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We propose an accurate numerical method to compute the electromagnetic scattering from three-dimensional (3D) arbitrarily shaped objects composed of inhomogeneous and biaxial metamaterials, whose permittivity and permeability are both anisotropic. The basic theory for the numerical method is to set up the linear equations by the method of moments (MOM) with pulse basis functions and point matching. The resulting matrix equation is solved by the conjugate gradient (CG) method combined with the fast Fourier transform (FFT) to reduce the storage requirements and CPU time of the computer. The accuracy of the proposed CG-FFT method has been validated. We have applied the method to investigate scattering by penetrable particles with inhomogeneous and anisotropic permittivity and permeability, which will be important and helpful to analyse the scattering characteristics of metamaterials. Finally, a large 3D gradient-index lens has been investigated by using the proposed method, and the numerical result has a good match to the theoretical prediction. [ABSTRACT FROM AUTHOR]

A novel two-level space volume partition (SVP) algorithm based on the ray-tracing technique is proposed to predict the spatial distribution of the steady-state sound field. The sound space is subdivided into voxels in two levels. The voxels of the level-I are of greater size and comparable to the space walls, and the ray- wall intersection points are calculated based on this level of voxels. Then each level-I voxel is hierarchically subdivided into small voxels of level-lI, the size of which is determined according to the needed solution in the sound field description. The sound field spatial distribution is predicted based on this level of voxels. A three-dimensional energy matrix is set up to memorize the spatial distribution of sound energy. The numbers of the row, column, and layer of the energy matrix are equal to those of the level-!! voxels, namely, each element in the energy matrix corresponds to a level-Il voxel. When a sound ray enters a voxel, its sound energy is calculated and recorded in the corresponding element of the energy matrix. When all the sound rays have been traced over the sound energy spatial distribution in the sound space has been established in the energy matrix. The sound pressure level (SPL) in a certain plane or along a certain line can be calculated and imaged directly from the energy matrix. The novel two-level SVP algorithm can finish the simulation more efficiently than the traditional SVP algorithm. Experiments were performed to measure the SPL in steady-state sound fields, and the results were consistent with the predicted results. [ABSTRACT FROM AUTHOR]

We have proposed a fast algorithm to study the electromagnetic (EM) scattering problems involving three-dimensional dielectric targets with inhomogeneous permittivity and permeability. Based on the volume equivalence principle, coupled volume integral equations are derived for the equivalent electric and magnetic current densities. Such integral equations are then solved using the conjugate gradient method combined with the fast Fourier transform (FFT), where the memory requirement is of the order N - the number of unknowns and the computational complexity is of the order N log N. The accuracy and efficiency of the proposed algorithm are verified by comparing numerical results with analytical results from the Mie series for dielectric spheres. We have applied the algorithm to investigate the EM scattering by small dielectric particles with high permittivity and permeability, which may be important to realize the artificial left-handed materials. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 305–310, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22116 [ABSTRACT FROM AUTHOR]

An acceleration technique to the fast multipole method (FMM) has been proposed to handle large-scale problems of periodic structures in free space with finite sizes based on the accurate sub-entire-domain basis functions. In the proposed algorithm, only nine (or 27) elements in the whole impedance matrix are required to be computed and stored for a two-dimensional (or three-dimensional) periodic structure, and the matrix-vector multiply can be performed efficiently using the combination of fast Fourier transform and FMM. The theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of O(N) with small constants, where N is the total number of unknowns. [ABSTRACT FROM AUTHOR]

Two efficient algorithms are proposed to analyze a large-scale periodic structure with finite size using the sub entire-domain (SED) basis functions and the conjugate-gradient fast Fourier transform (CG-FFT). The SED basis function is defined on the support of each single element of the periodic structure. In a simplified SED (SSED)-CG-FFT algorithm, all elements of the periodic structure share the same SED basis function. As a consequence, SSED-CG-FFT can be performed in the whole periodic structure. However, SSED-CG-FFT becomes less accurate if the gap between two unit elements is very small, where the single SED basis function cannot capture the strong mutual coupling. In order to consider the mutual coupling, an acëurate SED (ASED)-CG-FFT algorithm is proposed. In this algorithm, nine types of SED basis functions are employed to distinguish interior cells, edge cells, and corner cells. As a consequence, ASED-CG-FFT can be performed in all interior cells of the periodic structure. Comparing with the conventional method of moments with subdomain basis functions, the proposed algorithms are more efficient in both the computational complexity and the memory requirement Numerical results are given to test the validity and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

It has been observed that super resolution is possible in the electromagnetic imaging. In the first part of the paper, the possible resolution of image is investigated in the inversion of far-field data using the diffraction tomographic (DT) algorithm, where two cases are considered when the object is in a homogeneous space and in an air-earth half space. The study shows that the resolution of image for inversion of far-field data has been limited theoretically to 0.3536-0.5 wavelength using the DT algorithm in homogeneous-space problems, and it is even worse in half-space problems. If the transmitters and receivers are located in the near-field regime, however, the image resolution is less than 0.25 wavelength, which is the super-resolution phenomenon. In the second part of the paper, the physical reason for the super-resolution phenomenon is investigated using different electromagnetic Inverse scattering methods. The study has demonstrated that the information of evanescent waves in the measurement data and its involvement in inversion algorithms is the main reason for the super resolution. Four inversion algorithms are considered for half-space problems: the OT algorithm, the spatial-domain Born approximation (BA), the Born iterative method (BIM), and the distorted BIM (DBIM). The first two belong to linear inverse scattering, while the last two belong to nonlinear inverse scattering. Further analysis shows that DBIM provides a better super resolution than BIM, and BIM prosides a better super resolution than BA. Numerical simulations validate the above conclusions. [ABSTRACT FROM AUTHOR]

A multilevel algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. The algorithm termed "sparse data fast fourier transform" (SDFFT) is particularly useful for signal processing applications where only part of the k-space is to be computed--regardless of whether it is a regular region like an angular section of the Ewald sphere or it consists of completely arbitrary points scattered in the k-space. In addition, like the various nonuniform fast Fourier transforms, the O(N log N) algorithm can deal with a sparse, nonuniform spatial domain. In this paper, the parabolic reflector antenna problem is studied as an example to demonstrate its use in the computation of far-field patterns due to arbitrary aperture antennas and antenna arrays. The algorithm is also promising for various applications such as back-projection tomography, diffraction tomography, and synthetic aperture radar imaging. [ABSTRACT FROM AUTHOR]

It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while iris much more accurate titan the Bern approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires O(N²) computational load, where N is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy earth. When the buried objects are discretized with uniform rectangular mesh and the Green's functions are extended appropriately, the computational load eau be reduced to O(N log N) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the last ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms. [ABSTRACT FROM AUTHOR]

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many &kcirc; directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single &kcirc; direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

Proposes a diffraction tomographic algorithm for detecting three-dimensional dielectric objects buried in a lossy ground, using electric or magnetic dipoles as transmitter and receiver. Description of electric and magnetic dipole transmitter and receiver; Comparisons of original functions and reconstructed profiles using the approximate generalized Fourier transform; Reconstruction examples to show the validity of the algorithm.

An elliptical invisible cloak is proposed using a coordinate transformation in the elliptical-cylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a nearly circular cloak if the elliptical focus becomes very small. The advantage of the proposed invisibility cloak is that none of the parameters is singular and the changing range of all parameters is relatively small. [ABSTRACT FROM AUTHOR]