Patrick Dular

Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics

A method for defining global quantities related to fluxes and circulations is proposed in the frame of the finite element method. The definition is in perfect accordance with the discretized weak formulations of the problems. It therefore enables a natural coupling between local and global quantities in various formulations, while keeping a symmetrical matrix for the system, and then is open to the coupling of physical problems. Applications are given for electrostatics, magnetostatics and magnetodynamics.

Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms

A generalization of the Whitney complex is proposed, which is not now associated with simplices, i.e. tetrahedra in three dimensions, but with collections of three kinds of geometric elements: tetrahedra, hexahedra and prisms. Nodal, edge, facet and volume finite elements, i.e. mixed elements, associated with collections of those geometric elements, are defined. Base functions for approximation relative to these finite elements are defined and their properties are established. A geometric interpretation of these functions is given. >

A 3-D magnetic vector potential formulation taking eddy currents in lamination stacks into account

A method is developed to take the eddy currents in lamination stacks into account with the finite-element method using the three-dimensional (3-D) magnetic vector potential magnetodynamic formulation. It consists in converting the stacked laminations into continuums with which terms are associated for considering the eddy-current loops produced by both parallel and perpendicular fluxes. Two levels of accuracy are proposed. The best one is based on an accurate analytical expression of the eddy currents and makes the method adapted to a wide-frequency range, i.e., even for low skin depths in the laminations.

A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models

The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into account the eddy current effects in the stacked core without the need of modeling all laminations separately. A nonlinear constitutive magnetic law is considered. The system of nonlinear algebraic equations obtained after time discretization is solved by means of the Newton-Raphson scheme. By way of validation, the method is applied to a 3-D FE model of a laminated ring core with toroidal coil

A Galerkin projection method for mixed finite elements

The aim of the proposed method is the projection of an electromagnetic field belonging to a given function space (continuous or not) onto a discrete one spanned by finite element basis functions. This technique is useful for imposing inhomogeneous boundary conditions or volumic source fields, for calculating a dual field given the primal one or for mesh to mesh interpolation.

A general and natural method to define circuit relations associated with magnetic vector potential formulations

A procedure is proposed to deal with magnetic vector potential finite element magnetodynamic formulations and the definition of their associated circuit relations, involving voltages and currents, especially for massive inductors. It consists in solving two successive problems thanks to the use of edge elements, the first problem releasing the second one, which is especially useful for efficient nonlinear time stepping analyses.

Frequency-domain homogenization of bundles of wires in 2-D magnetodynamic FE calculations

A general approach for the frequency-domain homogenization of multiturn windings in two-dimensional (2-D) finite element (FE) calculations is presented. First, a skin and proximity effect characterization of the individual conductors, of arbitrary cross-section and packing, is obtained using a representative 2-D FE model. Herein, three excitation modes are considered, viz current and flux density in two perpendicular directions. In practical cases, the three modes are independent and the obtained frequency-dependent impedance and complex reluctivity tensor can be readily used in a FE model of the complete device. By way of example and validation, the method is applied to an inductor having an airgap and one of three different windings. The homogenized model produces global results (impedance versus frequency) that agree well with those obtained with a more precise FE model. In the latter, each turn of the winding is explicitly modeled and finely discretized.

A time-domain homogenization technique for laminated iron cores in 3-D finite-element models

The authors present a novel time-domain homogenization technique for laminated iron cores in three-dimensional (3-D) FE models of electromagnetic devices when using the magnetic vector potential formulation. The method is based on a polynomial orthogonal decomposition of the variation of the induction throughout the thickness of the laminations. The nonconstant components, due to skin effect, produce additional degrees of freedom and equations for the homogenized core. Insulating layers of finite width between the laminations (fill factor <1) are taken into account as well. A linear 3-D axisymmetric test case is considered. The results agree well with those obtained with the reference model, in which all laminations are finely discretized and the eddy currents are directly modeled.

Harmonic-balance finite-element modeling of electromagnetic devices: a novel approach

In this paper, a novel and easy-to-implement approach to the harmonic-balance finite-element modeling of electromagnetic devices is presented. The governing system of nonlinear algebraic equations is derived assuming an arbitrary (anisotropic) magnetic constitutive law. It is solved by means of the Newton-Raphson (NR) method, the elaboration of which is very simple thanks to the introduction of the differential reluctivity tensor. The method is validated by applying it to a three-dimensional and a two-dimensional voltage-driven model of a three-phase inductor. The convergence of the NR scheme and the accuracy of the obtained harmonic-balance current waveforms are studied.

A generalized source magnetic field calculation method for inductors of any shape

A general method to compute source fields in magnetostatics or magnetodynamics is presented for inductors of any shape. That source field is not the physical one because the zero divergence condition is not satisfied. However, the freedom so obtained is exploited to minimize its support as well as to reduce the CPU time. The use of edge finite elements enables its rigorous construction. A test problem illustrates the method.