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This paper compares three full-wave finite-element time-domain (FETD) formulations. The first is based on the vector wave equation; the others on Maxwell's equations, viz. the EBHD formulation that discretizes E→, B→, H→ and D→ and the EB formulation that discretizes only E→ and B→. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The implementation of a recent new hybrid integral- equation/vector finite-element method formulation applicable to inhomogeneous obstacle scattering in hollow waveguide, requiring discretization just of the obstacle, is presented. The integral equation links the given incident modes with the discontinuity-surface electric and magnetic fields. The finite-element equation is expressed in terms of the entire magnetic and surface electric field of the obstacle. Compatible vector finite-element basis function expansions are inserted, resulting in a pair of matrix equations soluble for the unknown electric and magnetic basis coefficients. Corresponding two-port scattering parameters are further derived. Test cases of posts in the TE10 waveguide, with details of the matrix constructions, are described. Numerical results verified against an established commercial code are given. The ability to model inhomogeneous, lossy, and multiple scatterers is demonstrated. [ABSTRACT FROM AUTHOR]

When using the finite element method, computational efficiency may be improved by using higher order elements. Typical 2-D triangular rectilinear elements cannot exactly model curved geometries, negating the advantage of higher order elements when such geometries are modeled. Curvilinear elements can be applied to such problems, and have significantly better computational efficiency than rectilinear elements when higher order elements are used. Results are shown for elemental basis orders ranging from CT/LN through full fifth order in rectilinear and curvilinear domains. [ABSTRACT FROM AUTHOR]

Hybrid finite element-boundary integral (FE-RI) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A key ingredient of finite-element analysis programs is the linear-algebra solver, typically either a linear-system solver or an eigensolver. The first part of this paper tries to justify why it is important to have recourse to publicly available software for addressing this part of the computation. A number of libraries are mentioned as successful examples that exhibit a series of desirable qualities. Although some of these libraries force the programmer to somewhat change the programming style and may be difficult to learn, the benefits usually pay off the extra effort. The second part of the paper describes one of these libraries in some detail, namely SLEPc, the Scalable Library for Eigenvalue Problem Computations, which is used to illustrate the benefits of modern software paradigms for scientific and engineering computing. [ABSTRACT FROM AUTHOR]

This paper relates to p -adaptive algorithms for the three-dimensional, full-wave,time-harmonic, electric field Galerkin procedure finite element method, using mixed- and/or complete-order elements. A quasi-static electric field condition for enhancing the performance of such algorithms is proposed. The condition is used to distinguish between mixed- and complete-order upgrades. A p -adaptive algorithm, driven by an explicit, residual-based error indicator, is presented. Within this algorithm, the effectiveness of the quasi-static condition is evaluated numerically by considering three common microwave engineering structures. [ABSTRACT FROM AUTHOR]

Recently proposed vector finite elements are compared to previously published elements, and independently implemented and validated in the context of rectangular waveguide analysis. Both mixed-order and full-order elements up to order two are considered. The use of quadrature (cubature) to evaluate the finite element system matrices is discussed. Details of some analytical work required before quadrature is applied are presented for several types of basis functions. For many RF applications, mixed-order elements offer optimal accuracy for a given number of degrees of freedom, and an empty ("through") waveguide solution verifies this, with similar convergence rates for mixed- and full-order elements of the same order. However, a capacitive iris in rectangular waveguide, with a solution dominated by the quasi-static electric field, motivates the use of full-order elements in such cases. Results for the electric fields in the vicinity of the iris also demonstrate the enhanced accuracy of the full-order elements here. This is further illustrated using a dielectric load in a waveguide, where complete order elements produce a better approximation of the normal jump discontinuity. Although this paper addresses guided wave problems, the results are also applicable to radiation and scattering problems. [ABSTRACT FROM AUTHOR]

The Finite-Element Method has become a common tool in the computational electromagneticist's toolbox over the past decade. During the decade of the 1990s, the method has evolved from an interesting approach with great promise for modeling structures that are difficult to model using competing methods, such as integral equation-based approaches, to a mainstream, commercially viable design tool. Although there are a number of excellent commercial finite-element-based design environmerits, it is still instructive for finite-element novices to write their own programs as an aid in understanding the potential, and limitations, of the method. Writing your own — albeit simple and limited — finite-element program will facilitate better understanding of how to make the most of the excellent commercial programs now on the market. This paper will outline various textbook and online sources of content that facilitates such a voyage of discovery. [ABSTRACT FROM AUTHOR]

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 FEMfMoM 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. [ABSTRACT FROM AUTHOR]

Starting with the Finite Element-Boundary Integral technique for the electromagnetic analysis of cavity backed structures, it is shown how the Fast Multipole Method can be applied to the BI component of this formulation. A new scheme is presented for controlling the error incurred by FMM that affords greater freedom when using the threedimensional FMM by allowing independent specification of the desired error level and the group far-interaction criterion. This scheme is also valid when FMM is applied to general, free-space, three-dimensional Method of Moments implementations. [ABSTRACT FROM AUTHOR]

In the December 2000 and August 2003 columns, the development of FEM codes for electromagnetics was dis cussed. Around a decade on, some new tools have been developed in computational science and engineering for the application of the FEM. This month's paper addresses the use of one of these, namely the FEniCS package, for the FEM solution of electromagnetic problems. [ABSTRACT FROM AUTHOR]