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The implementation and evaluation of a spherical perfectly matched layer (PML) within a Cartesian finite element method context using standard curl-conforming elements is presented in this paper. Results are compared to the long-standing 1st order absorbing boundary condition (ABC) and a new, rigorous implementation of a 2nd order ABC for curl-conforming elements. The 4 and 8 layer spherical PMLs are shown to offer very attractive levels of absorption, with reflections on the order of -60 to -70dB demonstrated. Numerical tests show that the guidelines for Cartesian PML absorbers, in terms of maximum conductivity, also carry over to the spherical PML. The 2nd order ABC is also shown to offer very good performance. Finally, coding issues for both the spherical PML and the analytical ABCs are briefly addressed. Index Terms--Absorbing boundary conditions (ABC), finite element method (FEM), perfectly matched layer (PML).

Hybrid finite element-boundary integral (FE-BI) formulations are widely used for electromagnetic analysis. In such analysis, estimation of the mesh-wide error distribution and global solution quality may be used to drive adaptive refinements. In this paper, an a posteriori error estimator based on the implicit, element residual method is constructed for the cavity FE-BI formulation, with dominant-mode coaxial port excitation. It is based on solving elemental variational boundary value problems of the error, using approximate, localized boundary conditions. Results show that the scheme can be applied to practical problems, yielding significant reductions in computational cost. Index Terms--A posteriori error estimation, adaptive analysis, boundary integral (BI), computational electromagnetics, finite element method (FEM).

Within the finite element method (FEM), there is always an error associated with the solution. Quantifying this error is a very important aspect of FE analysis, since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization, optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost. This paper presents an a posteriori error indicator for time-harmonic, electromagnetic analysis in three dimensions, when using a Galerkin FE approach with curl-conforming elements and including a nonlocal, boundary integral boundary condition as well as a dominant-mode port boundary condition. The error indicator is residual-based, of an explicit nature and constitutes a bound on an error energy measure. The error indicator is evaluated by presenting results relating to common microwave engineering applications, which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm. Index Terms--A posteriori error estimation, adaptive analysis, boundary integral (BI), computational electromagnetics, finite element method (FEM).

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. Index Terms--Base-station exposure, finite element method (FEM), method of moments (MOM), numerical dosimetry, specific absorption rate (SAR), whole-body SAR.

The Fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error. When the kernel is of convolution type, the discrete Fourier transform (DFT) can be used when evaluating the operator equation in the iterative schemes. However, the DFT imposes an artificial periodicity, thus changing the nature of the problem. The effect of this on the solution has been studied and convergence investigated by comparison with a method of moments (MoM) solution. A proposed method of avoiding the periodicity problem has also been studied. The effect of introducing losses in the medium surrounding the scatterer has also been investigated; provided losses are low, there is little effect on the solution.

Some comments are made on the above paper and a typographical error is corrected. Eigenvalue solutions for three-dimensional (3-D) cavities computed using an independently implemented finite-element code using edge-based elements are reported as verification of the tabulated formulas in this paper. The question of 'trivial' eigenvalues is briefly addressed. The extension of the tabulated formulas to diagonally anisotropic media is presented; it is shown to be very straightforward. Such media currently have significant applications as artificial absorbers in finite-element meshes. Index Terms - Artificial absorbers, diagonally anisotropic media, edge-based elements, finite-element method.