Scattered Field Formulation Research Articles

RCS SCATTERING ANALYSIS USING THE THREE-DIMENSIONAL MRTD SCHEME

A three-dimensional electromagnetic scattering model based on the multiresolution time-domain (MRTD) scheme is presented, in which we apply an anisotropic perfectly matched layer absorber for open boundary truncation to the MRTD scattering analysis. With use of an initial-condition excitation technique based on a pair of one-dimensional MRTD update equations, we develop an MRTD near-to-far-zone field transform to derive the scattered fields. We also adopt the pure scattered field formulation in order to obtain effective incident and scattered fields. With applications of the MRTD scheme, we construct the surface equivalent currents in the near field region and further derive the radar cross section (RCS) in the far-zone region for different scattering targets including perfectly electric conductors, lossless, and lossy dielectric targets. We show that the results derived from the MRTD scheme are in good agreement with those of the finite-difference time-domain (FDTD) method as well as the method of moments (MoM), while the MRTD scheme requires much less computer memory and CPU time for the same level of accuracy.

An effective algorithm for implementing perfectly matched layers in time-domain finite-element simulation of open-region EM problems

An algorithm is presented to implement perfectly matched layers (PMLs) for the time-domain finite-element (TDFE) simulation of two-dimensional open-region electromagnetic scattering and radiation problems. The proposed algorithm is based on the TDFE solution of a special vector wave equation similar to the one in an anisotropic and dispersive medium. The impact of the PML on the stability of the resultant TDFE solution is studied for a variety of temporal discretization schemes, and it is shown that the proposed algorithm for implementing PML can support unconditionally stable TDFE schemes. Both the total- and the scattered-field formulations are described, and numerical simulations of radiation and scattering problems are presented to validate the proposed PML algorithm for the mesh truncation of the TDFE solution.

Applications of the PSTD for scattering analysis

In this paper, we apply a pseudospectral time domain (PSTD) algorithm for calculation of the radar cross section of three-dimensional scattering objects. For the purpose of exciting an incident wave without leading to unwanted Gibbs' phenomenon, we utilize an initial condition-excitation technique. Meanwhile, we adopt the pure scattered field formulation to surmount a difficulty of introducing the incident field into computational space. In addition to accommodating a PSTD near-to-far-zone field transform for far-field computations in the algorithm, we develop a one-dimensional memory-saving storage technique for efficient truncation of computational boundary.

Hybrid PSTD‐FDTD technique for scattering analysis

AbstractThis paper employs a hybrid method that combines the pseudo‐spectral time‐domain (PSTD) algorithm and the finite‐difference–time‐domain (FDTD) method to analyze the scattering problems involving fine structures. In principle, the PSTD is applied in a direction with low‐density variation of structures but large computation volume, whereas the FDTD is used in other directions with high‐density variation and relatively small computation dimensions. In implementation of this hybrid algorithm, the pure scattered‐field formulation is utilized to introduce the incident wave, and a hybrid near‐to‐far‐zone field transform is developed for calculating the scattering width (SW) of the targets. The hybrid method is illustrated by analyzing two canonical scattering targets: a thin dielectric slab and a conductor‐backed dielectric slab. It is observed that the proposed algorithm is very accurate and efficient compared to the FDTD calculations for the same cases investigated. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 19–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10361

Plane wave scattering from frequency-selective surfaces by the finite-element method

This paper presents the application of the finite-element method (FEM) to the analysis of reflection and transmission coefficients, effective permittivity, and permeability of periodic structures to incident plane waves. The problem domain is reduced to a unit cell by using linked boundary conditions (LBCs) and the accuracy and efficiency of the procedure is improved by using the scattered field formulation and perfectly matched layers (PMLs). Examples of the analysis of frequency-selective surfaces (FSSs) derived from photonic bandgap materials (PBGs) and composite materials with negative effective permeability and permittivity are presented.

Analysis of optical waveguide structures by use of a combined finite-difference/finite-difference time-domain method.

We present a method for full-wave characterization of optical waveguide structures. The method computes mode-propagation constants and cross-sectional field profiles from a straight forward discretization of Maxwell's equations. These modes are directly excited in a three-dimensional finite-difference time-domain simulation to obtain optical field transmission and reflection coefficients for arbitrary waveguide discontinuities. The implementation uses the perfectly-matched-layer technique to absorb both guided modes and radiated fields. A scattered-field formulation is also utilized to allow accurate determination of weak scattered-field strengths. Individual three-dimensional waveguide sections are cascaded by S-parameter analysis. A complete 10(4)-section Bragg resonator is successfully simulated with the method.

Optimal FEM solutions of one-dimensional EM problems

Simple basis functions for weak and strong one-dimensional FEM formulations are proposed. These functions are of arbitrary order, of hierarhical type, and are not node based. They also satisfy automatically continuity conditions on the boundaries between elements and on medium discontinuities, for both the total field and (partial) scattered field formulations. The functions are applied in six different formulations of the FEM solution of a plane-wave propagation in (continuously and/or discontinuously) inhomogeneous medium. The error of the results is shown against the number of unknowns, for the order of elements ranging from 1 to 14. It is shown that all six formulations yield very accurate results, and that, with respect to the number of unknowns, entire-domain approximations (i.e. elements of higher order) are optimal. Copyright © 2001 John Wiley & Sons, Ltd.

Low Frequency Finite Difference Time Domain (FDTD) for Modeling of Induced Fields in Humans Close to Line Sources

The implementation of a low frequency line source as a source function in the finite difference time domain (FDTD) method is presented. The total–scattered field formulation is employed, along with a recently developed quasi-static formulation of the FDTD. Line-source modeling is important in the utility industry, where a more accurate prediction of the fields induced in workers in close proximity to power lines is required. The line-source representation is verified, and excellent agreement with analytic solutions is found for two object problems. A practical example of the electric fields and current densities induced in a human body in close proximity to a 60-Hz transmission line is evaluated. The results for predicted organ dosimetry for such a configuration are compared with predictions for the uniform electric field and demonstrate the induced fields and current densities can be significantly higher than originally predicted for the uniform electric field exposure on a ground plane.

Comparison study of the PSTD and FDTD methods for scattering analysis

This paper makes a comparison study by using both the pseudospectral time-domain (PSTD) and finite-difference time-domain (FDTD) methods for a two-dimensional (2-D) scattering analysis. The time-domain incident plane-wave pulse used in the PSTD technique is herewith simulated with an initial-condition excitation technique to eliminate the unwanted Gibbs phenomenon. The pure scattered-field formulation is utilized to surmount the difficulty of generation of the incident field, and a PSTD near-to-far-zone field transform is developed for the analysis of the scattering width (SW) of targets. It is found that the PSTD computed results agree well with those derived from the FDTD method, while the PSTD requires much less computational space and CPU time. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 220–226, 2000.

Characteristic-Based Finite-Volume Time-Domain Method for Scattering by Coated Objects

The characteristic-based finite-volume time-domain method is applied to analyze the scattering from conducting objects coated with lossy dielectric materials. Based on the characteristic-based finite-volume scheme, two numerical strategies are developed to model the electromagnetic propagation across different dielectric media. One introduces a connecting boundary to separate the total-field region from the scattered-field region. The other employs the scattered field formulation throughout the computational domain. These two strategies are verified by numerical experiments to be basically equivalent. A numerical procedure compatible with the finite-volume scheme is developed to guarantee the continuity of the tangential electric and magnetic fields at the dielectric interface. Rigorous boundary conditions for all the field components are formulated on the surface of the perfect electric conducting (PEC) objects. The numerical accuracy of the proposed technique has been validated by comparison with theoretical results.

MRTD electromagnetic scattering analysis

In this paper, we have developed a multiresolution time-domain (MRTD) scheme to analyze two-dimensional (2-D) scattering objects with comparison to the corresponding finite-difference time-domain (FDTD) method. We have applied an anisotropic perfectly matched layer (APML) absorber for open boundary truncation in the content of the MRTD scattering analysis. In addition, we have constructed an MRTD time-domain incident plane-wave pulse, and have developed an MRTD near-to-far-zone transform to evaluate scattered fields. In order to obtain effectively incident and scattered fields, we have adopted the pure scattered-field formulation in this research. To validate the developed MRTD approach, we have analyzed the scattering widths (SWs) for perfect electric conducting (PEC) and dielectric cylinders. We observed good agreement between the results derived from the MRTD and FDTD, while the MRTD scheme requires much less computer memory and computational time with the same level of accuracy. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 189–195, 2001.

A pseudospectral method for time-domain computation of electromagnetic scattering by bodies of revolution

We present a multidomain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In the BOR formulation of the Maxwell equations, the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r,z) plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution. A modified matched-layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time-domain boundary conditions along edges. Numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis-symmetric objects, including spheres, cone-spheres, and finite cylinders, is compared with results from the literature, illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods. To emphasize the versatility of the presented framework, we compute plane wave scattering by a missile and find satisfactory agreement with method-of-moment (MoM) computations.

A Parallel Finite-Volume Runge–Kutta Algorithm for Electromagnetic Scattering

A 3D explicit finite volume algorithm has been developed to simulate scattering from complex geometries on parallel computers using structured body conformal curvilinear grids. Most simulations for practical 3D geometries require a large number of grid points for adequate spatial resolution making them suitable to parallel computation. The simulations have been carried out using a multi-block/zonal approach in the message passing paradigm on the SP-2. Each zone is placed on a separate processor and inter-processor communication is carried out using the Message Passing Library/Interface (MPL/MPI). Integration of Maxwell's equations is performed using the four-stage Runge–Kutta time integration method on a dual grid. This method of integrating on a staggered grid gives enhanced dissipative and dispersive characteristics. A scattered field formulation has been used and the Liao boundary condition is used at the outer nonreflecting boundary. The far zone transformation has also been implemented efficiently, using specialized MPL functions to evaluate the far zone scattering results. Results show extremely good comparisons for scattering from the sphere and the ogive with the exact solution and standard FDTD type algorithms. Comparisons for nonaxisymmetric targets like the NASA almond with experimental data has also been found to be extremely good.

Time-Domain Electromagnetic Scattering Simulations on Multicomputers

A series of bistatic radar cross sections of a perfectly conducting sphere over a frequency range were processed on one shared and three distributed memory computers. A comparative study was conducted for both the total field and the scattered field formulations. The accuracy criteria for the grid point density per wavelength and the placement of the truncated far-field boundary were also established for the present characteristic-based finite volume scheme. The numerical accuracy of all simulations has been validated with theoretical results.

Finite difference time domain analysis of arbitrarily biased magnetized ferrites

The finite difference time domain method is extended to include three‐dimensional propagation in a saturated magnetized ferrite with an arbitrary direction of the biasing field. The recursive convolution method is used to include the frequency dependence of the ferrite. Both total and scattered field formulations are developed. This approach requires the additional storage of at most three complex numbers per cell. Transient scattering in two and three dimensions is used to demonstrate the accuracy of this approach.

EM Scattering Using Nonuniform Mesh FDTD, PML and Mur's ABC

ABSTRACT In this paper, techniques are presented to extend FDTD, PML and Mur's second order ABC to the non-uniform mesh case for scattering problems from a consideration of improving the efficiency of computer codes to run on parallel computers. An alternative method to obtain the space derivatives in non-uniform mesh FDTD and non-uniform mesh PML ABC is presented which provides a second order accuracy. Mur's second order ABC has also been extended to the non-uniform mesh case with a First order accuracy which is an improvement over an existing method. A method of extending the pure scattered-field formulation to the PML medium is described. The electric fields inside a single layer dielectric sphere as well as a three layer dielectric sphere illuminated by a sinusoidal uniform plane wave have been computed which compare well with the results from an exact formulation.

Error in the finite element discretization of the scalar Helmholtz equation over electrically large regions

Discretization error arising from a finite element solution of the scalar Helmholtz equation for open-region geometries is studied for the simple case of scattering from dielectric slabs. In electrically large homogeneous regions, the primary source of error is found to be phase error that increases progressively in a direction away from the boundary where the excitation is coupled into the computational domain. The error can be reduced by using smaller cell sizes, using higher order polynomial basis functions, or using a modified scattered field formulation that couples the excitation into the equation in a different manner. Since the scattered field formulation locates the phase reference within the scatterer, that formulation is likely to produce more accurate numerical solutions in the immediate vicinity of the scatterer than the total field formulation, especially if the scatterer is far from the boundaries of the computational domain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>