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This paper deals with the fast computation of the quasi‐static fields induced in a conductor with a locally perturbed shape along the longitudinal axis and extruded along the transversal one. Besides, the material is composed of several homogeneous layers with parallel faces. The method used here is based on writing Maxwell's equations in a curvilinear system, which leads to a more simple expression...
This paper deals with the development of a semi‐analytical model for the fast computation of the quasi‐static field induced by any eddy current probe in a 3D conductor of complex shape. The workpiece is considered as a planar half‐space mock‐up with an interface air conductor characterized by an arbitrary 2D surface a(x, y). The curvilinear coordinate method consists in introducing a change of coordinates...
Two different techniques for the analysis of nonlinear, periodic eddy‐current problems are compared using a three‐dimensional benchmark problem. The methods are the parallel time periodic finite element method and the time periodic fixed‐point technique.
The issue of waveport modeling for the numerical simulation of electromagnetic devices using the discontinuous Galerkin time‐domain (DGTD) method is investigated. A new implementation of the waveport boundary condition (WPBC) is presented along with a fast evaluation of the required convolution. The performance of the WPBC for the DGTD simulation is then compared with that of the first‐order absorbing...
Proper generalized decomposition (PGD) is a promising model order reduction (MOR) technique to solve partial differential equations (PDEs). It usually bases on an explicit variable‐separated formulation of the problems to be solved. However, it can be expensive to derive the separated formulations. Also, the PGD process can become inefficient because of the massive separated terms. Another way of...
This work is concerned with the numerical treatment of the system of three‐dimensional frequency‐domain (or time‐harmonic) Maxwell equations using a high order hybridizable discontinuous Galerkin (HDG) approximation method combined with domain decomposition (DD) on the basis of hybrid iterative‐direct parallel solution strategies. The proposed HDG method preserves the advantages of classical DG methods...
The Multiple Multipole Program is a Trefftz method approximating the electromagnetic field in a domain filled with a homogeneous linear medium. MMP can easily handle unbounded domains; yet, it cannot accommodate inhomogeneous or nonlinear materials, situations well within the scope of the standard finite element method. We propose to couple FEM and MMP to model Maxwell's equations for materials with...
We propose four approaches to solve time‐harmonic Maxwell's equations in ℝ3 through the finite element method (FEM) in a bounded region encompassing parameter inhomogeneities, coupled with the multiple multipole program (MMP) in the unbounded complement. MMP belongs to the class of methods of auxiliary sources and of Trefftz methods, as it employs point sources that spawn exact solutions of the homogeneous...
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