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Geometric interpretation of discrete approaches to solving magnetostatic problems

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2 Author(s)
F. Trevisan ; Univ. di Udine, Italy ; L. Kettunen

The finite-element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate to field problems on the discrete level. Although the finite-element technique is explained typically in terms of variational or weighted-residual approaches, another, less familiar way is available to introduce the same ideas geometrically. Using magnetostatics as an example, we will show how finite-element-type system matrices can be developed by exploiting the geometric properties of so-called Whitney elements. The simple interpretation we gain thereby enables us to view also the convergence properties of finite-element-type schemes in an intuitive way.

Published in:

IEEE Transactions on Magnetics  (Volume:40 ,  Issue: 2 )