Perfect Conductor and Impedance Boundary Condition Corrections via a Finite Element Subproblem Method

Abstract

Abstract⎯ A finite element subproblem method is developed to correct the inaccuracies proper to perfect conductor and impedance boundary condition models, in particular near edges and corners of conductors, for a large range of conductivities and frequencies. Local corrections, supported by fine local meshes, can be obtained from each model to a more accurate one, allowing efficient extensions of their domains of validity.

Progressive inductor modeling via a finite element subproblem method

“…where µ p is the magnetic permeability (possibly function of b p in a nonlinear material), σ p is the electric conductivity, and h s,p and j s,p are VSs [2], [3]. They can be remnant fields in magnets or fixed current densities in conductors.…”

“…for changes from µ q and σ q for previous SP q to µ p and σ p for SP p in some regions [2], [3]. Also, BCs are defined for SSs, possibly expressed from previous solutions, i.e.…”

“…Instead of solving a complete inductor problem, including coil conductors and magnetic cores, it is here proposed to perform successive finite element (FE) calculations via a subproblem (SP) method (SPM) [1]- [3], mainly by separating the material regions, and giving them models of different accuracy levels. The aim is to lighten the computational efforts in the preliminary stages of a design, e.g.…”

“…in parameterized analyses, before refining the models. The idea of source and reaction fields is considered but, at the difference with the common method that adds these fields in the whole domain to define the total field, the source fields are here to be defined, via projections, only in the FE mesh of the added regions as local volume sources (VSs) [1]- [3]. They can even be initially reduced to the boundary of the added region, as local surface sources (SSs), which is an important aspect developed here, in particular for efficient calculations with source fields calculated via the Biot-Savart law.…”

Model refinements of transformers via a subproblem finite element method

“…It is based on a finite element (FE) subproblem (SP) method (SPM) with magnetostatic and magnetodynamic problems solved in a sequence on different adapted meshes [1]- [5], from simple 1-D models up to accurate 3-D models, in a large frequency range, of the magnetic circuits and their windings (stranded or massive coils). Each step of the SPM aims at improving the solution obtained at previous steps via any coupling of the following changes, defining model refinements: change from ideal to real (with leakage flux) flux tubes [1], change from 1-D to 2-D to 3-D [2], change of material properties [1]- [3] (e.g., from linear to nonlinear), change from perfect to real materials [4], change from single wire to volume conductor windings [4], [5], and newly developed change from homogenized [6] to fine models (cores as lamination stacks and coils as wire or foil windings, with the details affecting their high frequency behaviors). The methodology involves and couples numerous techniques that have been developed by the authors and, up to now, only applied for simplified test problems [1]- [5].…”