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Journal Articles Numerical Methods for Partial Differential Equations Year : 2003

Exponential meshes and three-dimensional computation of a magnetic field

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Abstract

We describe the simulation of an exterior problem using a magnetic field deriving from magnetostatics, with a numerical method mixing the approaches of C. I. Goldstein and L.-A. Ying. This method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain. On this mesh, we use an edge elements discretization and a recently proposed mixed formulation. In this paper, we provide both a theoretical and numerical study of the method. We establish an error estimate, describe the implementation, propose some preconditioning techniques and show the numerical results. We also compare these results with those obtained from an equivalent boundary elements approach. In this way, we retain that our method leads to a practical numerical implementation, a saving of storage, and turns out to be an alternative to the classical boundary elements method.

Dates and versions

hal-00730196 , version 1 (07-09-2012)

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Cite

Jacques Laminie, François Alouges, Séraphin Mefire. Exponential meshes and three-dimensional computation of a magnetic field. Numerical Methods for Partial Differential Equations, 2003, 19 (5), pp.595-637. ⟨10.1002/num.10064⟩. ⟨hal-00730196⟩
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