Peter P. Silvester

Spurious solutions to vector diffusion and wave field problems

Deterministic problems involving the vector Helmholtz and diffusion equations often exhibit spurious solutions when they are solved using finite-element methods. These nonphysical solutions arise from the same causes as the well-known spurious propagating modes encountered in high-frequency modal analyses. Using postprocessing techniques, these nonphysical solutions are shown to be responsible for inaccuracies in both modal and deterministic solutions throughout the frequency spectrum. Solution accuracy is recovered through use of mixed-order elements that are known to produce spectrally correct finite-element solutions. >

Effective computational models for anisotropic soft B-H curves

The flux density B for a magnetic field H in a soft magnetic material is given by the derivatives of the stored coenergy density with respect to the components of H. Any single-valued nonlinear tensor permeability may therefore be stored compactly, and retrieved with little computation, by storing its coenergy density as a function of position in H-space. In a dual form, H can be found by differentiating the stored energy density with respect to the components of B. Computational experiments show that sufficient accuracy can be achieved using cubic splines or other C/sup 2/-continuous approximating functions. >

Differentiation of finite element approximations to harmonic functions (EM field computation)

Derivatives of finite-element solutions are essential for most postprocessing operations, but numerical differentiation is an error-prone process. High-order derivatives of harmonic functions can be computed accurately by a technique based on Greens second identity, even where the finite element solution itself has insufficient continuity to possess the desired derivatives. Data are presented on the sensitivity of this method to solution error as well as to the numerical quadratures used. The procedure is illustrated by application to finding second and third derivatives of a first-order finite-element solution. >

Sensitivity maps for metal detector design

Eddy-current or permeability-contrast based metal detectors may be characterized by static sensitivity maps, a new graphic representation that maps detector response to a standardized infinitesimal object in a static field. A sphere is shown to be a suitable standard object because its behavior describes, to within multiplicative constants, objects of arbitrary conductivity and permeability. Static sensitivity maps take full account of both the excitation and detection coil shapes. They are compact, easy to understand, closely related to industrial testing procedures, and likely to prove a useful design tool. Their usefulness is illustrated by examples based on a metal detector for which published data exist.

MODAL NETWORK REPRESENTATION OF SLOT-EMBEDDED CONDUCTORS

ABSTRACT A conductor or group of conductors in a slot can be given a circuit representation exact for any form of terminal excitation if the surrounding iron is not very heavily saturated. The exact network has infinitely many R-L branches, but for most practical purposes it is sufficient to consider only a few. Determination of the network parameters requires solution of one field problem only, all subsequent calculations being of a circuit type and usually quite simple.

Differentiation of finite-element solutions of the Poisson equation

A technique, based on Greens second identity, is developed for accurate computation of first and second derivatives of potential functions in fields governed by Poissons equation. The method is not sensitive to data error, and derivatives can be computed to an accuracy at least comparable to that of the potential itself. In C0-continuous finite-element solutions, where second derivatives do not exist, several correct significant figures are still available in the second derivatives. Test data are presented on the sensitivity to solution error as well as the numerical quadrature used. The procedure is illustrated by finding first and second derivatives of a first-order finite-element solution of Poissons equation in a square region. >

Sensitivity of metal detectors to spheroidal targets

The sensitivity of magnetic metal detectors to prolate or oblate spheroidal targets depends both on the semiaxis ratio and on the orientation of the spheroid polar axis relative to the local magnetic field. A spherical target produces null response only if the generator and detector coil magnetic fields are orthogonal, but the spheroid possesses a null direction for a large range of magnetic field orientations. A spheroid can therefore be made undetectable by rotating it into a particular orientation. The existence of such blind-position angles is investigated theoretically in detail and families of curves are given to illustrate them in a particular case.

Numerical differentiation in magnetic field postprocessing

Postprocessing encompasses graphic display and numerical computation. The critical process in this work is numerical differentiation. Methods of numerical differentiation of approximate solutions may be divided into three groups: direct numerical differentiation, smoothing methods based on superconvergence properties, and methods that exploit properties the solution is known to possess though the numerical approximation does not. The choice of method is determined by the problem, as well as the use to which derivatives are put: graphical display, local field calculation, mesh refinement or a a posteriori error estimation. The paper compares current derivative extraction methods and reviews progress in this field, with particular attention to superconvergent patch recovery and methods based on Greens second identity. A new modification of the method based on Greens second identity is presented, to include inhomogeneous and discontinuous materials.

Symbolic generation of finite elements for skin-effect integral equations

Skin effect at high frequencies and electrostatics of good conductors can be formulated as an integal equation, whose solution by finite elements requires evaluation of integrals with Greens function kernels. The singular element integrals are computed analytically by a program in the Maple language, after recasting the integrals by coordinate transformations that render all singularities one-dimensional. Tables of singular integrals are given for elements up to order 4. >

Introducing computer structure by machine simulation

A simple computer simulator used to introduce freshmen engineering students to machine structure through assembly programmable is described. A four-week course module is described, suited to the IEEE curriculum recommendations. It is built around a simulator called Simian and an accompanying assembler keyed to the IEEE-694 standard. Simian simulates a byte-addressable 32-bit machine, continuously displaying register contents and selected portions of memory. Version of Simian exist for both Unix and MS-DOS, permitting students to use it both in the laboratory and on personal computers. Learning time for Simian itself, a critical parameters in simulators designed for teaching, is 1-2 hours for students with little prior computer experience. >