Laurent Santandrea

Calculation of eddy currents with edge elements on non-matching grids in moving structures

In this paper we present a nonconforming nonoverlapping domain decomposition method to approximate the eddy current problem, formulated in terms of the electric field variable, in nonstationary structures. This approximation, that allows for nonmatching grids at the sliding interface, is based on the mortar element method combined with edge elements in space and finite differences in time. Numerical results illustrate how the method works and the influence of the free part movement on the electric field distribution.

Adaptive Mesh Refinement and Probe Signal Calculation in Eddy Current NDT by Complementary Formulations

A local error estimation and adaptive meshing method for finite element analysis in eddy current nondestructive testing problems is proposed. Two dual formulations using Whitney elements have been applied to solve the magnetodynamic problem. By using this property of complementary, different error estimators were defined and were studied. These estimators are used for determining the mesh refinement zones. Numerical evaluations are given at the end of the paper, where the procedure of the adaptive meshing is presented and validated.

Torque calculation with conforming and nonconforming movement interface

This work analyzes the use of conforming and nonconforming movement techniques for torque calculation with high-order hierarchic interpolation in electrical machines thin air gaps. For the nonconforming movement formulation, the Lagrange multipliers are used. The moving band is used for the conforming case. The behavior of torque results as a function of interpolation order and air-gap thickness is discussed. In order to compare formulations, results for two thin air-gap machines are shown

Thin Crack Modeling in ECT with Combined Potential Formulations

The finite element modeling of thin cracks in ECT using a-psi and t-Phi combined vector-scalar potential formulations is presented with edge and nodal Whitney element discretization. The crack is treated as a non-conductive surface on which appropriate conditions are applied. A team workshop benchmark problem has been solved

Calculation of eddy currents in moving structures using a finite element method on non‐matching grids

This paper deals with the numerical simulation of eddy current distributions in non‐stationary geometries with sliding interfaces. We study a system composed of two solid parts: a fixed one (stator) and a moving one (rotor) which slides in contact with the former. We also consider a two‐dimensional mathematical model based on the transverse electric formulation of the eddy current problem whose approximation is performed via the mortar element method combined with the standard linear finite element discretization in space and an implicit first order Euler scheme in time. Numerical results underline the influence of the rotor movement on the current distribution and give an estimate of the power losses with respect to the rotor angular speed.

Mesh Refinement in Eddy Current Testing With Separated T-R Probes

In this paper we are interested in FEM mesh refinement procedure in ECT problems with separated T-R (Transmitter and Receiver probes) probes. Local error estimators used for a posteriori h-type mesh refinement are presented. They are based on the complementarity of the E and H formulations. A new estimator is proposed combining the solutions obtained by feeding alternatively the transmitter and the receiver. This estimator proves to be very accurate compared to classical ones.

An Overlapping Nonmatching Grid Mortar Element Method for Maxwell's Equations

In this paper, a new finite element mortar approach with moving nonmatching overlapping grids is introduced. The bidirectional transfer of information between the fixed and moving subdomains is realized for each new position of the moving part. Two numerical examples are presented to support the theory: 1) an electrostatic problem with known solution, to state the optimality of the method and 2) an eddy current nondestructive testing configuration, to underline the flexibility and efficiency of the proposed approach.

Use of Overlapping Finite Elements for Connecting Arbitrary Surfaces With Dual Formulations

In this paper, a method for the connection of non-conform arbitrary surfaces by overlapping finite element method is presented. Both scalar and vector degrees of freedom are considered. The use of reference elements allows to simplify the implementation of the method. Examples show the reliability of the method.

Modeling of magnetization curves of partially coupled superconducting filaments with dependence of current density according to applied magnetic field

The quality of magnetic field in the Large Hadron Collider (LHC) main magnets is determined by persistent currents distribution in the superconducting filaments. An examination of the magnetization of these superconducting filaments during the fabrication of the superconducting cable is thus necessary. A finite-element code is developed for prediction of the magnetization. We could compute the magnetization of coupled, partially coupled, and noncoupled superconducting filaments in two dimensions. We could also add the dependence of the current density according to the magnetic field. The effect of the space between the filaments has been studied too

FEM Technique for Modeling Eddy-Current Testing of Ferromagnetic Media With Small Skin Depth

The modeling of eddy-current testing problems, by means of finite elements, requires us to carefully consider the skin effect. When the material to inspect has a small skin depth compared with the other dimensions of the problem, which is a typical situation in the case of ferromagnetic media, the classical FEMs can become unsuitable in terms of mesh quality or computation time. In this paper, the overlapping FEM is implemented to efficiently consider the skin effect. 3-D problems are studied and the validity of the proposed approach is shown.