New Publications are available for Maxwell theory: general mathematical aspects
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New Publications are available now online for this publication.
Please follow the links to view the publication.Implications of Galilean electromagnetism in numerical modeling
http://dl-live.theiet.org/content/conferences/10.1049/cp.2011.0062
The purpose of this article is to present a wider frame to treat the quasi-static limit of Maxwell's equations. We discuss the fact that there exists not one but indeed two dual Galilean limits, the electric and the magnetic one. We start by a re-examination of the gauge conditions and their compatibility with Lorentz and Galilean covariance. By means of a dimensional analysis on fields and potentials we first emphasize the correct scaling yielding the equations in the two limits. With this particular point of view, the gauge conditions of classical electromagnetism are continuity equations whose range of validity depend on the relativistic or Galilean nature of the underlying phenomenon and have little to do with mathematical closure assumptions taken without physical motivations.Completeness of smoothed particle hydrodynamics (SPH) method and its corrective methods in time-domain electromagnetics
http://dl-live.theiet.org/content/conferences/10.1049/cp_20080211
In this paper, a comparison completeness of the three kernel approximations that are commonly used in smoothed particle hydrodynamics (SPH) to polynomial functions and their derivatives is conducted. Those are applied for the time domain Maxwell's curl equations and the numerical results is compared with analytic solution. It is shown that the smoothed particle method for Maxwell's equations - smoothed particle electromagnetics (SPEM) - has a high potential in computational electromagnetics and nanostructure.Fundamental features of the EMX software
http://dl-live.theiet.org/content/conferences/10.1049/cp_20040504
This paper describes fundamental features of the EMX software suite (formerly referred to as 3DPIC), a package for electromagnetic and electrostatic particle-in-cell simulation in general geometry. In particular, the finite element basis functions are derived in a general differential geometric context, which makes clear how they may be generated from a single scalar function. The present work discusses exclusively the electromagnetic content of EMX, ie. no particles. An application of EMX to serpentine mode couplers is discussed. The procedure adopted for the construction of the elements in EMX is to introduce a scalar approximating function.New 3D discontinuous sheet for finite element time domain modelling of thin metallic films
http://dl-live.theiet.org/content/conferences/10.1049/ic_20020175
A dual surface method is presented for the modelling of thin metallic film surfaces. Improved accuracy is achieved over existing single surface techniques by way of enforcing the field discontinuity across the thin film layer. The implementation of the discontinuous sheet in the wave equation is described for the time domain finite element method. The computational domain, a closed boundary microwave heating system, is discretised using edge elements. Results are presented where the use of the discontinuous sheet is considered in a food active package application placed within a multimode microwave applicator. (2 pages)MNM - a novel technique for the iterative solution of matrix equations arising in the method of moments formulation
http://dl-live.theiet.org/content/conferences/10.1049/ic_20020158
The Maxwell and Markov method (MNM), which also takes advantage of the knowledge of the previous solutions to extrapolate, though it does so in a way that is different from those of Altman and Mittra (see IEEE Transactions on Antennas and Propagation, vol.47, p.744 -51, 1999) is discussed. It is based on an estimation of the solution vector-to be used as an initial guess-derived by using the solutions at two or three previous frequencies as entire domain basis functions, following an application of Gram-Schmidt orthogonalization procedure. The computational time involved in generating the estimate is negligible when compared to that of the method of moments (MoM) matrix generation and the iterative solution, because the matrix equation to be solved for the purpose of estimation is very small-typically only two or three. (2 pages)Numerical computation of transient quasistatic electric fields
http://dl-live.theiet.org/content/conferences/10.1049/ic_20020145
In many problems involving applications ranging from microwave substrates to high voltage isolators, capacitive and conductive effects have to be simultaneously taken into account, whereas inductive phenomena can be neglected. This means that the quasistatic electric field intensity is curl free and can hence be described by an electric scalar potential, but both the conduction and displacement current density have to be considered. In case of time harmonic problems, the use of the complex notation allows the constant permittivity and conductivity of linear materials to be described by a complex permittivity or, equivalently, by a complex conductivity. In problems with general time variation or ones involving nonlinear material properties, a transient treatment is necessary. The aim of this paper is to summarise the differential equations and boundary conditions for the electric scalar potential in this case and to describe its solution by the finite element method (FEM). The FEM discretisation is shown to lead to a set of ordinary differential equations which can be solved by time stepping. A numerical example is also presented. (2 pages)Physical processes in electromagnetism
http://dl-live.theiet.org/content/conferences/10.1049/ic_19960307
Electromagnetism is a difficult subject but also a fascinating one. The difficulties are of two kinds: conceptual or physical and mathematical or computational. In other words there are the ideas and there is the language in which the ideas are clothed. Of course a complete separation between these is impossible, nevertheless it is desirable to clarify the concepts before getting involved with the detailed mathematics. At least this is the procedure most suited to engineers who find abstract mathematics difficult. It is also the method which is historically correct, because Michael Faraday knew no formal mathematics and even Maxwell preferred mental pictures to mathematical equations. The mistaken idea that Maxwell's theory is the same as Maxwell's equations is due to Heinrich Hertz. The author discusses the physical ideas of electromagnetism. (4 pages)The computation of electrostatic fields and space charge effects
http://dl-live.theiet.org/content/conferences/10.1049/ic_19950072
Discusses the use of the finite element method (FEM) in solving electrostatic field problems. The standard procedure for applying the FEM is to start from Maxwell's equations along with Gauss's theorem. The governing equation for electrostatic field problems can be solved using the FEM when the charge density is a known quantity. Of significant interest has been the case when the charge density is not known ahead of time, and is due to currents being produced from the surface of electrodes. These currents are also affected by the presence of other charges emanating from the electrodes, such that a very complex situation arises in which the space charges have to be computed, including the electric fields they produce. (2 pages)Advances in finite-difference time-domain (FD-TD) numerical modeling techniques for Maxwell's equations
http://dl-live.theiet.org/content/conferences/10.1049/cp_19950258
Prompted to a significant degree by perceived limitations of the method of moments, there has been an explosion of interest in the engineering electromagnetic wave community in direct solutions of the fundamental Maxwell's curl equations on space grids in either the time or frequency domain. The finite-difference time domain (FD-TD) method introduced by Yee (1966), has received perhaps the most attention during this period because of its simplicity and robustness. Advances in FD-TD modeling techniques have further improved its modeling accuracy and expanded its range of applications. These advances are succinctly summarized under the sections: 1. Berenger perfectly matched layer absorbing boundary condition; 2. Dispersive, nonlinear, and gain material models; 3. Active circuit device models; 4. Planar unstructured meshes; and 5. Software development for massively parallel computers. (6 pages)A new vision of numerical methods for the solution of Maxwell's equations related to the FD-TD method; application to general anisotropic media
http://dl-live.theiet.org/content/conferences/10.1049/cp_19940036
Some proposals of numerical methods of solution of Maxwell's equations have appeared in which different meshes and orders of approximation have been used. The relation between finite difference and finite volume has also been pointed out. In this paper a complementary point of view is proposed by the use of the general Stokes' theorem to express Faraday's and Ampere's laws as volume-surface equations. Isotropic materials are treated first, then an application to anisotropic media is introduced through an example.TLM and Maxwell's equations
http://dl-live.theiet.org/content/conferences/10.1049/cp_19940004
Applying the method of moments to Maxwell's equations, the two-dimensional TLM method is derived from first principles of field theory. Sampling Maxwell's equations with pulse functions yields three discretized field equations for the three electric and magnetic field components at the center of a TLM cell. For the field components at the cell boundaries, the mean values of the field components in the two neighbouring TLM cells are taken. The authors call these mean values the cell boundary mean (CBM) values. Introducing the CBM values of the electric and magnetic field components yields four discretized field equations per TLM unit cell. Applying the cell boundary mapping, they obtain four discretized field equations for wave amplitudes which determine the scattering matrix of the two-dimensional TLM method uniquely.Analytical solution of electromagnetic scattering by a general gyrotropic sphere
http://dl-live.theiet.org/content/journals/10.1049/iet-map.2011.0230
Electromagnetic scattering by a general gyrotropic sphere is discussed in terms of spherical vector wave functions. From the source-free Maxwell's equations and Fourier transform, the eigenvalue and eigenvectors of the electric field in a source-free gyrotropic medium can be obtained. The electromagnetic fields may then be obtained in terms of spherical vector wave functions in a source-free gyrotropic medium. Applying the continuous boundary conditions of electromagnetic fields on the surface between the free space and gyrotropic sphere, the spectral coefficients of the transmitted fields inside a gyrotropic sphere and the scattered fields in an isotropic medium (free space) can be obtained exactly by expanding spherical vector wave eigenfunctions. Numerical results are provided for some representative cases. Results from this study and those from an adaptive integral method are in agreement.Application of the transmission line matrix method to the analysis of scattering by three-dimensional objects
http://dl-live.theiet.org/content/journals/10.1049/ip-map_19951916
The transmission line matrix (TLM) method is applied to the analysis of electromagnetic scattering from finite-sized conducting and dielectric objects. The TLM method is a general numerical method for obtaining an approximate solution to the time-dependent form of Maxwell's equations in the presence of geometrically complex environments. The three-dimensional symmetrical-condensed TLM node together with a total/scattered field formulation and a local absorbing boundary condition are applied. Numerical results for a variety of conducting and dielectric objects demonstrate the accuracy of the method. Various guidelines for the successful application of the method to this class of problem are provided.-transform-based complex envelope alternating direction implicit perfectly matched layer algorithm for modelling Drude dispersive source-free wave equation finite-difference time domain applications
http://dl-live.theiet.org/content/journals/10.1049/iet-map.2010.0246
In this study, <i xmlns="http://pub2web.metastore.ingenta.com/ns/">Z</i>-transform-based complex envelope alternating direction implicit wave equation perfectly matched layer (CE-ADI-WEPML) formulation is presented for modelling Drude dispersive finite-difference time domain (FDTD) applications with band-limited sources. In the proposed formulation, the constitutive relation of the dispersive medium is implemented in the FDTD algorithm by means of the bilinear <i xmlns="http://pub2web.metastore.ingenta.com/ns/">Z</i>-transform method. Numerical examples carried out in two-dimensional domains show that the proposed formulation is more accurate than the classical ADI-WEPML and also maintains the accuracy of the CE full-wave Maxwell's equations with significant reduction in the CPU time and memory storage requirements.Systematic split-step perfectly matched layer formulations for modelling dispersive open region finite difference time domain applications
http://dl-live.theiet.org/content/journals/10.1049/iet-map.2010.0244
A systematic unconditionally stable split-step perfectly matched layer absorbing boundary condition formulations are presented for modelling open region dispersive electromagnetic applications. The proposed formulations are based on the incorporating Strang time-splitting approach and the Crank–Nicolson scheme into the complex envelope finite-difference time-domain (CE-FDTD) algorithm. Numerical examples carried out in two-dimensional domains show that the proposed formulations provide better accuracy than the alternating direction implicit FDTD counterpart with a considerable reduction in the central processing unit time requirement.Propagation in bianisotropic media — reflection and transmission
http://dl-live.theiet.org/content/journals/10.1049/ip-map_20010215
A systematic analysis for solving the wave propagation problem in a general bianisotropic, stratified medium is presented. The method utilises the concept of propagators, and the representation of these operators is simplified by introducing the Cayley–Hamilton theorem. The propagators propagate the total tangential electric and magnetic fields in the slab and only outside the slab do the up- and down-going parts of the fields need to be identified. This procedure makes the physical interpretation of the theory intuitive. The reflection and the transmission dyadics for a general bianisotropic medium with an isotropic (vacuum) half-space on both sides of the slab are presented in a co-ordinate-independent dyadic notation, as well as the reflection dyadic for a bianisotropic slab with perfectly electric backing (PEC). In the latter case the current on the metal backing is also given. Some numerical computations that illustrate the algorithm are presented.Finite difference solution of EM fields by asymptotic waveform techniques
http://dl-live.theiet.org/content/journals/10.1049/ip-map_19960749
A new finite difference technique for the solution of electromagnetic (EM) field problems is presented. It is based on complex-frequency hopping (CFH), which is an expanded asymptotic waveform evaluation approach recently proposed in the circuit simulation area with great sucess in solving large linear lumped and distributed circuits. The Maxwell's equations, as well as the special case—Helmholtz equations, are formulated into a set of linear ordinary differential equations by spatial finite difference, and the equations are solved by asymptotic waveform evaluation. The technique is guaranteed to be stable and offers potential speed up over existing finite difference approaches, for example, the finite difference frequency domain (FDFD) and the finite difference time domain (FDTD) for comparable accuracy. Examples of frequency-domain analysis of waveguides and dielectric cylinders are provided.General scheme for electromagnetic reflection and transmission for composite structures of complex materials
http://dl-live.theiet.org/content/journals/10.1049/ip-map_19951533
A time-harmonic electromagnetic planewave obliquely incident on a stratified composite structure consisting of different types of complex (bianisotropic) media is considered. A modified invariant imbedding method is used to calculate the reflection and transmission, and the internal fields are calculated through a Green function approach. A characteristic feature of the approach is that it is based on a wave splitting that is not related to the media which make up the composite structure, but is always defined with respect to a vacuum. Several advantages of this approach are identified and it is compared to other approaches. Numerical results for the co- and cross-polarised reflection and transmission coefficients for TE and TM modes for a composite structure are presented.Application of vector parabolic equation method to urban radiowave propagation problems
http://dl-live.theiet.org/content/journals/10.1049/ip-map_19990567
The vector parabolic equation method is applied to the modelling of radiowave propagation in the urban environment. As a paraxial version of Maxwell's equations it allows full treatment of 3D electromagnetic scattering which was not possible with scalar versions of the algorithm. The method allows detailed specification of the building geometry and electrical parameters. This approach is particularly useful for accurate modelling of scattering by a single building or a group of buildings at microwave frequencies. The method is validated using an iterative integral equation method and known analytical results. Examples include scattering by a building with hemispherical roof and scattering by a group of buildings with sloping roofs.Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations
http://dl-live.theiet.org/content/journals/10.1049/el_20030416
The Crank-Nicolson method is an unconditionally stable, implicit numerical scheme with second-order accuracy in both time and space. When applied to solve Maxwell's equations in two-dimensions, the resulting matrix is block tri-diagonal, which is very expensive to solve. The Douglas-Gunn algorithm is used to subdivide the update procedure into two sub-steps. At each sub-step only a tri-diagonal matrix needs to be solved for one field component. The other two field components are updated explicitly in one step. The numerical dispersion relations are given for the original Crank-Nicolson scheme and for the Douglas-Gunn modification. The predicted numerical dispersion is shown to agree with numerical experiments, and its numerical anisotropy is shown to be much smaller than that of the ADI-FDTD.Unconditionally-stable FDTD method based on Crank-Nicolson scheme for solving three-dimensional Maxwell equations
http://dl-live.theiet.org/content/journals/10.1049/el_20040420
The approximate-factorisation-splitting (CNAFS) method as an efficient implementation of the Crank-Nicolson scheme for solving the three-dimensional Maxwell equations in the time domain, using much less CPU time and memory than a direct implementation, is presented. At each time step, the CNAFS method solves tridiagonal matrices successively instead of solving a huge sparse matrix. It is shown that CNAFS is unconditionally stable and has much smaller anisotropy than the alternating-direction implicit (ADI) method, though the numerical dispersion is the same as in the ADI method along the axes. In addition, for a given mesh density, there will be one value of the Courant number at which the CNAFS method has zero anisotropy, whereas the Crank-Nicolson scheme always has anisotropy. Analysis shows that both ADI and CNAFS have time step-size limits to avoid numerical attenuation, although both are still unconditionally stable beyond their limit.High-order accurate split-step FDTD method for solution of Maxwell's equations
http://dl-live.theiet.org/content/journals/10.1049/el_20073521
The split-step finite difference time domain (SS-FDTD) method characterised by unconditional stability is becoming an important numerical method in computational electromagnetics. Proposed is a new high-order accurate unconditionally stable SS-FDTD method, which is derived from the exponential evolution operator. Compared with the conventional SS-FDTD method, the numerical dispersion of the new method is greatly reduced.Long time stable compact fourth-order scheme for time domain Maxwell's equations
http://dl-live.theiet.org/content/journals/10.1049/el.2010.1204
A compact staggered backward differentiation method (CSBD(4,4)) is proposed. Theoretical analyses of numerical stability and dispersion are straightforward, and comparisons with the staggered backward differentiation method (SBD(4,4)) are provided. It shows that the numerical dispersion of the proposed scheme is greatly reduced.Efficient hybrid TDFEM-PSTD method
http://dl-live.theiet.org/content/journals/10.1049/el_20050364
A novel hybrid pseudo-spectral time domain method (PSTD) and time domain finite element method (TDFEM) scheme is proposed. Compared with TDFEM-FDTD, the TDFEM-PSTD greatly alleviates the Courant limit on spatial discretisation, as only two cells per wavelength are needed. For the same accuracy, numerical simulations clearly show that the proposed hybrid method is more robust and efficient than the FEM-FDTD.Green dyadic and dipole radiation in triaxial omega medium
http://dl-live.theiet.org/content/journals/10.1049/el_19960393
A triaxial omega medium, which can be artificially realised by embedding three types of omega-shaped particles in an isotropic host medium, is proposed. The Green dyadic and the electromagnetic field of a dipole radiator are presented, by introducing a set of auxiliary fields and coordinate transformation.Weakly conditionally stable FDTD method for analysis of 3D periodic structures at oblique incidence
http://dl-live.theiet.org/content/journals/10.1049/el.2011.4007
For analysing the 3D periodic structures at the oblique incident, a weakly conditionally stable finite-difference time-domain method is proposed by applying the Crank-Nicolson (CN) scheme to the field transformation technique. By splitting the space operator matrix in a special way, the transformed Maxwell's equations can be subdivided into two sub-steps for an efficient implementation. The proposed method does not need to introduce additional field components to handle the extra time terms and the time step size is only determined by one space discretisation.Radiation pressure
http://dl-live.theiet.org/content/journals/10.1049/piee.1978.0165
Electromagnetic waves, sound waves, the waves of a vibrating string etc carry momentum and exert, on an obstacle in their path, a force equal to the rate of momentum change produced by the obstacle. A very general energy theorem is applied to the calculation of the momentum, and shows that, in an unbounded medium, waves of intensity <i xmlns="http://pub2web.metastore.ingenta.com/ns/">J</i> have momentum <i xmlns="http://pub2web.metastore.ingenta.com/ns/">J</i>/<i xmlns="http://pub2web.metastore.ingenta.com/ns/">v</i><sup xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sup> per unit volume, where <i xmlns="http://pub2web.metastore.ingenta.com/ns/">v</i> is the velocity of propagation. In a dispersive medium the phase velocity must be used to calculate the radiation pressure, i.e. the radiation force per unit area, in terms of intensity.Appendix A: Application of the Lorentz reciprocity theorem to scattering
http://dl-live.theiet.org/content/books/10.1049/pbew024e_appendixa
<p xmlns="http://pub2web.metastore.ingenta.com/ns/">There are in current use several reciprocity theorems, all of which are often loosely referred to as “the” reciprocity theorem. We apply here the version developed by H. A. Lorentz.</p>Making waves: London, Liverpool, Dublin and Karlsruhe 1882-88
http://dl-live.theiet.org/content/books/10.1049/pbht036e_ch6
<p xmlns="http://pub2web.metastore.ingenta.com/ns/">This chapter reviews the work of Oliver Heaviside on Maxwell's theory. It features several formulas that derived by him including the energy transfer formula.</p>Maxwell
http://dl-live.theiet.org/content/books/10.1049/pbht020e_ch3
<p xmlns="http://pub2web.metastore.ingenta.com/ns/">James Clerk Maxwell's interest in electromagnetic theory was almost certainly inspired initially by another young Cambridge wrangler, William Thomson (later Lord Kelvin), who in 1846-47 had made a mathematical investigation into the similarities between electromagnetic phenomena and elasticity. In the course of this investigation, he had examined the equations of equilibrium of an incompressible elastic solid in a state of strain and he had shown that elastic displacement was analogous to the distribution of electric forces in an electrostatic field. Thomson's memoir was concerned with equilibrium conditions but its results were such as to suggest to Maxwell a few years later that the analogies between elastic strain and electrostatic forces might be extended and applied to the propagation of electromagnetic forces through an appropriate medium. One of the first steps in following this line of thought was to investigate the possible characteristics of an appropriate medium and, having been greatly impressed with his reading of Faraday's Experimental Researches in Electricity, and with his whole concept of lines of force, Maxwell commenced by translating Faraday's ideas into mathematical terms.</p>Modified indirect boundary element technique and its application to electromagnetic potential problems
http://dl-live.theiet.org/content/journals/10.1049/ip-h-2.1992.0052
A modified indirect boundary element formulation is developed following a weighted residual approach. In this formulation, the fictitious source density, which appears in the integral equations of the method, is distributed on a surface which is exteriorly separated from the physical field boundary of the problem. The method does not require the evaluation of singular integrals and produces undeteriorated solutions at geometric discontinuities. The technique is applied to two-dimensional electromagnetic potential problems, and several examples are investigated.Global geometry of electromagnetic systems
http://dl-live.theiet.org/content/journals/10.1049/ip-a-3.1993.0023
Engineering calculations of electromagnetic systems require information about both local fields and global system parameters. This information depends on the local geometry, the global topology and the relation between the two. Maxwell's differential equations describe the local geometry with its four-dimensional space-time metric. These equations are greatly simplified when they are expressed in terms of differential forms, in which physical and geometrical information is combined. The paper shows the geometrical significance of the conservation of electric charge and of the gauge invariance of the potentials. Global topology is explored in terms of the interaction of differential forms and the structure of the manifold containing the system. It is shown that this depends on integral relationships which cannot be inferred from the differential equations. It is also shown that the gauge invariance of the potentials is related to the phase properties of state functions in quantum mechanics, a relationship which provides a further link between geometry and physical interaction.Electromagnetic induction in terms of the Maxwell force instead of magnetic flux
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19990381
The conventional treatment of induced EMFs in terms of magnetic flux leads to problems with the concepts of ‘flux-cutting’ and ‘flux-linking’ which have attracted much discussion and controversy, particularly when applied to devices with moving parts. Maxwell's own ‘general equations’ tend to be ignored. They did not include the ‘Maxwell’ field equation relating induced <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>E</i></strong> fields to changes in the flux density, <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>B</i></strong> , but developed an alternative view based on the magnetic vector-potential <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>A</i></strong> . The practical role of <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>A</i></strong> in the computation of EMFs and inductances suggests that it has corresponding conceptual advantages, including the relative simplicity of the <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>A</i></strong> field of a current element. <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>B</i></strong> is viewed as a symbol for the differential of <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>A</i></strong> , thus reversing their customary roles, and removing the difficulties caused by the conventional treatment. It is shown that the use of <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>A</i></strong> to describe the magnetic effects of the source currents helps to provide a clearer view of induction, and resolve the various problems and apparent anomalies. The relativistic relationship between the magnetic and electric fields is described most simply in terms of the potentials, and answers the much-debated question of the meaning of motion when applied to a uniform <strong xmlns="http://pub2web.metastore.ingenta.com/ns/"><i>B</i></strong> field.Large systems of equations in a discrete electromagnetism: formulations and numerical algorithms
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_20050849
The description of discrete electromagnetic fields is achieved with the Maxwell grid equations, a set of matrix equations representing a spatial discretisation of Maxwell's equations in integral form on a dual mesh pair. Based on this matrix formalism the calculation of electromagnetic fields requires efficient techniques for the solution of commonly large, sparse systems of linear or nonlinear algebraic, differential–algebraic and ordinary differential equations. Field formulations and modern numerical-solution algorithms especially for the solution of static and quasistatic electric and magnetic fields are presented. Numerical schemes for fast-varying transient and time-harmonic current-driven or resonator electromagnetic fields are added. Details such as regularisation techniques, the modelling of motion-induced eddy currents, possible field excitation sources and the algorithmic treatment of ferromagnetic material properties are addressed. The numerical schemes include error-controlled adaptive time-domain algorithms featuring advanced extrapolation methods, linearisation methods for the nonlinear algebraic systems of equations with the possible inclusion of ferromagnetic hysteresis modelling and iterative solution methods for large sparse linear systems of equations.Comment: Dwight-Bewley paradox
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19970994
MNM: a technique for the iterative solution of matrix equations arising in the method of moments formulation
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_20020636
The advent of the fast multipole method (FMM) and other techniques for carrying out the matrix vector product in an efficient manner, in the context of the method of moments (MoM) formulation, has made it possible for us to take a quantum leap forward towards solving a class of large problems involving perfectly conducting scatterers. Among a plethora of different iterative algorithms available in the literature, the conjugate gradient (CG) and its variants are among the most widely used. The speed with which convergence to the correct solution is achieved in employing this iteration algorithm, is dependent upon the choice of the pre conditioner, as well as the initial guess. The authors focus on introducing a technique the (Maxwell and Markov technique, referred to herein as MNM) for choosing the initial guess. This can help reduce the number of iterations and, consequently the solution time, over the typical choice of a zero initial guess in the context of CG. The application of the method is illustrated via a number of numerical examples that combine the FMM with MNM, to derive the solution of representative electromagnetic scattering problems.Comment: Dwight–Bewley paradox
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19970921
Huygens' principle in electromagnetics
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19960218
A simple way of deriving Huygens' principle in electromagnetic and transmission-line theory is given without recourse to Green's functions and Green's formulas.Efficient description of fine features using digital filters in time-domain computational electromagnetics
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_20020541
The use of digital filters for the description of perforated metal plates in the time-domain transmission-line modelling (TLM) method is presented. The frequency-domain Prony method is used to approximate the analytic scattering coefficients of perforated plates using Laplace-domain functions. These functions are transformed into the -domain and the resulting digital filters are embedded into the TLM mesh. Three types of perforated plates are studied and the results obtained for the shielding effectiveness of equipment enclosures having perforated plates are shown.Synthesis of symmetric and asymmetric planar optical waveguides
http://dl-live.theiet.org/content/journals/10.1049/iet-opt_20060090
A novel and accurate refractive index profile synthesis method for planar optical waveguides is presented and demonstrated using the transmitted near-electric-field-data. This method is based on the inverse transmission-line (TL) technique. From Maxwell's equations, a TL equivalent circuit (electric T-circuit) for the refractive index profile of a planar optical waveguide is derived. The authors demonstrate how to use this model to carry out the inverse problem and synthesise the exact refractive index profile numerically from near-field-data. The TL method can reconstruct arbitrary refractive index profiles for planar optical waveguides that support singlemode or multimodes. The cases of both symmetric and asymmetric arbitrary refractive index profile planar waveguides are discussed. The accuracy of the reconstructed waveguides is examined numerically.Reduced vector potential formulations for FI<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sup>TD schemes
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_20020567
Finite integration implicit time domain (FI<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sup>TD) schemes for transient magneto-quasistatic problems have so far been developed for a magnetic field description based on a modified vector potential formulation. A reduced vector potential formulation for these schemes is introduced, where the magnetic field is additively decomposed into a source part originating from the exciting coil currents, which thus can be modelled independently of the computational grid, and a part resulting from the presence of eddy currents due to electric conductivity and/or the nonlinear material behaviour. Numerical tests for 3-D transient problems show an improved convergence behaviour of the iterative CG-algorithm with respect to the new formulation.Reply: Dwight–Bewley paradox
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19970922
Maxwell equations for the generalised Lagrangian
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19960164
The author deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the action integral. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor <i xmlns="http://pub2web.metastore.ingenta.com/ns/">F<sup>ik</sup></i>. Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The Maxwell equations obtained are quite similar to the well-known Maxwell equations.Definitions and roles of the electromagnetic field vectors
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19990026
Contrasting views on electromagnetic fundamentals, usually associated with physicists and engineers, are summarised in the roles allocated to the field vectors. Whereas most engineers view the electrical and magnetic flux densities <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">D</strong> and <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">B</strong> as analogous quantities, while <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">E</strong> and <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">H</strong> both denote field strength, to the physicist the vectors <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">E</strong> and <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">B</strong> are sufficient measures of the field, in vacuo, and <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">D</strong> and <strong xmlns="http://pub2web.metastore.ingenta.com/ns/">H</strong> are paired as auxiliary quantities. The underlying differences of understanding have led to a plea by physicists for greater agreement. The paper shows that the use of the retarded potentials as the primary measures of the field gives a clear and unambigous definition of each of the field vectors, and shows the need for eight, not four. This helps to clarify the conceptual difficulties underlying much debate. It suggests that simplicity of understanding requires the adoption of the physicist's view, but that this need not imply any major changes in the ways in which the field vectors are used by engineers.Interaction of moving charge and toroidal coil
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19990180
In classical electromagnetics the interaction between charged particles and electric circuits in relative motion ought to conserve both momentum and energy. The paper examines a hypothetical ‘toroidal generator’ in which a charged particle is fired along the major axis and through a toroidal coil. By keeping the speeds low, and keeping the geometry simple, and by considering a resistive coil, it is possible to keep account of all the flows of energy and momentum, in and out of the components of the system and through the surrounding fields.Dwight-Bewley paradox
http://dl-live.theiet.org/content/journals/10.1049/ip-smt_19960429
The concept of motional induced EMF is implicitly based on a reference frame relative to which the magnetic field pattern is unchanging or stationary, and uses the relative velocity <i xmlns="http://pub2web.metastore.ingenta.com/ns/">v</i> between the frame and the conductor in the expression <i xmlns="http://pub2web.metastore.ingenta.com/ns/">B v l</i>. For ease of conception, the velocity may be taken as that between the field pattern itself and the conductor. Where there are multiple field patterns in relative motion, no ‘velocity’ can be ascribed to the resultant field pattern relative to any object, fixed or moving. Therefore the EMF induced in a conductor situated in such a field cannot be expressed as a single motional EMF, but must be found by superposition of EMFs induced by the individual fluxes. From the impossiblity of applying the <i xmlns="http://pub2web.metastore.ingenta.com/ns/">B v l</i> rule to the resultant flux, Bewley concludes that the EMF in the conductor is not motional but variational. It is shown here, mathematically from a consideration of reference frames, and physically from the fact of electromechanical energy conversion taking place, that Bewley's assertion is invalid and that the EMF is in fact motional, not variational. The <i xmlns="http://pub2web.metastore.ingenta.com/ns/">B v l</i> rule is then generalised for application to such situations.Finite element analysis of electromagnetic interaction with uniform moving medium
http://dl-live.theiet.org/content/journals/10.1049/el_19951145
A finite element vector formulation for studying the electromagnetic interaction with infinitely long cylinders of arbitrary cross-section moving along their axes, is presented. The problem is solved in the laboratory reference frame by using the Minkowski transformed constitutive equation to take into account body motion. The formulation is verified by analysing simple structures for which an analytical solution is known.New method for numerical solution of Maxwell equations
http://dl-live.theiet.org/content/journals/10.1049/el_19950182
The method, using differential-Thompson transformation (DTTR) combined with the finite difference time domain (FDTD) technique for solving the Maxwell equations, is applied for the first time to the field of electromagnetic scattering. The numerical results show its advance on previous approaches.