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The matrix form of the reciprocity relationship for the ABCD matrix of a general distributed microwave circuit featuring multiple ports is revisited. The correct reciprocity relationship is used to identify mistakes previously made in the derivation of key relations in the vector-short-open-calibration (VSOC) deembedding methodology, which is commonly used for removing the effect of port discontinuities in the Method-of-Moments-based electronic design automation (EDA) models of microwave circuits, digital interconnects, and other structures. Numerical results demonstrating the impact of the incorrect reciprocity relation on the accuracy of VSOC deembedding are provided.

A methodology for objective empirical comparisons of competitive computational methods for solving bioelectromagnetics problems is presented. The proposed comparison methodology consists of three steps: 1) a problem of interest is identified, models that represent the range of possible model fidelities are chosen, quantities of interest are clearly specified, and precise quantitative measures of computational costs and errors (including when a reliable reference is missing) are defined; 2) multiple methods are used to solve the problem; for each solution, computational costs are measured and errors in the quantities of interest are calculated; and 3) error-versus-cost tradeoffs of the methods are compared. To demonstrate the methodology’s effectiveness, the power absorbed in a human model illuminated by an impressed time-harmonic Hertzian dipole in the ultrahigh-frequency band is computed by solving the problem of interest using three competitive methods [adaptive integral method (AIM), generalized minimal residual fast Fourier transform method, and finite-difference time-domain method], and the methods’ performances are compared. For example, the comparison reveals that for the baseline case of a spherical head phantom, AIM with a surface-based model has 100–300 $\times$ faster solution time for ~5% error or, alternatively, has 2.5–3 $\times$ less error for ~104 s solution time versus the other numerical methods.

A novel lumped-port model is presented to improve the accuracy of integral-equation solvers for extracting network parameters. A small gap region in the domain of analysis is identified as a two-terminal port, and the fields in the gap are linked to the lumped-circuit voltage/current definitions by enforcing the following conditions: 1) The line integrals of the electric field along straight paths in the gap are equal to the port voltage. 2) The current conducted into/out of the gap region is identical and equal in magnitude to the port current. The port model is implemented by modifying the traditional method-of-moments solution to use a novel divergence-conforming testing function at the gap as well as half-basis functions connected across the gap. Numerical results show the proposed model can outperform existing lumped-port models.

An FFT-based algorithm is presented for rapidly post-processing the integral-equation based solution of scattering problems to evaluate the fields at an arbitrary number of nearby points. The proposed algorithm uses a similar approach to the adaptive integral method (AIM) but contends with the fact that the fields are not Galerkin tested with basis functions but instead point tested. It reduces the computational costs compared to the brute-force method, especially when the number of observer points is large.

A computational benchmark suite is presented for quantifying the performance of modern RCS simulations. The suite contains a set of scattering problems that are organized along six dimensions and range from basic to challenging. It also includes reference solutions, performance metrics, and recommended studies that can be used to reveal the strengths and deficiencies of different simulation methods.

The adaptive integral method (AIM) is used to solve the basic, moderate, and hard classes of problems in the Austin Benchmark Suite for Computational Bioelectromagnetics. Performance data, including computational costs and errors, are shown for both fast and efficient simulations run on a supercomputer cluster.

The current versions (v2.3) of AustinMan and AustinWoman anatomical voxel models are presented with the methodology used to generate them from the Visible Human Project's color cross-sectional anatomical images. Both models are freely available online and documented in detail to increase their reproducibility. Visualizations of the models are shown to highlight their complexity.

The dearth of verification, validation, and performance benchmarks is identified as a roadblock to further progress in computational electromagnetics. The necessary ingredients for a useful benchmark suite are an application-specific list of problems, reference solutions, performance (error and computational cost) measures, and online databases publicizing comparisons. Computational cost comparisons are particularly difficult, rare, and important. As a case study, a benchmark suite for comparing existing and future computational bioelectromagnetics methods is developed.

Different types of multiscale problems encountered in classical electromagnetics are discussed. A nomenclature is proposed that is useful for identifying the difficulty of a problem and the suitability of a computational method for solving it.

A fast integral-equation method is used to quantify the performance of UHF-band antennas near high-fidelity anatomical models of the human body. The surface-volume electric-field integral equation pertinent to the analysis is solved by employing triangular and voxel antenna-body meshes. Traditional basis/testing functions are defined throughout the model except at the antenna feed port: A finite-gap port model is used and novel basis/testing functions are introduced at the port to improve input impedance calculations. The computational costs are reduced by using a parallel FFT-accelerated surface-preconditioned iterative solver. The resulting method is used to compare the return loss and radiation pattern of an asymmetric meandered flare dipole antenna in three cases: (i) when it is in free space, (ii) when it is placed next to a homogeneous block body model, and (iii) when it is placed next to AustinMan and AustinWoman anatomical models. The results demonstrate the suitability of the proposed method for assisting the design of wearable antennas.

To aid the design of power- and spectrum-efficient implanted antennas, efficient computational methods that can account for the presence of nearby inhomogeneous and dispersive human tissues are needed. While layered planar or spherical tissue models are often used to represent the antenna environment, the increasing fidelity and availability of anatomical human models can enable site-specific modeling, more accurate analysis, and better designs. Simulating radiation from antennas near/on/in anatomical human models, however, gives rise to large-scale problems as the latest high-fidelity models are composed of over 100 million voxels (J. W. Massey et al., 34th Annu. Conf. Bioelectromagn. Soc., June 2012). Such large problems can be solved by coupling the surface and volume electric-field integral equations and using a preconditioned, parallel FFT-accelerated iterative solver (F. Wei and A. E. Yilmaz, USNC/URSI Rad. Sci. Meet., July 2013). Unlike traditional finite-difference time-domain based methods, this approach (i) does not require the antenna model to conform to a regular grid to avoid staircasing errors and (ii) accurately models complex antennas by using irregular meshes. Moreover, as is the case for integral-equation methods in general, it requires meshing neither free space (to propagate fields) nor an extended computational domain (to truncate the problem with local boundary conditions that approximate the radiation condition); therefore, for antennas outside the body, this approach does not require the region between the antenna and the body to be meshed. For antennas implanted in voxel-based anatomical human models (by removing tissue voxels at the antenna site from the human model and inserting the antenna mesh), however, the method becomes impractical because it requires the transition region between the antenna and human tissues to be meshed such that the mesh conforms to both the irregular (triangular/tetrahedral) antenna mesh and the voxel tissue mesh.

An increasing number of anatomically accurate voxel-based human models, developed from medical images, are becoming available for bioelectromagnetic analysis (J. W. Massey et al, Proc. 34th Annu. Mtg. Bioelectromagn. Soc, June 2012). Because the staircased boundaries in these models limit the accuracy of the numerical analysis, smooth surface-based human models are desired. Although it is relatively simple to extract one organ/tissue from a voxel model and obtain a smoothed surface model by applying a surface construction algorithm (W. Lorensen and H. Cline, Proc. SIGGRAPH, July 1987), the resulting independently processed surfaces are in general not compatible (e.g., they can intersect) and therefore cannot be easily combined to obtain a surface-based human model. Case studies with multilayer spherical head phantoms show that a significant portion of the error in voxel-based models occurs in the outermost layer. Thus, accuracy improvements can be achieved even if only the skin of the human model is smoothed. This, however, gives rise to a different compatibility issue — matching the unstructured, triangulated mesh of the skin to the underlying voxel mesh of the body. In this article, an integral-equation approach is used to circumvent this limitation and benefit from voxel-based models with improved skin.

To support the continuing proliferation of wireless devices that operate near/on/in the human body in the UHF band (0.3-3 GHz), antenna properties (input impedance, radiation patterns, etc.) must be characterized in the presence of human models. In recent years, a significant number of different anatomically accurate high-fidelity human models have been developed for these problems (Massey et al., 34th Annu. Conf. Bioelectromagnetics Society, 2012). With a few exceptions, almost all human models developed to date are based on voxels because the underlying data sets are 2-D medical images, e.g., CT, MRI, and cross-sectional images, and because it is extremely challenging to smooth these models while maintaining their accuracy. Given the difficulty of the problem, it should be expected that voxel-based models will continue to dominate the available human models in the future. As a result, computational methods that are based on regular meshes, such as the finite-difference time-domain (FDTD) and conjugate gradient FFT (CG-FFT) methods, have clear advantages for analyzing scattering from human models; in fact, these methods remain the two most popular approaches in bioelectromagnetics. When antennas must be modeled, however, the classical FDTD and CG-FFT methods constrain the antenna to conform to a regular mesh to avoid significant staircasing errors. Recently, a massively parallel and preconditioned version of the adaptive integral method (AIM) has been used to analyze antennas near human models (F. Wei and A. E. Yilmaz, Int. Conf. on Electromag. in Advanced Applicat., 869-872, 2012). The AIM approach allows irregular meshes to be used when discretizing integral equations because it introduces an auxiliary regular grid to accelerate the method of moments solution. Thus, arbitrarily shaped, located, and oriented antennas can be modeled accurately by using triangular surface and tetrahedral volume meshes when AIM is used. Discretizing voxel-based human models with tetrahedral volume meshes, however, is inefficient. It requires splitting each voxel into five or more tetrahedra and assigning the voxel's material properties to these tetrahedra; this increases the number of elements/unknowns without adding any information on material properties and boundary locations. In this article, the AIM procedure is modified to use mixed basis functions; specifically, voxel-based volume basis functions (rooftops) are used in the human model and triangle-based surface and tetrahedron-based volume basis functions are used in the antenna region. While a single auxiliary grid is used to enclose both the human and antennas models, the remaining AIM parameters (number of auxiliary grid points and the near-zone correction size assigned to the basis functions) are optimized separately for the different types of basis functions. The mixed basis functions are observed to reduce the iterative solution time by a factor of ~5-10.

Interference alignment (IA) is a cooperative transmission technique for the interference channel. This paper describes two testbeds that implement real-time Multiple-input multiple-output (MIMO) IA for a network with three 2-antenna user pairs using software defined radio techniques: a PC-based testbed for rapid prototyping of potential IA protocols and an embedded testbed for evaluating IA under real-world computational constraints. The IA implementations rely on a wired backbone to share global channel state information (CSI) and a shared clock for frequency and timing synchronization. The testbeds are used to demonstrate the viability of IA, and to compare its robustness with several alternative transmission strategies, such as 2 × 2 MIMO TDMA, in terms of sum-rates. Results show that we are able to successfully achieve over-the-air IA in our three-user 2×2 MIMO testbed. The paper highlights key challenges with the practical realization of IA that are encountered while developing the testbed and identifies areas for future research.

The effectiveness of a time-domain differential-equation and a frequency-domain integral-equation solver are contrasted for bioelectromagnetic analysis. The two fundamentally different methods are compared empirically in terms of their accuracy and efficiency for benchmark problems.

Various error norms that can be used to quantify the accuracy of large-scale, high-fidelity bioelectromagnetic simulations are presented. The merits of the norms are highlighted and they are used to compare large-scale benchmark simulations for voxel-based and CAD models of multi-layered spherical head and leg phantoms.

A homogenization model is applied to describe the wave interaction with finite three-dimensional metamaterial objects composed of periodic arrays of magnetodielectric spheres and is validated with full-wave numerical simulations. The homogenization is based on a dipolar model of the inclusions, which is shown to hold even in the case of densely packed arrays once weak forms of spatial dispersion and the full dynamic array coupling are taken into account. The numerical simulations are based on a fast surface-integral equation solver that enables the analysis of scattering from complex piecewise homogeneous objects. We validate the homogenization model by considering electrically large disk- and cube-shaped arrays and quantify the accuracy of the transition from an array of spheres to a homogeneous object as a function of the array size. Simulation results show that the fields scattered from large arrays with up to one thousand spheres and equivalent homogeneous objects agree well, not only far away from the arrays but also near them.