Steve McFee

A tunable volume integration formulation for force calculation in finite-element based computational magnetostatics

A generalized formulation for net magnetostatic loading force calculation is derived from the Maxwell stress expression. The formulation yields a combined surface and volume integration method based on the magnetic flux density and an arbitrary scalar function g. The most interesting feature of the technique is its flexibility. For one choice of g, the method reduces to a distributed Maxwell stress scheme; for another, it yields a generalized version of the Coulomb virtual work implementation. With the introduction of an intelligent g-function based on local field-error, the new formulation yields a fully automatic method suitable for extracting accurate and consistent forces from imperfect numerical solutions. It is implemented for two-dimensional first-order finite elements, and two illustrative test problems are analyzed. The performance of the scheme is compared to the Maxwell stress and Coulomb approaches. >

Towards accurate and consistent force calculation in finite element based computational magnetostatics

Force calculations based on numerical field solutions represent an important step in the design of many electro-magneto-mechanical devices. Ensuring that the calculated forces are as accurate as possible for a given field solution is a requirement for any viable design system. This paper is concerned with the errors encountered in numerical force calculation and methods which avoid them.

Adaptive finite elements analysis of microwave and optical devices using hierarchal triangles

It is pointed out that adaptive methods using hierarchal triangles can automatically determine a good distribution of free parameters for the finite-element analysis of microwave and optical devices. Such methods avoid repeated mesh refinement; instead, they vary the polynomial order of the elements in different parts of the mesh. A simple yet effective method for hierarchal adaptation for high-frequency finite-element analysis is developed and evaluated. A simple wavelength criterion was shown to yield an effective initial distribution of degrees of freedom for the adaptive analysis of the microwave and optical devices considered. >

Towards optimal h-p adaptation near singularities in finite element electromagnetics

One of the most important problems of hybrid h-p adaption in finite element electromagnetics has been the accurate and efficient resolution of the singularities associated with sharp material edges and corners. One of the key obstacles has been the lack of objective standards by which to evaluate and compare adaptive control strategies. A set of optimal adaption benchmarks for the fundamental electromagnetic point and line singularity models is presented. The primary adaption procedures and control schemes are evaluated and compared. The absolute and relative performance of the competing approaches is discussed. >

Optimal discretization based refinement criteria for finite element adaption

One of the major research issues in adaptive finite element analysis is the feedback control system used to guide the adaption. Essentially, one needs to resolve which error data to feedback after each iteration, and how to use it to initialize the next adaptive step. Variational aspects of optimal discretizations for scalar Poisson and Helmholtz systems are used to derive new refinement criteria for adaptive finite element solvers. They are shown to be effective and economical for h-, p- and hp-schemes.

Automatic mesh generation for h-p adaption

In p-adaption, the density of degrees of freedom is controlled by adjusting the polynomial order of the finite elements. An ideal mesh is therefore as coarse as possible, subject to the constraint that the elements are not too thin. An algorithm capable of producing such meshes is described. The algorithm adds nodes to the mesh in a way which avoids thin triangles. It can also work in conjunction with a specified node density, and is therefore suitable for combined h-p adaptation. Sample meshes are presented for a dielectric waveguide structure, and an electric machine. >

Nested tetrahedral finite elements for h-adaption

A new tetrahedral finite element is proposed, which allows h-refinement to proceed simply, without the need to pay attention to the geometric quality of the elements. The new element is used to find the capacitance of various three dimensional structures h-adaptively. For one example, the h-adaptive mesh contains six times fewer degrees of freedom of a uniformly-refined mesh of equivalent accuracy.

Parallel Post-Processing Techniques for Fast Radar Cross-Section Computation

Parallel processing methods for accelerating radar cross-section (RCS) calculation for general 3D conducting targets are investigated and evaluated. The main focus of this work is to develop methodologies that exploit the use of parallel computing environments during the post-processing phase of general method of moments (MoM) programs used for surface integral equations. The primary objective of this research is to examine the processor requirements incurred when multiple processors are used to solve for an overall RCS in a parallel manner. A secondary goal of this study is to evaluate the solution accuracy of asymptotic waveform evaluation (AWE) based techniques used in conjunction with this parallel post-processing approach. A selection of illustrative and informative computational examples for benchmark RCS targets are solved and compared to direct MoM reference solutions using the CLUMEQ Supercomputing Centre at McGill University

Parallel and distributed processing for h-p adaptive finite-element analysis: a comparison of simulated and empirical studies

Parallel processing techniques have been widely promoted as a feasible, and even promising, solution to the very high computational costs associated with practical h-p adaptive finite-element analysis software tools for electromagnetic device design and system performance simulation. A combination of emulated and empirical studies designed to explore the validity of these claims are presented and compared. Practical parallel processing efficiency results, computed for Sun E450 and v880 parallel workstation platforms (four processors each), are reported.

Irregular triangles for finite element analysis in electromagnetics

The advantages and related costs of using irregular triangles for the finite element analysis (FEA) of electromagnetic systems are investigated. The modelling flexibility and efficiency of purely localized h-refinements for triangles are illustrated and evaluated. Practical implementation and application details for irregular triangle FEA modules are presented and discussed.