A numerical absorbing boundary condition for finite difference andfinite element analysis of open periodic structures

In this paper we present a novel approach to deriving local boundary conditions, that can be employed in conjunction with the Finite Difference/Finite Element Methods (FD/FEM) to solve electromagnetic scattering and radiation problems involving periodic structures. The key step in this approach is to derive linear relationships that link the value of the field at a boundary grid point to those at the neighboring points. These linear relationships are identically satisfied not only by all of the propagating Floquet modes but by a few of the leading evanescent ones as well. They can thus be used in lieu of absorbing boundary conditions (ABCs) in place of the usual FD/FEM equations for the boundary points. Guidelines for selecting the orders of the evanescent Floquet modes to be absorbed are given in the paper. The present approach not only provides a simple way to derive an accurate boundary condition for mesh truncation, but also preserves the banded structure of the FD/FEM matrices. The accuracy of the proposed method is verified by using an internal check and by comparing the numerical results with the analytic solution for perfectly conducting strip gratings     

Incremental unknowns preconditioning for solving the Helmholtz equation

An efficient preconditioner is developed for solving the Helmholtz problem in both high and low frequency (wavenumber) regimes. The preconditioner is based on hierarchical unknowns on nested grids, known as incremental unknowns (IU). The motivation for the IU preconditioner is provided by an eigenvalue analysis of a simplified Helmholtz problem. The performance of our preconditioner is tested on the iterative solution of two‐dimensional electromagnetic scattering problems. When compared with other well‐known methods, our technique is shown to often provide a better numerical efficacy and, most importantly, to be more robust. Moreover, for the best performance, the number of IU levels used in the preconditioner should be designed for the coarsest grid to have roughly two points per linear wavelength. This result is consistent with the conventional sampling criteria for wave phenomena in contrast with existing IU applications for solving the Laplace/Poisson problem, where the coarsest grid comprises just one interior point. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Analysis and optimization of waveguide multiapplicator hyperthermiasystems

A method is proposed for determining the excitation coefficients of an antenna array operating in a large rectangular waveguide and used as a hyperthermia system. The excitation coefficients of the array elements are optimized for attaining an improved specific absorption rate (SAR) distribution around a deep-seated tumor. The method is applied to a two-dimensional problem of a piecewise homogeneous post in a waveguide representing a section of the human torso. The array is operating below the cutoff frequency of the dominant mode of the waveguide. Numerical simulations have been performed to check the effectiveness of this approach. The results show that by using the proposed optimization method, SAR distributions can be improved     

Optimal excitation of multiapplicator systems for deep regionalhyperthermia

A method is proposed for determining the excitation amplitudes and phases of the elements of electromagnetic multiapplicator systems for optimizing the specific absorption rate (SAR) distribution around a deep-seated tumor. In this method, the ratio of the power dissipated in the tumor to a weighted summation of the powers supplied to the surrounding regions is optimized. The optimization procedure is combined with a recently proposed effective technique for analysis of various electromagnetic scattering and interaction problems. The general principle is applied to a two-dimensional problem of a piecewise homogeneous cylinder heated by an array of electric current filaments placed outside the cylinder. Numerical simulations are performed to check the effectiveness of the approach. The results demonstrate that using this optimization method, improved SAR distributions can be achieved. The extension to three-dimensional configurations is discussed.     

Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model

A moment solution is presented for the problem of transverse magnetic (TM) scattering from homogeneous dielectric cylinders. The moment solution uses fictitious filamentary currents to simulate both the field scattered by the cylinder and the field inside the cylinder and in turn point-matches the continuity conditions for the tangential components of the electric and magnetic fields across the cylinder surface. The procedure is simple to execute and is general in that cylinders of arbitrary shape and complex permittivity can be handled effectively. Metallic cylinders are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure.     

Dual-Vivaldi wideband nanoantenna with high radiation efficiency over the infrared frequency band

A dual-Vivaldi nanoantenna is proposed to demonstrate the possibility of wideband operation at IR frequencies. The antenna geometry design is guided by the material properties of metals at IR frequencies. According to our numerical results, this nanoantenna has both high radiation efficiency and good impedance-matching properties over a wide frequency band (more than 122%) in the IR frequency band. The design is based on the well-known Vivaldi antenna placed on quartz substrate but operating as a pair instead of a single element. Such a pair of Vivaldi antennas oriented in opposite directions produces the main lobe in the broadside direction (normal to the axes of the antennas) rather than the usual peak gain along the axis (end fire) of a single Vivaldi antenna. The dual-Vivaldi nanoantenna is easy to fabricate in a conventional electron-beam lithography process, and it provides a large number of degrees of freedom, facilitating design for ultra-wideband operation.     

Comparison of residual-stress variation with depth-analysis techniques for the hole-drilling method

Numerous data-analysis techniques have been developed to determine residual-stress information from strain data obtained from the hole-drilling method. The most commonly used technique for data analysis was developed by Rendler and Vigness (which forms the basis of the standard described in ASTM E837-85). A numerical development which was a model of the hole-drilling procedure has been used to determine stress variation with depth. A rigorous finite-element method to specifically analyze stresses in discrete hole increments has been developed. To evaluate these data-analysis techniques, three different computer-simulated stress fields are compared. The stress fields include a uniaxial stress that is constant with depth, a bending stress that varies linearly with depth, and a subsurface stress reversal. (The basis for this comparison is a finite-element developed technique. Its accuracy will be discussed later.) All data-analysis techniques showed excellent agreement for the uniaxial stress constant with depth test case. However, for the other two stress fields, significant discrepancies were apparent. Results are compared and discussed.     

New designs of ultra wide-band communication antennas using agenetic algorithm

The paper investigates new designs of loaded wire antennas with broad-band characteristics. A two-step design procedure is proposed for the design. First, different unloaded antennas configurations are examined with a view to identifying candidates that exhibit the lowest voltage standing wave ratio (VSWR) and highest gain characteristics. Multi-armed antennas with straight wire segments that branch off symmetrically from a central stem are found to be excellent potential candidates. Next, the antenna with the best performance is loaded with resonant tank circuits and a matching network is designed. The loads can enhance the antenna characteristics to yield high gain and low VSWR by modifying the current distribution and can force it to radiate nearer to the horizon in the elevation plane with an almost omnidirectional pattern in the azimuth plane. An efficient optimization procedure based on the genetic algorithm is employed to simultaneously determine the load components, their locations, and the parameters of the matching network. Several examples of four- and eight-arm antennas with bandwidth of 7.5:1 and 15:1 illustrate the effectiveness of the design procedure     

A fast physical optics (FPO) algorithm for high frequency scattering

A novel algorithm referred as the fast physical optics (FPO) for computing the back-scattered field over a range of aspect angles and frequencies is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency scattering regime. The proposed algorithm is, also, directly applicable to fixed angle bistatic configurations and a variety of single scattering formulations. The method comprises two steps. First, a decomposition of the scatterer into subdomains and computation of the pertinent scattering characteristics of each subdomain. Second, interpolation, phase-correction and aggregation of the scattering patterns of the subdomains into the final pattern of the whole body. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT. The proposed method is especially suited for generation of synthetic data for radar imaging simulation.