A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.

A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

A perfectly matched layer (PML) absorbing material composed of a uniaxial anisotropic material is presented for the truncation of finite-difference time-domain (FDTD) lattices It is shown that the uniaxial PML material formulation is mathematically equivalent to the perfectly matched layer method published by Berenger (see J Computat Phys, Oct 1994) However, unlike Berenger's technique, the uniaxial PML absorbing medium presented in this paper is based on a Maxwellian formulation Numerical examples demonstrate that the FDTD implementation of the uniaxial PML medium is stable, equal in effectiveness as compared to Berenger's PML medium, while being more computationally efficient

An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices

A novel implementation of perfectly matched layer (PML) media is presented for the termination of FDTD lattices. The implementation is based on the stretched coordinate form of the PML, a recursive convolution, and the use of complex frequency, shifted (CFS) PML parameters. The method, referred to here as the convolutional PML (CPML), offers a number of advantages over the traditional implementations of the PML. Specifically, the application of the CPML is completely independent of the host medium. Thus, no modifications are necessary when applying it to inhomogeneous, lossy, anisotropic, dispersive, or nonlinear media. Secondly, it is shown that the CFS–PML is highly absorptive of evanescent modes and can provide significant memory savings when computing the wave interaction of elongated structures, sharp corners, or low-frequency excitations. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 334–339, 2000.

Convolution PML (CPML): An efficient FDTD implementation of the CFS–PML for arbitrary media

An alternative formulation of the "perfectly matched layer" mesh truncation scheme is introduced. The present scheme is based on using a layer of diagonally anisotropic material to absorb outgoing waves from the computation domain. The material properties can be chosen such that the interface between the absorbing material and free space is reflection-less for all frequencies, polarizations, and angles of incidence. This approach does not involve a modification of Maxwell's equations and is easy to implement in codes that allow the use of anisotropic material properties.

A perfectly matched anisotropic absorber for use as an absorbing boundary condition

Prior to abour 1990, the modeling of electromagnetic engineering systems was primarily implemented using solution techniques for the sinusoidal steady-state Maxwell's equations. Before about 1960, the principal approaches in this area involved closed-form and infinite-series analytical solutions, with numerical results from these analyses obtained using mechanical calculators. After 1960, the increasing availability of programmable electronic digital computers permitted such frequency-domain approaches to rise markedly in sophistication. Researchers were able to take advantage of the capabilities afforded by powerful new high-level programming languages such as Fortran, rapid random-access storage of large arrags of numbers, and computational speeds that were orders of magnitude faster than possible with mechanical calculators. In this period, the principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .

9 – Computational Electromagnetics: The Finite-Difference Time-Domain Method

A non-linear inverse scattering algorithm is presented that uses a local shape function (LSF) approximation to parametrize very strong scatterers in the presence of a transient excitation source. The LSF approximation was presented recently in the context of continuous-wave (CW) excitation and was shown to give good reconstructions of strong scatterers such as metallic objects. It is shown that the local (binary) shape function may be implemented as a volumetric boundary condition in a finite-difference time domain (FDTD) forward scattering solver. The inverse scattering problem is then cast as a non-linear optimization problem where the N-dimensional Frechet derivative of the scattered field is computed as a single backpropagation and correlation using the FDTD forward solver. Connection between the new algorithm and a similar method employing the distorted Born approximation is shown. Computer simulations show that the LSF method employing a FDTD forward solver has superior convergence properties over the corresponding distorted-Born algorithm.

https://iopscience.iop.org/article/10.1088/0266-5611/9/5/005/pdf

Time-domain inverse scattering using the local shape function (LSF) method

Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an efficient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear theory is that it accounts for multiple scattering effects within the scatterers which often give rise to distortions in an image. A new method to invert strong scatterers, such as metallic scatterers, is presented. © 1996 John Wiley & Sons, Inc.

Nonlinear diffraction tomography: The use of inverse scattering for imaging

The authors' previous inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an efficient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear theory is that it accounts for multiple scattering effects within the scatterers which often give rise to distortions in an image. A new method to invert strong scatterers, such as metallic scatterers, is presented. >

Nonlinear diffraction tomography-the use of inverse scattering for imaging

We describe a step-frequency microwave radar imaging system that is suitable for nondestructive evaluation (NDE) and ground-penetrating radar (GPR) applications. The system includes a computer-automated microwave measurement apparatus along with nonlinear inverse scattering imaging algorithms. Through the use of an inverse Fourier transform, the SFR data is transformed into a synthetic time-domain pulse, and imaging algorithms are applied to the time-domain data. A calibration procedure involving the use of calibration targets is described in order to remove pulse distortions due to the effective aperture and dispersive nature of the antennas, as well as those distortions due to connectors, transmission lines, directional couplers and amplifiers. Reconstructions of various metallic and dielectric scattering objects including metallic rods, glass rods and plastic PVC pipes from real measurement data collected in our laboratory are shown.

W.H. Weedon

Papers

A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

Time-domain inverse scattering using the local shape function (LSF) method

Nonlinear diffraction tomography: The use of inverse scattering for imaging

Nonlinear diffraction tomography-the use of inverse scattering for imaging

Step-frequency radar imaging for nondestructive evaluation (NDE) and ground-penetrating radar (GPR) applications