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Communication Dans Un Congrès Année : 2016

A Efficient Integral Formulation for Electric Thin Region

Résumé

Different works have shown the interest of using Volume Integral Method (VIM) for 3D magnetic field analysis the main advantage being that the air region does not need to be meshed. Moreover solving Maxwell's equations by Green's Function Integral Equation Method has known a renewed interest in recent years, with the development of matrix compression algorithms (FMM, ACA) which greatly improves storage and resolution of full matrix systems. In this work we propose a specific formulation dedicated to thin region, based on a VIM circuit approach with the use of current meshes as unknowns. The formulation proposed allows solving electric thin regions problems or volume regions treated by surface impedance boundary conditions. Dynamic effects along the thickness of the thin region can be taking into account thanks to the use of an equivalent complex conductivity. Non simply connected regions are naturally taken into account thanks to a circuit approach, by the determination of a fundamental branch independent loop matrix Mc. For obtaining a quick and efficient matrix Mc, an unusual procedure is developed, with the help of the curl connectivity matrix Cc. The Cc matrix, which rely nodes and edges on the surface mesh, can be easily obtained from the finite element Whitney representation. In practice this incidence Cc matrix gives directly an independent branch loop matrix in the case of simply connected thin regions. In presence of non-simply connected regions, the matrix Cc is adapted thanks to a specific algorithm which allows determining the missing loops. Moreover, this approach allows obtaining a good convergence of the system when using an iterative solver. The figure below illustrates an example of a multiply connected conducting problem, with the use of a surface impedance boundary condition. Starting from the Cc matrix, two supplementary loops are found, corresponding to the eddy currents rotatable along the torus and the section. An example of a non-simply connected conducting problem (eddy currents on a torus)
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Dates et versions

hal-01306850 , version 1 (25-04-2016)

Identifiants

  • HAL Id : hal-01306850 , version 1

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Gérard Meunier, Jean-Michel Guichon, Olivier Chadebec, Jonathan Siau. A Efficient Integral Formulation for Electric Thin Region. EMF'2016 (10th International Symposium on Electric and Magnetic Fields), Apr 2016, Lyon, France. ⟨hal-01306850⟩
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