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On the property of the curl-curl matrix in finite element analysis with edge elements

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1 Author(s)
H. Igarashi ; Fac. of Eng., Kagawa Univ., Takamatsu, Japan

This paper discusses properties of the curl-curl matrix in the finite element formulation with edge elements. Moreover, the observed deceleration in convergence of the CG and ICCG methods applied to magnetostatic problems through the tree-cotree gauging is explained on the basis of the eigenvalue separation property. From the eigenvalue separation property it follows that neither minimum nonzero eigenvalue of the curl-curl matrix nor maximum one increase through the tree-cotree gauging. Hence it is concluded that the condition number of the curl-curl matrix tends to grow by its definition. Moreover, the maximum eigenvalue tends to keep constant whereas the minimum nonzero eigenvalue reduces. This property also makes the condition number worse

Published in:

IEEE Transactions on Magnetics  (Volume:37 ,  Issue: 5 )