# Three‐dimensional eddy current analysis in unbounded domains by a DEM‐BEM formulation

Three‐dimensional eddy current analysis in unbounded domains by a DEM‐BEM formulation Purpose – To propose a novel 3D hybrid approach, based on a discrete formulation of Maxwell equations (the cell method – CM), suitable for solving eddy current problems in unbounded domains. Design/methodology/approach – Field equations for magnetodynamics are expressed directly in algebraic form thanks to the CM. The eddy current problem inside bulk conductors is formulated in terms of discrete modified vector potential, whereas magnetic scalar potential is used in order to model the free space. The CM is coupled to the boundary element method by using a surface boundary operator, which maps the surface magnetic fluxes to the surface magnetic scalar potentials. This leads to a unique set of linear equations to be solved in terms of discrete potentials. The eddy currents in bulk conductors are then obtained from discrete potentials. Findings – It is shown that formulation of hybrid approaches can be simplified by expressing field equations directly in algebraic form without need of weighted residual techniques. An original strategy, based on Green's formula for the magnetic scalar potential, is proposed in order to couple conducting parts to the exterior domain. Research limitations/implications – Conducting bodies with multiply connected parts cannot be modelled by the proposed approach, since it is based on the magnetic scalar potential. The resulting global matrix is partially dense and non‐symmetric; therefore, standard iterative solvers such as GMRES have to be used. Practical implications – The proposed approach can be suitably used for analyzing eddy current problems involving models with high degree of complexity, large air domains and moving parts. These are typical of induction heating processes. Originality/value – This paper proposes a new 3D hybrid approach, based on a discrete formulation of Maxwell equations. A novel coupling strategy relying on integral electromagnetic variables, i.e. magnetic fluxes and magnetic scalar potentials, is devised in order to solve uniquely for eddy currents inside conducting bodies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

# Three‐dimensional eddy current analysis in unbounded domains by a DEM‐BEM formulation

, Volume 27 (2): 7 – Mar 7, 2008
7 pages

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# References (7)

Publisher
Emerald Publishing
ISSN
0332-1649
DOI
10.1108/03321640810847742
Publisher site
See Article on Publisher Site

### Abstract

Purpose – To propose a novel 3D hybrid approach, based on a discrete formulation of Maxwell equations (the cell method – CM), suitable for solving eddy current problems in unbounded domains. Design/methodology/approach – Field equations for magnetodynamics are expressed directly in algebraic form thanks to the CM. The eddy current problem inside bulk conductors is formulated in terms of discrete modified vector potential, whereas magnetic scalar potential is used in order to model the free space. The CM is coupled to the boundary element method by using a surface boundary operator, which maps the surface magnetic fluxes to the surface magnetic scalar potentials. This leads to a unique set of linear equations to be solved in terms of discrete potentials. The eddy currents in bulk conductors are then obtained from discrete potentials. Findings – It is shown that formulation of hybrid approaches can be simplified by expressing field equations directly in algebraic form without need of weighted residual techniques. An original strategy, based on Green's formula for the magnetic scalar potential, is proposed in order to couple conducting parts to the exterior domain. Research limitations/implications – Conducting bodies with multiply connected parts cannot be modelled by the proposed approach, since it is based on the magnetic scalar potential. The resulting global matrix is partially dense and non‐symmetric; therefore, standard iterative solvers such as GMRES have to be used. Practical implications – The proposed approach can be suitably used for analyzing eddy current problems involving models with high degree of complexity, large air domains and moving parts. These are typical of induction heating processes. Originality/value – This paper proposes a new 3D hybrid approach, based on a discrete formulation of Maxwell equations. A novel coupling strategy relying on integral electromagnetic variables, i.e. magnetic fluxes and magnetic scalar potentials, is devised in order to solve uniquely for eddy currents inside conducting bodies.

### Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Mar 7, 2008

Keywords: Eddy currents; Electromagnetic induction; Magnetic fields; Heat treatment