David B. Davidson

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.

GPU-Accelerated Method of Moments by Example: Monostatic Scattering

In this paper, we combine and extend two of our previous works to provide a more complete solution for the GPU acceleration of the Method of Moments, using CUDA by NVIDIA. To this end, the formulations of the original 1982 Rao-Wilton-Glisson paper are revisited, and the scattering analysis of a square PEC plate is considered as a simple example. One of the primary contributions of the paper is to serve as a guide for the implementation of other GPU-accelerated computational electromagnetic routines. As such, this provides a background on general-purpose GPU computation, as well as insight into the finer details of the implementation. The results computed compared well with reference values. From a performance point of view, the GPU implementation was found to be significantly faster. The fastest measured speedup for one of the phases of the Method of Moments computations was more than a factor of 140. This translated into a speedup of about a factor of 45, when the entire Method of Moments solution process for the problem was considered.

An introduction to spectral domain method-of-moments formulations

The capacitance per unit length of a microstrip transmission line is obtained using a spectral-domain method-of-moments (MoM) formulation. The paper emphasizes this problem as a teaching tool to introduce students of electromagnetics to this technique. Firstly, the derivation of the spectral-domain Greens function is outlined. Using this, the relevant integral equation is derived to which the Galerkin MoM approach is then applied. The MoM problem is solved in the spectral domain by also transforming the expansion and weighting functions. The inverse Fourier transform is then applied to find the spatial-domain charge distribution, and, hence, capacitance. The issues that arise here - both of selecting how much of the spectrum to include, and how to choose the number of integration points - are discussed, and the results of typical numerical experiments are presented. The time required to compute the elements of the immittance matrix is shown to be 0(N/sup 3/); the use of translational symmetry (and thus Toeplitz matrix structure) to reduce this is outlined. Classroom experience with this material is discussed. Finally, a hybrid spectral/spatial-domain formulation, introducing asymptotics, is outlined to accelerate the evaluation of the immittance matrix.

Scattering and absorption by thin metal wires in rectangular waveguide-FDTD simulation and physical experiments

The high-frequency internal impedance model of a round ohmic conductor is incorporated into the subcell thin-wire formulation of the finite-difference time-domain method to model the microwave properties of metal wires. For magnetic metals, such as steel, an effective conductivity is introduced to account for the increase in ohmic loss due to the high-frequency permeability. Physical experiments with half-wave resonant copper- and steel-wire inclusions, supported by a dielectric slab in a standard S-band rectangular waveguide, support the formulation.

Rigorous, Auxiliary Variable-Based Implementation of a Second-Order ABC for the Vector FEM

The finite element method (FEM) is commonly used for electromagnetic radiation and scattering analysis. When an infinite, free space exterior domain needs to be incorporated into the method, a radiation boundary condition must be enforced. An approach which has received considerable attention, is to employ approximate conditions, known as absorbing boundary conditions (ABCs), that preserve the sparsity of the original FEM system upon discretization. In the case of time-harmonic analysis based on the vector wave equation in three dimensions, the symmetric, spherical Bayliss-Turkel-type ABCs of first- and second-orders are well-established. The second-order version is expected to be more accurate, however when using the standard curl-conforming approach to FEM discretization, an implementation difficulty is encountered, relating to successive derivatives being required of the nonconforming field components. This issue is addressed here by introducing a scheme where the nonconforming first-order derivatives are projected onto a suitably conforming auxiliary field, of which another derivative can then be taken instead. Additional computational costs are minimal and the scheme retains the symmetry of the standard formulation. Numerical results demonstrate the superior performance of the rigorously implemented second-order ABC over its first-order counterpart

Accurate Beam Prediction Through Characteristic Basis Function Patterns for the MeerKAT/SKA Radio Telescope Antenna

A novel beam expansion method is presented that requires employing only a few Characteristic Basis Function Patterns (CBFPs) for the accurate prediction of antenna beam patterns. The method is applied to a proposed design of the MeerKAT/SKA radio telescope, whose antenna geometry is subject to small deformations caused by mechanical or gravitational forces. The resulting deformed pattern, which is affected in a nonlinear fashion by these deformations is then sampled in a few directions only after which the interpolatory CBFPs accurately predict the entire beam shape (beam calibration). The procedure for generating a set of CBFPs—and determining their expansion coefficients using a few reference point sources in the sky—is explained, and the error of the final predicted pattern relative to the actual pattern is examined. The proposed method shows excellent beam prediction capabilities, which is an important step forward towards the development of efficient beam calibration methods for future imaging antenna systems.

Recent progress on the antenna simulation program FEKO

This paper describes recent progress with FEKO, an antenna simulation program. FEKO uses the method of moments (MoM), and also offers users a hybrid MoM/physical optics for suitable electrically large problems. Current work on UTD hybridisation is outlined, as well as work on the pre- and post-processors. The performance of FEKO in high-performance computing environments is discussed. The incorporation of a rigorous stratified media treatment is reviewed and current plans for FEM hybridisation briefly outlined.

A parallel processing tutorial

An overview of parallel computing is provided, with reference to numerical analysis and, in particular, to computational electromagnetics. The history of parallelism is reviewed, and the general principles are provided. The two main types of parallelism encountered, pipelining and replication are discussed, and an example of each is described. A parallel algorithm for forming a matrix-vector product is presented and analyzed. This is then used as the core of a parallel conjugate gradient algorithm. The theoretically predicted efficiency and the measured efficiency are compared. A glossary and a brief discussion of the available literature on parallel processing are included.<<ETX>>

Numerical Evaluation of High-Order Finite Element Time Domain Formulations in Electromagnetics

This paper compares three full-wave finite-element time-domain (FETD) formulations. The first is based on the vector wave equation; the others on Maxwells equations, viz. the EBHD formulation that discretizes E rarr, B rarr, H rarr and Drarr and the EB formulation that discretizes only E rarr and B rarr. The latter two formulations use a combination of 1- and 2-form discretization to avoid an auxiliary mesh. A novel method for making the EBHD formulation operational is presented. Conditions for finite-difference time-domain (FDTD)-like explicit operation are discussed. The formulations are compared numerically by solving a three-dimensional cavity and a rectangular waveguide using high-order field representations up to mixed fourth order. The error balance between time integration and field representation is investigated. Difficulties in making the EBHD formulation operational which have not previously been addressed in the literature are discussed and worked around. Novel numerical results show that the EBHD formulation has serious performance limitations.

The role of chirality and resonance in synthetic microwave absorbers.

Summary Microwave absorption by a lossy dielectric material containing thin metal wires is considered. The wires are bent to create either chiral, non-chiral or racemic unit cells. No physical mechanism is found to support patents which were granted between 1990 and 1993, and related claims in the engineering literature, that chirality is the key to improved microwave absorbers. Instead, in synthetic composites which employ thin metal wires in a lossy dielectric host, half-wave resonance of the inclusions – not their geometric shape – is identified as the mechanism responsible for enhanced absorption. It is also found that – even in an essentially lossless host – resonant steel wires, whether chiral or not, can strongly absorb electromagnetic waves.