Search results

Problem 11 of the TEAM workshops for eddy current code comparison is a hollow conducting sphere in a uniform magnetic field. The applied field varies with time as a step function, requiring a fully transient solution. A total of 13 sets of results are presented in this paper from various groups employing 12 different computer codes. The numerical results are compared with an analytic solution to the problem.

Problem 6 of the International Workshop for Eddy Current Code Comparison is a hollow sphere in a uniform sinusoidal field. A total of 21 solutions, employing 17 different computer codes, are described and compared with analytic results. Several kinds of codes including 2‐D finite element, 3‐D finite element, and boundary element were found to give satisfactory solutions.

Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed” formulations have been elusive up to now. We propose one, based on a particular gauge, div(σ α)=−σ ²μ v, close to the “Lorenz gauge” of several recent publications, but not identical if one does not assume a piecewise uniform conductivity.

Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.

Problem 2 of the International Workshop for Eddy Current Code Comparison is a hollow cylinder with its axis perpendicular to a uniform sinuosoidal field. A total of 10 solutions, employing 9 different computer codes, are described and compared with analytic results. Most codes were 2‐D finite element and were found to give satisfactory solutions.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Two variational formulations of the eddy‐current problem in a bounded domain are considered. The first is based on the scalar magnetic potential and the vector potential of eddy currents; the second on the scalar and vector magnetic potentials. For both formulations existence and uniqueness of exact and approximate (finite element‐Galerkin's) solutions are proved. The correlation between the error of approximation and the error of the finite element solution is established.

Vector potential formulations of Maxwell’s equations need to be gauged, otherwise nodally based finite element approximations lead to an ill conditioned linear system. In this paper alternative Lorentz gauge formulations will be analysed. Particular attention will be paid to the conditions to be applied at material interfaces, bearing in mind ease of implementation in a finite element code and efficiency of solution. The methods discussed are designed to cope with the most challenging physical situations, namely, multiply connected abutting conductors made of different materials.

The purpose of this paper is to investigate the use of the finite element (FE) method in calculating accurate field gradients to achieve good estimates of aberration coefficients in accelerator tubes.

Gradient fields up to third order are calculated using FE calculations with higher order basis functions. A commercial code with the ability to use high order basis functions was embedded within the MathCad system which provides a convenient interface for evaluating the aberration coefficients. Analytic and realistic models are used to test the methodology.

It is shown that the ability to use higher order FEs achieves sufficient accuracy and smoothness to allow the third order aberration coefficients to be determined with confidence.

The results demonstrate the importance of using higher order basis FEs in determining optical properties of accelerator tubes and other particle optical devices.