Spurious modes are eliminated from finite-element vector potential electromagnetic field calculations by transforming the basic dynamic equation into modal coordinates. First, model basis functions are obtained by solving the dynamic equation for its characteristic eigenvectors. The direct solution is then expressed as a sum of these basis vectors multiplied by unknown modal amplitudes. Matrices and loads are also transformed into modal coordinates. The resulting modal dynamic equation may then be solved using a variety of analysis techniques. If the basis is chosen to be divergence-free, then solutions are free of spurious modes. The standard penalty function method is shown to be an efficient means of constructing a divergence-free basis. Examples of modal eigenvalue analysis are discussed. Results are independent of the penalty parameter used.
Brauer, J.R., Arturo Cifuentes, L.A. Larkin, and B.E. MacNeal. "Elimination of Finite Element Spurious Modes Using a Modal Transformation Technique." IEEE Transactions on Magnetics 26, no. 5 (September 1990): 1765-1768.
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