T-Ω formulation with higher order hierarchical basis functions for non simply connected conductors

Ahmed Khebir,Ruben Specogna,Pawel Dlotko,Bernard Kapidani,Ammar Kouki

doi:10.1109/cefc.2016.7816343

Ahmed Khebir, Ruben Specogna + Show 3 more

Open Access

https://doi.org/10.1109/cefc.2016.7816343

Copy DOI

Abstract

This paper extends the T-Ω formulation for eddy currents based on higher order hierarchical basis functions so that it can deal with conductors of arbitrary topology. To this aim we supplement the classical hierarchical basis functions with non-local basis functions spanning the first de Rham cohomology group of the insulating region. Such non-local basis functions may be efficiently found in negligible time with the recently introduced DS algorithm.

Highlights

This paper considers the problem of computing the so-called eddy currents [1] that come up in an electrically conducting body when it is immersed in a slowly varying magnetic field h
We propose to perform the topological preprocessing with the DS algorithm which is, to the best of the authors knowledge, the first and so far the only fully automatic, provably correct, and fast way of obtaining cohomology generators
The main contribution of [20] and our paper is exactly to combine the use of cohomology theory [3] to the well-known T-Ω Finite Element formulation using hierarchical higher-order basis functions

Summary

Introduction

This paper considers the problem of computing the so-called eddy currents [1] that come up in an electrically conducting body when it is immersed in a slowly varying magnetic field h. If one wants to solve the eddy current problem with the magnetic scalar potential Ω in configurations containing topologically nontrivial conductors (e.g., conductors with “handles” like a torus), representatives of first cohomology group generators of insulator are the most efficient mean to make the problem well defined.

Results

Conclusion