Open Boundary Field Problems Research Articles

The Impedance of Two Parallel Plates

The impedance of two parallel plates affected by eddy currents due to skin and proximity effects is found analytically. To the author’s best knowledge, the formula for the reactance is new and incorporates its dependency on the distance between the plates. This part of the reactance is not affected by eddy currents. The analytical formulas are used to discuss the variation of the impedance with the ratio of width w of the plates to the penetration (skin) depth δ. It is shown that at high frequency the normalized resistance increases linearly with w/δ, whereas the normalized eddy current-dependent part of the reactance is inversely proportional to w/δ. This article also computes the problem numerically by the finite-element method, which is used as a tool to verify and compare. Numerical convergence analysis suggests that the open boundary field problem does not converge to the analytical solution as the aspect ratio of the plates increases. Hence, the assumption of parallel field lines should be used with caution.

Tackling Inhomogeneous Open Boundary Designs by the Finite-Element Method

In the course of designing and analyzing electromagnetic devices, open boundary field problems often need to be solved. The mapping of the infinite exterior of a finite circular region onto the interior of that closed circular region has emerged and established itself as one of the best methods. However, as a result of the work done in the past in solving homogenous exterior regions, this paper shows that this mapping method has been mistakenly taken to apply only when the exterior consists of air or, at best, some other homogeneous medium. This paper validates the method for problems with uniformly inhomogeneous exterior regions and makes possible the solution of a new class of problems by this powerful method.

Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic field

AbstractEddy currents are investigated in a ferromagnetic bar travelling in a transverse magnetic field. Such an open boundary field problem is analysed by a hybrid approach based on Galerkin finite element formulation coupled with a separation of variables. A steady state is considered, introducing time‐periodic boundary conditions. The resultant system of non‐linear equations is solved by an iterative procedure based on Brouwer's fixed‐point theorem. Numerical results are presented for a bar of circular cross‐section made of cast steel or cast iron. Selected examples of the field distribution and characteristics of eddy‐current power losses are enclosed in graphic form. Copyright © 2003 John Wiley & Sons, Ltd.

Fixed‐point technique in computing nonlinear eddy current problems

Eddy currents are investigated in a ferromagnetic bar exposed to a transverse magnetic field. Such an open boundary field problem is analysed applying the Galerkin finite element method coupled with a separation of variables. A steady state is considered, introducing time periodic conditions. The resultant system of nonlinear equations is solved using an iterative procedure based on Brouwer's fixed‐point theorem referred to the nonlinear material reluctivity. Numerical results are presented for a massive conductor made of cast steel and cast iron. The eddy‐current distribution and characteristics of power losses are illustrated in a graphic form.

MAGNETIC FIELD COMPUTATIONS IN THE INTERIOR AND EXTERIOR REGIONS BY USING INFINITE ELEMENTS

This paper describes numerical tests for a three dimensional infinite element suitable for finite element modelling of open boundary field problems. The infinite element has four nodes and is compatible with conventional cuboids. The effectiveness of the infinite element in the interior — finite element region is shown by comparing the accuracy and the CPU time when various boundary conditions are applied. The possibility of computing the external fields is also illustrated.

The application of the database method for 3-D open boundary field computation

A method for 3-D open boundary field problems, the database method, was developed previously by the authors (1990). The significance of the database method mainly depends on its universality and its applicability to practical problems. Several approaches in addition to those given previously are developed. They make the database method more universal, more applicable, and more convenient for users. Emphasis is placed on two new problems: (1) database generalization for different boundary conditions of geometrical symmetry and (2) condensed storage of database data. Two examples are used to show the applicability and effectiveness of the database method for various kinds of 3-D field problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A general transformation for open boundary finite element method for electromagnetic problems

A general transformation applicable to the solution of open boundary field problems using the finite element method is presented and discussed. The principle of the solution method lies in the spatial mapping of the infinite unbounded region, exterior to the main region of interest, onto a finite region, followed by the solution of the closed boundary problem for two connected regions. This technique, in the form presented, can be used in a standard finite element package without the need for any software modification, can be fully automated, and can be used in the presence of material inhomogeneities as well as anisotropies. Practical applications of the proposed technique are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A three-dimensional infinite element for modeling open-boundary field problems

A three-dimensional infinite element is considered which has four nodes and is compatible with conventional cuboids. The infinite element is being developed for exterior potential problems governed by Laplace's equation. The element is formulated in such a simple way that closed-form expressions for the element matrix are obtained. The element can easily be incorporated into existing finite element codes and its use does not destroy the symmetry and bandedness of the resulting system of equations. Two numerical examples are given. >

AN EFFICIENT OPEN BOUNDARY FINITE ELEMENT METHOD FOR ELECTROMAGNETIC PROBLEMS

An efficient approach for the solution of open boundary field problems with the finite element method is presented. The principle of the solution method consists in the spatial mapping of the infinite unbounded region, exterior to the main region of interest, onto a finite region and then in solving the closed boundary problem for two connected regions.

Efficient hybrid finite element-boundary element method for 3-dimensional open-boundary field problems

Highly storage-efficient choices of boundary meshes are devised for hybrid finite element-boundary element analysis in three dimensions, and a computationally efficient algorithm to solve the resulting matrix equations is developed. The boundary mesh makes use of cylindrical symmetry to produce block circulant boundary element matrices with proper choices of basis functions, and results in up to 64-fold reduction in matrix storage. The block circulant nature of the boundary element matrices provides a numerically efficient algorithm for solution of the coupled matrix equations. To demonstrate its efficiency, this hybrid scheme is applied to a three-dimensional magnetostatic field problem, proving storage and computational efficiency. This hybrid scheme is more advantageous than the pure finite-element method with approximate boundary conditions. and allows large three-dimensional open boundary field problems to be solved in small workstations. >

On the solution of open boundary field problems using the finite-element method

On the solution of open boundary field problems using the finite-element method