Higher order 3D isoparametric finite elements for improved magnetic field calculation accuracy

The formulation and application of second-order isoparametric three-dimensional magnetic vector potential finite elements is described. For a hexahedral finite element, detailed expressions are derived for all the shape functions and their derivatives. A patch test is passed by hexahedrons of both f...

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Bibliographic Details
Published in:IEEE transactions on magnetics 1991-09, Vol.27 (5), p.4185-4188
Main Authors: Brauer, J.R., Larkin, L.A., MacNeal, B.E.
Format: Article
Language:English
Subjects:
Accuracy
Deformable models
Electromagnetism
electron and ion optics
Exact sciences and technology
Finite element methods
Fundamental areas of phenomenology (including applications)
Magnetic fields
Magnetostatics
Pathology
Permeability
Physics
Shape
Steel
Testing
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Summary:The formulation and application of second-order isoparametric three-dimensional magnetic vector potential finite elements is described. For a hexahedral finite element, detailed expressions are derived for all the shape functions and their derivatives. A patch test is passed by hexahedrons of both first and second orders. An extremely coarse mesh of both element orders is used to model the pathological problem of a closed steel loop deformed in three-dimensional space. The first-order elements are shown to give only 2.4% of the correct magnetic field in the steel, while the second-order elements are shown to give 80 to 96% of the correct magnetic field.< >
ISSN:0018-9464
1941-0069
DOI:10.1109/20.105024