J. D'Angelo

Three-dimensional vector potential analysis for machine field problems

Modern electrical plant and machinery have to be designed to operate at high power densities at minimum cost and optimal efficiency with a high degree of reliability during operation. These stringent requirements necessitate accurate performance prediction at the design stage. As a first and important step in this process, the magnetic field distribution must be evaluated taking full account of the geometrical complexity of the field region, magnetic saturation of the iron parts, and circulating currents in conducting media. The advent of digital computers has spurred the development of sophisticated numerical techniques to accomplish this task with a high degree of precision. In this paper, three-dimensional vector potential solution methods for linear and nonlinear diffusion and magnetostatic field problems are presented. The methods are illustrated by numerical examples where feasible. This research has been partially funded by the Electric Power Research Institute, Palo Alto, California under EPRI contract RP 1288-1.

A new scalar potential formulation for three-dimensional magnetostatic problems

A new scalar potential formulation for three-dimensional problems is described. This formulation avoids cancellation errors within ferromagnetic objects and discontinuities and nonuniqueness of a scalar potential outside these objects. These deficiencies are peculiar to reduced and total scalar potential formulations, respectively. The finite-element discretization is applied to the new scalar potential formulation, and a novel approach to smoothing and extension of finite-element solutions is presented. Some numerical results obtained using the new scalar potential formulation are reported.

Finite Element Methods for the Solution of RF Radiation And Scattering Problems

ABSTRACT This paper presents the methods and results of using partial differential equation techniques for the solution of RF radiation and scattering problems. Specifically, frequency domain finite elements coupled with absorbing boundary conditions are extensively covered. Two-dimensional and three-dimensional formulations and computational results are presented. The two-dimensional formulation uses standard finite elements with either the Engquist-Majda or Bayliss-Turkel absorbing boundary conditions. The three-dimensional formulation also uses absorbing boundary conditions and finite elements, however, new, non-standard finite element basis functions specifically developed for vector field problems are used. These vector finite element basis functions are known as “edge-elements.” [1]

On the use of local absorbing boundary conditions for RF scattering problems

Results are presented for combining the finite-element method with two types of absorbing boundary conditions (ABCs): the Engquist-Majda and the Bayliss-Turkel. The results are compared with closed-form solutions and with the results of hybrid techniques. Both absorbing boundary conditions are of the second order. All of the examples are for two-dimensional frequency-domain scattering problems. It is found that the Bayliss-Turkel ABC is more accurate than the Engquist-Majda type. Additionally, the Bayliss-Turkel ABC allows the exterior boundary to be brought closer to the object of interest, thereby reducing the number of unknowns and the computational effort. However, the Bayliss-Turkel ABCs become complicated if the exterior boundary is not circular. >

Finite element applications in electrical engineering

A description of the finite element method and its specialization to low-frequency electrical applications is presented. Field plots of illustrative examples of devices are also shown. Attention is given to some of the problems encountered in modeling two- and three-component vectors, the use of edge elements, and force calculations. Accurate and computationally economical one-component vector potential methods for 2-D magnetostatic and eddy current problems appear to be the representation of choice. A total scalar potential solution for electrostatic fields and a modified reduced scalar potential solution described here for the 3-D magnetostatic problem may prove most suitable. >

A new point of view on the mathematical structure of Maxwell's equations

It is emphasized that the Maxwell equations have a peculiar mathematical structure which leads to boundary value problems with an overspecified number of partial differential equations and an underspecified number of boundary conditions. An attempt is made to reduce these boundary value problems to standard mathematical formulations with equal numbers of partial differential equations and boundary conditions. It is demonstrated that these formulations have some attractive features which appreciably facilitate their finite element discretizations. A numerical example involving scattering of plane electromagnetic waves from a perfect conducting thin plate illustrates the discussion. >

Finite element analysis of large wavelength antenna radome problems for leading edge and radar phased arrays

A method for determining the RF performance from antenna radome configurations based on a frequency-domain finite-element method is presented. The application of this analysis on the design of antenna arrays in aircraft leading edges and radar radomes is discussed. The modeled antenna array elements can be driven with arbitrary amplitude and phase weighting for sidelobe tapering and phased steering of the pattern. The understanding of near-field radiation and coupling interactions is an important design aid. Physical phenomena such as resonances are observed in the predicted near-field results. >

Hybrid finite element/boundary element analysis of a stripline notch array

The results of a two-dimensional finite-element/boundary-element time-harmonic analysis of an eight-element stripline notch phased array are presented. The hybrid finite-element/boundary-element method can be used for both near and far-field radiation and scattering analysis. The boundary-element method is used for the exterior far-field region, and the finite-element method is used for the near-field antenna/scatterer region. Predictions are given and compared with measured results of array-element pattern, gain vs. frequency, and array scanned pattern.<<ETX>>

Three-component, two-dimensional analysis of the eddy current diffusion problem

In many electrical engineering applications, one is required to solve the electromagnetic field problem taking into account the effect of induced currents in conducting parts. Since the geometry of the structure is complex and the source distribution, in many cases, is multidimensional, a truly three-dimensional analysis is required to obtain the eddy current distribution in the volume of the conducting structure. This 3D analysis not only is difficult and cumbersome, but also yields a field distribution that is difficult to comprehend. It is, therefore, necessary to construct simpler two-dimensional models as a step in understanding and validating three-dimensional models. Previously, 2D analyses concentrated on a one-component formulation of the eddy current diffusion problem in a 2D geometry. These techniques are inadequate to obtain the eddy current distribution in the presence of a flaw, as occurs in nondestructive evaluation applications. In this paper, a new three-component formulation is presented to represent source current and eddy current fields accurately. The method is validated by comparison with closed form solutions for simplified geometries.

Parallel computing for RF scattering calculations

Three-dimensional RF scattering calculations for objects of realistic complexity, which require parallel computational methods in order to be feasible for design tradeoff studies, are discussed. Two basic approaches to obtaining parallel speed improvements are vectorization and full parallel processing. In the latter category are shared-memory and distributed-memory multiprocessor machines. The approaches to parallel computation are reviewed, and the changes required to adapt RF scattering analysis to each major parallel architecture are considered. A comparison of conversion effort and execution performance is presented for representative computers. >