD is indeed a robust, versatile and powerful algorithm in solving various electromagnetic problems.

A new broadband planar offset antenna is described based on the T-shaped microstrip feeding structure in this paper. This antenna is optimized by the finite difference time domain (FDTD) and genetic algorithms (GA). The results show the impedance bandwidth of this antenna is from 1.864 to 6.643 GHz for S11 les -10 dB (VSWRles2), much higher than that of usual slot patch antenna, the far-filed pattern almost remain the same as that of the T-shaped microstrip feeding antenna

The finite difference time domain method and finite element methods have proven to be highly effective techniques for the full wave analysis of microwave circuits and resonators. The finite difference time domain (FDTD) method is highly efficient, explicit and parallelizable. Finite element methods have been used in the frequency domain and in the time domain using implicit methods. Implicit methods require a solution of a linear system of equations at each time step. For the finite element time domain (FETD) algorithm to be competitive with the FDTD, the number of time iterations required for a simulation must be significantly less. An unconditionally stable FETD algorithm is used. The variational formulation is based on the vector wave equation. Unconditional stability is achieved by using a modified Newmark-Beta time integration technique. In addition, this algorithm is implemented on parallel message passing computers using a finite element tearing and interconnecting scheme. Some numerical examples based on cavity resonator problems are presented to demonstrate the efficiency and accuracy of the method and the parallel efficiency of the algorithm.

With the development of modern precision optical systems, optical detecting system requires the accuracy of wavefront aberration to arrive to sub-nanometer level. When the incident field with polarization information, the polarization information will have a significant impact on the accuracy of measurement results by interacting with polarization-sensitive optical components in the lateral shearing interferometer. We propose the integrated interferometer wavefront sensor (IIWS) system, which is based on the traditional lateral shearing interferometer. This wavefront is sheared by a two-dimension diffraction grating in our system, the two-dimension diffraction grating is the key element to analysis the metrology performance. When using a different grating period and shearing direction, the wavefront shearing and phase shifting with polarization information will produce different error, moreover the impact will vary in the different diffraction orders. In this paper, calculation is based on the finite difference time domain (FDTD) algorithm. When calculation of different polarization state distribution of the incident field, the interaction analysis of shearing phase shifted grating and incidence light play an important role in error analysis. Finally we can get the effect of polarization for grating performance.

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, 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 study investigated the propagation of a mechanical wave in a two-dimensional phononic structure. The influence of material from which metaatom rods were made on the phononical properties of the structure was investigated. Rods made of amorphous Zr55Cu30Ni5Al10 and polypropylenes were compared. The Finite Difference Time Domain (FDTD) algorithm was used to carry out the simulation. Next, theoretical and experimental analysis of the intensity of the mechanical wave was carried out. Frequency response of a regular phononic structure was also analyzed.