Three-dimensional finite, boundary, and hybrid element solutions ofthe Maxwell equations for lossy dielectric media

Finite, boundary, and hybrid element approaches are presented as numerical methods for computing electromagnetic (EM) fields inside lossy dielectric objects. These techniques are implemented as computer algorithms for solving the Maxwell equations in heterogeneous media in three dimensions. Algorithm verification takes the form of comparisons of test cases with analytic solutions. Computed results for each technique are in good agreement with exact solutions, especially in light of the coarse computational grid resolutions used. Implementation was in FORTRAN on a moderate-sized computer (MicroVax II). The basic problem formulation is quite general; however, it has direct application in hyperthermia as a cancer therapy where the EM fields produced inside the patient by external sources are of interest. An example of the application of these numerical methods in a three-dimensional clinical setting is shown     

Comments on `Riemann-Green function solution of transientelectromagnetic plane waves in lossy media'

In commenting on the above-named work by O.R. Asfar (see ibid., vol.EMC-32, no.3, p.228-31, Aug. 1990), the commenter notes that one can write infinitely many solutions for the associated magnetic field strength that will all satisfy Maxwell's equations, but Maxwell's equations cannot tell which one of these infinitely many solutions is the right one. It is further pointed out that the physical significance of the magnetic current density term used became clear when transients in lossy media were investigated with Lorentz's equations of electron theory, which allow for the fact that electric charges are always connected with particles having a mass, whereas Maxwell's original equations do not contain the concept of mass. A physical explanation for this is offered, and attention is given to the creation of the singularity in Maxwell's equations that make sit impossible to obtain the associated magnetic field strength without some limit process     

Comments, with reply, on `Electric field of a transmission lineover a multilayered media'

The commenter points out that the general solution for the electric field of a current line source of alternating current over a stratified earth of any number of layers published in the above letter (see ibid., vol.75, no.1, p.170-171, 1987) was obtained by him in a paper that he published 24 years ago. The authors acknowledge Wait's prior claim, observing that parallel research of this sort is too often encountered     

Comments on `On the use of metallized cavities in printed slotarrays with dielectric substrates' [and reply]

Statements concerning a method used in a cited reference in the above named work (ibid., vol.AP-35, no.5, pp.477-87, 1987) are refuted and the method of analysis discussed is clarified. The original author acknowledges the clarification and agrees with the resulting interpretation of the method     

Comments on `A practical end-of-life model for semiconductordevices' [and reply]

Several observations are made on the above-named work by M.S. Ash and H.C. Gorton (see ibid., vol.38, no.4, p.485-93, Oct. 1989) concerning gradual performance deterioration in semiconductor devices. The commenter suggests that the development of predictive tools for reliability assessments involving long-term deterioration in such devices requires that careful attention be paid to the operational physics of the device, including temperature-dependent characteristics. An author's reply is included     

Comments on "Spheroidal vector wave eigenfunction expansion of dyadic Green's functions for a dielectric spheroid" [and reply]

Dudley and Johnson (see ibid., vol.50, p.XX XX, Nov. 2002) comments that Li, Leong, Kooi and Yeo (see ibid., vol.49, p.645-659, April 2001) formulate in detail the dyadic Green's functions for the dielectric spheroid stating that one result of their derivations, the singularity of the electric Green's dyadics is extracted. They also comment that there is nothing formally wrong with extracting the delta function. They object strongly, however, to the authors stating that they have extracted "the singularity of the electric Green's dyadics." They have not done so. Li et. al. reply that they, are grateful for the comments of Dudley et. al clarifying the singular behavior of the electric and magnetic field Green's dyadics. They intended to state "irrotational part of the electric dyadic Green's function" which is highly singular, but misused the term, "singularily of the dyadic Green's function".     

Time-domain integration of the Maxwell equations on finite elements

An explicit time-domain integration scheme is developed for finite-element spatial discretization of the Maxwell equations. A generalized wave equation is used in weak form, which is free of vector parasites when discretized on single C⁰ elements. The use of integral lumping renders the mass matrix diagonal with no necessary degradation in accuracy. The explicit method which results combines the economy of established finite-difference techniques with the geometric flexibility of finite elements. Test problems representative of practical hyperthermia applications show agreement with analytic and frequency-domain finite-element methods, and confirm scaling arguments on run-time and memory     

Comments on ``The QPSX MAN' [with authors' reply]

For original article see ibid., vol.26, no.4, p.20 (1988). The commenter contends that the authors of the above-mentioned article miscompare dual bus and dual ring topologies. He addresses what he believes should be the main point of interest to the telephone companies when they are assured that QPSX will measure up to the public network requirements, namely, reliability and maintainability. He uses QPSX and FDDI to compare dual bus/dual ring reliability, showing that QPSX is less reliable. The original authors refute Dr. Rocher's comments regarding the reliability of QPSX, and they emphasize that the numerous other advantages of QPSX listed in their article stand undiminished     

Coupling finite element and integral equation solutions usingdecoupled boundary meshes [electromagnetic scattering]

A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E _tan is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail     

Comments on `New practical Bayes estimators for the 2-parameterWeibull distribution' [and reply]

The commenter maintains that an expression in the above-mentioned paper (ibid., vol.R-31, p.194-7, June 1982) on which the results are based is wrong, and therefore the results are wrong. The author rebuts the commenter's argument point by point     

Comments `Surface losses in transmission lines' [and reply]

The commenter argues that the treatment of a uniform plane wave impinging obliquely on a lossy half plane in the above-titled paper by D.A. de Wolf (see ibid., vol.34, no.4, p.22-6, Aug.1992) is fundamentally incorrect. In reply, de Wolf agrees with the commenter's objections, but points out that they pertain only to his first, heuristic, derivation. He then examines why his apparently absurd derivation yielded the right answer     

Comments on “Multiphase systolic algorithms for spectraldecomposition” [and reply]

Comments that the paper by Liu and Yao (see ibid., vol.40, no.1, p.190, 1992) presented an efficient algorithm for spectral decomposition, but the parallel algorithm and architecture for the Hessenberg reduction has a problem. The matrix obtained from the unitary similarity transformation is not necessarily a Hessenberg matrix. The authors reply that the Hessenberg reduction described is not in the Hessenberg form. Only the first column is in its proper form. There are many ways to overcome such a problem. One simple way is to use the multiphase rectangular systolic array     

Comments on `an optimized output stage for MOS integrated circuits' [and reply]

An interesting approach to improving the performance of MOS off-chip drivers has previously been described (see ibid., vol.10, no.2, p.106 (Apr. 1975)). The selection of the optimization criterion is discussed.     

Comments on `Minimum variance beamforming with phase-independentderivative constraints' [and reply]

The commenter points out that the idea of controlling only the magnitude response of a beam to achieve a flat main beam response, as discussed in the above-titled paper by C.-Y. Tseng (ibid., vol.40, no.3, p.285-94, Mar. 1992), is not new and was discussed by M.H. Er (1988). The author apologizes for the oversight and points out that the paper also covers issues that were not addressed by Er     

Comments on `Two-port higher mode circular microstrip antennas'[and reply]

The commenter maintains that the definitions of the line current and line voltage given in the above paper (ibid., vol.36, no.3, p.309-21, Mar. 1988) do not follow the standard transmission line equations. He offers an alternative definition. The author replies that the problem is due to a misleading figure, and he clarifies his work     

Comments on “Hall Effect Imaging” [and reply]

Recently, Wen, Shah, and Balaban (The Encyclopedia of Physics, 2nd ed., New York, VCH, 1990) presented two novel and elegant methods for imaging electrical conductivity. In their first method, they placed a conducting sample in a steady magnetic field and applied an ultrasound pulse. The resulting motion of the conductor in the magnetic field produced a measurable voltage. In their second method, they applied a high-frequency voltage to a conducting sample in a steady magnetic field and recorded the ultrasound signal. Here, Roth and Wikswo make two points about this work: 1) The “Hall effect” is not the physical basis for Wen et al.'s techniques, and 2) their work has close experimental and theoretical connections to previous studies of magnetoacoustic imaging. In their reply, disagreeing with Roth et al., Wen and Balaban say that they did not propose two imaging methods. Their paper presented two realizations, the forward and reverse modes, of the same imaging method. They are the reciprocal versions of the same linear electrodynamic process, namely, the conversion between electrical energy and mechanical energy by the Lorentz force. In reply to Roth et al.'s statement that “the name “Hall effect imaging” is misleading” Wen and Balaban say that they extended the idea of the classical Hall effect to describe “Hall-effect imaging” because the initial motion of the charges is not driven by an electric field but by direct mechanical force     

Comments on "Synthesis of adaptive monopulse patterns" [and reply]

In the recent paper (see ibid., vol.47, no.5, p.773-4, May 1999) Fante determines the weight vector w/sub /spl Delta// for the difference beam subject to the constant slope of the ratio /spl Delta///spl Sigma/. Junhao Xie states that the method is quite general and that the sum/difference beam weight vector should be simplified further.     

Comments on “transmission techniques for digital terrestrialTV broadcasting” [and reply]

We are responding to the paper by Sari et al. (see ibid., vol.33, no.2, p.100, 1995), referred to as SKJ, in which it is claimed that single-carrier (SC) transmission with frequency-domain equalization (FDE) is generally superior to coded orthogonal frequency-division multiplexing (COFDM) for terrestrial broadcasting. After pointing out a few additional considerations and briefly discussing the questions of carrier frequency offset and the effect of transmitter nonlinear distortion, we deal with the main issue: the performance of the two systems in the presence of strong echoes as would be encountered in single-frequency networks (SFNs). Any high performance communication system should incorporate sophisticated error-correction methods to achieve the desired performance. Therefore, a comparison based on uncoded or even trellis-coded transmission performance, as presented in SKJ, does not properly represent the tradeoffs involved in SC vs. COFDM terrestrial broadcast. A comparison should be based upon the most powerful practical coding system. For example, based on existing knowledge, a concatenated block and trellis coding system that incorporates adequate interleaving and maximum-likelihood decoding (using channel state information) offers a good solution. Using these techniques, we give an example of the performance of both kinds of systems with echoes ranging up to 0 dB. We find that it is possible to make the bit error rate of both systems improve with large echoes. SKJ reply that the basic message they want to convey through their article is that a well designed single-carrier system (with frequency-domain equalization) achieves similar performance to COFDM while avoiding its two well known problems of sensitivity to nonlinear distortion and carrier synchronization difficulties