Solution Of Electromagnetic Field Problems Research Articles

A Quasi-Moment-Method empirical modelling for pathloss prediction

ABSTRACT The main objective of this paper is to introduce a novel approach to empirical modelling for the prediction of propagation pathloss, in wireless radio communication systems. The method, here referred to as the ‘Quasi-Moment-Method’ (QMM), has its basis in the solution of the classical least square approximation problem, in a manner similar to the method of moments, for the solution of electromagnetic field problems. By using existing basic models to prescribe ’basis’ functions, associated unknown coefficients are determined through the solution of simple matrix equations. A comparative analysis with some published measurement data revealed that the QMM consistently outperformed models developed with other approaches. Typically, the ECC-33 models, modified using the QMM, for an outdoor case, recorded a root-mean-square-error value of 0.33 dB, as against 20.083 dB due to a corresponding published optimised model.

Sliding Non-Conforming Interfaces for Edge Elements in Eddy Current Problems

In this work, a flexible discretization technique for the approximate solution of electromagnetic field problems with rotating parts, based on non-conforming (NC) interfaces of Nitsche-type, is investigated. This approach enables the use of edge elements of the first and second kind for the discretization of the magnetic vector potential without posing severe restrictions on gaps and overlaps of elements on both sides of the rotating interface. It improves the computational efficiency, compared to other NC interface formulations because no additional unknowns are introduced, and edge elements of different polynomial order can be coupled with this approach. The applicability is shown in two numerical examples, involving a cylindrical NC interface between a stationary and a rotating domain.

Complete analytical solution of electromagnetic field problem of high-speed spinning ball

In this article, a small sphere spinning in a rotating magnetic field is analyzed in terms of the resulting magnetic flux density distribution and the current density distribution inside the ball. From these densities, the motor torque and the eddy current losses can be calculated. An analytical model is derived, and its results are compared to a 3D finite element analysis. The model gives insight into the torque and loss characteristics of a solid rotor induction machine setup, which aims at rotating the sphere beyond 25 Mrpm.

Energy absorption by ferromagnetic nanoparticles in hyperthermia therapy

Abstract A numerical method is developed for estimation of temperature distributions inside tissues heated by external RF hyperthermia with external circular coil. The computational method relies on a solution of electromagnetic field problem in sinusoidal steady state. The heat transfer problem is treated in three dimensions with axis symmetry model. Than the bioheat diffusion equation under a steady-state condition is solved to determine the temperature distributions inside tumour and surrounding tissues. The heat removal due to the blood circulation is also taken into account. Numerical results are presented for heat generated by ferromagnetic nanoparticles in order to minimize negative effects of radiofrequency radiation.

An efficient wavelet-based solution of electromagnetic field problems

This work investigates the applicability of wavelet transform in electromagnetic field problems. A new approach to the numerical solution of the electric field integral equation (EFIE) is proposed. Rather than applying wavelet bases directly to obtain new discretizations, we exploit the available wavelet bases to obtain more efficient solution algorithms for the classical discretizations. We discretize the EFIE using the method of moments (MoM). The discrete wavelet transform (DWT) is then applied to the resulting dense algebraic system. This procedure involves O(N^2) operations and leads to a sparse matrix problem. Solving this sparse matrix system by iterative methods requires only O(Nlog2N) operations whereas O(N^3) operations are required for the traditional methods. Comparisons of the run-times, number of iterations and error estimations are made for different iterative methods and for different sizes of the matrix equations. The advantages and shortcomings of the presented methods are discussed and the best choices are singled out.

Computational Electromagnetism

The field of computational electromagnetism is dedicated to the design and analysis of numerical methods for the approximate solution of electromagnetic field problems. Since the exploitation of electromagnetic phenomena is one of the foundations of modern technology, computational electromagnetics is of tremendous industrial relevance: in a sense, it is peer to computational solid and fluid mechanics and huge research efforts are spent on developing and enhancing simulation methods and software for electromagnetic field computations. For a long time, computational electromagnetism remained a realm of engineering research with applied mathematics shunning the area. This was in stark contrast to elasticity and fluid mechanics, where mathematicians have been involved in the development of numerical methods from the very beginning. Maybe, the blame has to be laid on the incorrect belief of mathematicians who thought that the laws governing the behavior of electromagnetic fields basically boil down to well understood second-order elliptic problems. Fortunately, the past fifteen years have seen a real surge of mathematical research activities in the area of computational electromagnetism. This resulted in insights that have begun to have a big impact on the numerical methods used in engineering and industrial environments. A prominent example is the explanation of so-called spurious solutions that can arise when using continuous “nodal” finite elements for the discretization of certain electromagnetic boundary value or eigenvalue problems, respectively. Another example is the appreciation of so-called edge finite elements and the construction of multilevel iterative solvers for the low-frequency setting. Meanwhile, computational electromagnetism can claim to be a major area of numerical mathematics and scientific computing in its own right. This prompted us to ask the Mathematisches Forschungsinstitut Oberwolfach to host a one week workshop on computational electromagnetism, the first of its kind. Reflecting the growing importance of the subject, this workshop has been one of a series of events dedicated to mathematical issues in the computation of electromagnetic fields. We would like to mention, the NSF-CBMS Regional Conference in the Mathematical Sciences about “Numerical Methods in Forward and Inverse Electromagnetic Scattering”, held in Golden, CO, June 3–7, 2002 (from which the book [2] arose), and the “LMS Durham Symposium on Computational methods for Wave Propagation in Direct Scattering”, Durham, England, July 15–25, 2002 (see [1]). This Oberwolfach workshop brought together some 50 experts in computational electromagnetism. The majority of the participants were applied mathematicians, but a sizable number of people with a background in engineering also attended, as appropriate for a field with close ties to engineering and the applied sciences. Nevertheless, the workshop had a clear mathematical focus, emphasizing rigorous theory, principles and ideas. Throughout, the presentations matched these expectations. A total of 29 presentations were given, of which ten were survey lectures offering broader treatment of a particular subject. As is typical of an event that targets a specific area of application, it arose that a broad range of mathematical issues and techniques was addressed. Although it will certainly not do justice to many presentations, we will try categorize the talks as follows: We would like to add our personal impression that two families of methods have been received with particular interest during the workshop:

Geometric Multigrid Algorithms Using the Conformal Finite Integration Technique

A geometric multigrid algorithm is proposed for the solution of electromagnetic field problems using the mesh independent boundary resolution capabilities of the conformal finite integration technique (CFIT), maintaining the separation of metric free incidence matrices and averaging material operators. With the construction of conservative grid-transfer operators, exact and approximate algebraic construction principles for the coarse grid material matrices are proposed based on the CFIT. A validation of the presented algorithmic approach and experimental results on the improved efficiency and the asymptotical complexity of the algorithm are achieved for an electrostatic test problem.

Applications of MLSDQ method for analysis of electromagnetic fields

ABSTRACTThis paper presents a novel application of the moving least square differential quadrature (MLSDQ) method to the solution of electromagnetic field problems. The MLSDQ is a new method proposed very recently for solution of nonlinear partial differential equations and has been successfully applied to the study of the bending behaviour of plates. In this paper, the applicability and accuracy of the MLSDQ method to electromagnetic problems will be examined. Two examples of electrostatic field and eddy current problems are studied and the numerical results are in excellent agreement with the analytical solutions.

Numerical errors in the scalar potential formulations used in low-frequency field problems

This paper examines the sources of numerical errors in the reduced scalar potential solution of electromagnetic field problems. A number of ways by which some of these errors may be eliminated are put forward and numerical results for the 3D geometry of an iron core inductor are compared and explanations have been attempted.

Higher order interpolatory vector bases on prism elements

Triangular prism elements are useful in numerical solutions of electromagnetic field problems since they permit a three-dimensional (3-D) geometry to be generated by the extrusion of a triangular mesh. Few applications have employed vector basis functions on prism elements and the extension to distorted prisms reported in the literature apparently does not ensure cell-to-cell continuity. In this paper, we define interpolatory higher order curl- and divergence-conforming vector basis functions of the Nedelec type on prism elements, with extension to curved prisms, and discuss their completeness properties. Vector bases of arbitrary polynomial order are given and various results to confirm the faster convergence of higher order functions are presented.

Extrapolation of time-domain responses from three-dimensional conducting objects utilizing the matrix pencil technique

In this paper, we use the matrix pencil approach to extrapolate time-domain responses from three-dimensional (3-D) conducting objects that arise in the numerical solution of electromagnetic field problems. By modeling the time functions as a sum of complex exponentials, we can eliminate some of the instabilities that arise in late times for the electric-field integral equation in the time domain. However, this method can also be utilized for extending the responses obtained using a finite-difference time-domain (FDTD) formulation.

Neuro-computation techniques in sampled-data electromagnetic field problems

In this paper, a technique is introduced by which to extend the applicability of the existing analytic solutions of electromagnetic field problems to cases where random-noisy-sampled data (such as measurement outputs) are available, rather than analytic input functions. We address those problems for which a theoretical solution exists in the form of a superposition of some basis functions. The algorithm introduced employs this same set of basis functions, and finds the expansion coefficients by the use of an iterative error-minimization technique, which resembles those found in the process of training of artificial neural networks. In cases where the expansion functions are orthonormal, guaranteed fast convergence is proved. As well, we show how neuro-computation techniques can be employed to circumvent the effects of various types of measurement errors and noise. Satisfactory performance of the algorithm is shown for a test problem driven by random inputs corrupted with various levels of Gaussian noise. >

The parallel computation of solutions to electrostatic problems using multigrid techniques

AbstractThe application of multigrid techniques to the computation of the static solutions of electromagnetic field problems governed by Laplace's equation is described. This technique is compared with the conventional successive over‐relaxation (SOR) method for solving finite difference problems. In contrast to SOR, the number of iterations of multigrid needed to achieve convergence is largely independent of the grid size. It is shown that the relative performance of multigrid is excellent on large grids where the number of iterations of SOR needed to achieve convergence becomes prohibitively large. The technique is illustrated by applying a parallel implementation of multigrid to find a quasistatic solution of a boxed microstrip problem.

A new wire node for modeling thin wires in electromagnetic field problems solved by transmission line modeling

A three-dimensional wire node for the numerical solution of electromagnetic field problems by transmission line modeling is discussed. The wire node can represent thin wires in a coarse mesh, thus substantially increasing computational efficiency. The scattering matrix for the node is given, together with a simulation result and comparisons with another method. >

Exact-image method for Gaussian-beam problems involving a planar interface

The exact-image method, recently introduced for the solution of electromagnetic field problems involving sources above a planar interface between two homogeneous media, is shown to be valid also for sources located in complex space, which makes its application possible for Gaussian-beam analysis. It is demonstrated that the Goos-Hanchen shift and the angular shift of a TE-polarized beam are correctly given as asymptotic results by the exact-reflection-image theory. Also, the apparent-image location giving the correct Gaussian beam transmitted through the interface is obtained as another asymptotic check. The theory described here makes it possible to calculate the exact coupling from the Gaussian beam to the reflected and refracted beams as well as to the surface wave.

The versatility of a multiformulational approach in the solution of electromagnetic field problems

In this paper the usefulness of a multiformulational approach to the numerical computation of electromagnetic fields of technical interest, including coupled problems, is discussed. Several field computation problems arising from various application areas are presented to sample some of the many formulations required to face the existing computational needs. The problems are solved by means of a code designed for a multiformulational management of field computation, and the versatility of the approach and the obtained results are discussed.

The potential integral for a polynomial distribution over a curved triangular domain

AbstractAn expression is derived for the potential at an arbitrary point due to a general polynomial distribution of source over a curved triangular domain. The expression is important for the numerical solution of electromagnetic field problems and generalizes the cases of linear and uniform distributions solved previously.

Interactive computer aided design of electric machines and electromagnetic apparatus (invited)

The design of electromagnetic devices in industry is still largely done using traditional techniques. Early computing facilities were costly to use and limited to alphanumeric applications. The application of numerical methods, mainly finite elements, to the solution of electromagnetic field problems, proved to be difficult to implement initially due to input/output problems. These difficulties were completely obviated by the advent of inexpensive microcomputers and low cost interactive graphics. However, it is still uncommon to find these new methods being employed as part of the normal electrical design process. Meanwhile, in parallel, there has been a massive growth of computer-aided methods applied to all aspects of mechanical engineering design and drafting, CADCAM. The trend is towards small, powerful, expandable, dedicated computer systems equipped with high resolution interactive graphics, which can be connected via a fast datalink. These are commonly available, complete with software, as turnkey systems. The advantages of CADCAM are manifold: Lower costs, higher productivity, higher quality products, with shorter lead times. The introduction of CADCAM will result in organisational as well as technical changes. The major change will be in the way people think.

The potential due to a uniform source distribution over a triangular domain

AbstractAn exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.

A computer package for the solution of electromagnetic field problems

A computer package for the solution of electromagnetic field problems