Oszkar Biro

On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents

Various magnetic vector potential formulations for the eddy-current problem are reviewed. The uniqueness of the vector potential is given special attention. The aim is to develop a numerically stable finite-element scheme that performs well at low and high frequencies, does not require an unduly high number of degrees of freedom, and is capable of treating multiple connected conductors. >

Edge element formulations of eddy current problems

Abstract Various formulations of eddy current problems in terms of scalar and vector potentials are reviewed in the paper. The vector potentials are approximated by edge finite elements and the scalar potentials by nodal ones. The formulations are ungauged, leading, in most cases, to singular finite element equations systems. Special attention is paid to ensuring that the right-hand sides of the equations systems are consistent. The resulting numerical schemes prove to be as robust as the corresponding Coulomb gauged approaches realized by nodal elements.

Finite element analysis of 3-D eddy currents

The authors review formulations of three-dimensional (3-D) eddy current problems in terms of various magnetic and electric potentials. The differential equations and boundary conditions are formulated to include the necessary gauging conditions and thus to ensure the uniqueness of the potentials. Different sets of potentials can be used in distinct subregions, thus facilitating an economic treatment of various types of problems. A novel technique for interfacing conducting regions with an electric vector and a magnetic scalar potential to eddy-current-free regions with a magnetic vector potential is described. Finite-element solutions to several large eddy-current problems are presented. >

On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems

An overview of various finite element techniques based on the magnetic vector potential for the solution of three-dimensional magnetostatic problems is presented. If nodal finite elements are used for the approximation of the vector potential, a lack of gauging results in an ill-conditioned system. The implicit enforcement of the Coulomb gauge dramatically improves the numerical stability, but the normal component of the vector potential must be allowed to be discontinuous on iron/air interfaces. If the vector potential is is interpolated with the aid of edge finite elements and no gauge is enforced, a singular system results. It can be solved efficiently by conjugate gradient methods, provided care is taken to ensure that the current density is divergence free. Finally, if a tree-cotree gauging of the vector potential is introduced, the numerical stability depends on how the tree is selected with no obvious optimal choice available.

Finite‐element analysis of controlled‐source electromagnetic induction using Coulomb‐gauged potentials

A 3-D finite‐element solution has been used to solve controlled‐source electromagnetic (EM) induction problems in heterogeneous electrically conducting media. The solution is based on a weak formulation of the governing Maxwell equations using Coulomb‐gauged EM potentials. The resulting sparse system of linear algebraic equations is solved efficiently using the quasi‐minimal residual method with simple Jacobi scaling as a preconditioner. The main aspects of this work include the implementation of a 3-D cylindrical mesh generator with high‐quality local mesh refinement and a formulation in terms of secondary EM potentials that eliminates singularities introduced by the source. These new aspects provide quantitative induction‐log interpretation for petroleum exploration applications. Examples are given for 1-D, 2-D, and 3-D problems, and favorable comparisons are presented against other, previously published multidimensional EM induction codes. The method is general and can also be adapted for controlled‐so...

Numerical analysis of 3D magnetostatic fields

Formulations of three-dimensional magnetostatic fields are reviewed for their finite-element analysis. Partial differential equations and boundary conditions are set up for various kinds of potentials. Besides the method using two scalar potentials, several vector potential formulations are also discussed. Galerkin techniques combined with the finite element method are applied for the numerical solution of the boundary value problems. The effect of gauging the vector potential upon the numerical performance is investigated. Solutions by different formulations to a simple test problem and a benchmark problem involving relatively thin saturated iron plates are presented. The latter is compared to measured results. >

Different finite element formulations of 3D magnetostatic fields

Several finite-element formulations of three-dimensional magnetostatic fields are reviewed. Both nodal and edge elements are considered. The aim is to suggest remedies to some shortcomings of widely used methods. Various formulations are compared based on results for Problem No. 13 of the TEAM Workshops, a nonlinear magnetostatic problem involving thin iron plates. >

A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements

An advanced A-V method employing edge-based finite elements for the vector potential A and nodal shape functions for the scalar potential V is proposed. Both gauged and ungauged formulations are considered. The novel scheme is particularly well suited for efficient iterative solvers such as the preconditioned conjugate gradient method, since it leads to significantly faster numerical convergence rates than pure edge element schemes. In contrast to nodal finite element implementations, spurious solutions do not occur and the inherent singularities of the electromagnetic fields in the vicinity of perfectly conducting edges and corners are handled correctly. Several numerical examples are presented to verify the suggested approach.

Complex representation in nonlinear time harmonic eddy current problems

Several possibilities are presented to deal with nonlinearity in ferromagnetic media in the case of time harmonic excitation in steady state, without losing simplicity in describing the potentials by means of complex peak values. The main idea is to introduce a fictitious time independent and inhomogeneous material to take into account the nonlinear relationship between the field quantities. Four methods are shown and investigated on a 3D time harmonic eddy current problem, using the T,/spl Phi/-/spl Phi/ finite element formulation. The vector potential is represented by means of edge elements and the scalar potential by nodal elements. The results obtained are compared with transient computation.

FEM and evolution strategies in the optimal design of electromagnetic devices

The application of evolution strategies to the optimal design of electromagnetic devices is investigated. The corresponding field analysis is performed by the finite element method. The strategies involve a simplified simulation of biological evolution. They are especially advantageous in the case of strongly nonlinear optimization problems. The three strategies used are the (1+1), the