A. Genon

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. >

Transformation methods in computational electromagnetism

The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.

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.

Modelling of electromechanical relays taking into account movement and electric circuits

This paper presents a numerical modelling of an electromechanical relay connected with an electric excitation circuit. This transient modelling not only takes into account the classical electromagnetic equations of the device but also the movement and circuit equations. The use of the finite element-boundary element coupling method facilitates the computation of the movement while the actual coupling with circuit equations is necessary for an accurate and reliable representation of transient phenomena. >

Modeling of ferromagnetic materials in 20 finite element problems using Preisach's model

A complete 2-D finite-element modeling for ferromagnetic materials is described. It is based on the definition of an adapted constitutive law which has to be completed by an hysteresis model like Preisachs one. A representation of the irreversible part of the ferromagnetic behavior by equivalent currents is given; a classical nonlinear system must be solved finally. Some numerical results are presented to underline the physical capacities of the method. Quantities like remanent induction and demagnetizing field can be calculated by this method. >

A discrete sequence associated with mixed finite elements and its gauge condition for vector potentials

A sequence of finite element spaces built on tetrahedra, hexahedra and prisms, is presented, and gauge condition for vector potential is shown to be well defined in these spaces. Results are presented for a modified vector potentials formulation for 3D eddy current problems. >

A coupling between electric circuits and 2D magnetic field modeling

A method which enables coupling between equations of electric circuits consisting of a lumped element RLC configuration and a magnetic field model is presented. The coupling between the finite-element and the boundary-element methods is used to compute the magnetic field produced by conductors excited by an electric circuit. The conductors involved in this computation may be connected according to any circuit topology and mixed with lumped elements. The method presented is general and allows a transient simulation of eddy current nonlinear problems with conductors excited by electric circuits. >

A posteriori error estimation and adaptive meshing using error in constitutive relation

The paper presents a method to control the quality of finite element solutions error in the constitutive relation. An a posteriori estimator is built up. Its construction is general and gives quantitative results about the accuracy of the solution. Both problems of control of quality and mesh optimisation are also discussed. Several examples are presented. A method used to compute a magnetic field that verifies Amperes law using only local calculations is presented.

Magnetostatic and magnetodynamic mixed formulations compared with conventional formulations

Mixed formulations are characterized by the use, of not only one kind of unknown, but of two distinct kinds of unknowns. Some well-known mixed finite elements are well suited to the approximation of electromagnetic fields. Several characteristics of magnetostatic and magnetodynamic mixed formulations are presented and discussed. The use of nodal, edge, facet and volume mixed elements enables their natural and rigorous discretization. Their advantages compared with conventional formulations are pointed out.

Error estimation and mesh optimisation using error in constitutive relation for electromagnetic field computation

This paper presents a complete methodology to control the quality of electromagnetic field computation using the finite element method. An error estimate is built up using the error in the constitutive relation. Proof is made that this estimate relates to the exact error in some cases. Both problems of control of quality and mesh optimisation are then discussed.