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| Symplectic finite element formulation for three-dimensional electromagnetic field and computation of cavity resonances |
| Revised:April 29, 2004 |
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| DOI：10.7511/jslx20063059 |
| KeyWord:resonant cavity,duality system,maxwell's equations,finite element,eigenvalue |
| ZHENG Chang-liang CHEN Jie-fu |
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| Abstract: |
| Based on the form of duality system of Maxwell's equations and the variational principle for dual variables,a symplectic finite element formulation for 3D electromagnetic fields is derived in details.In order to maintain the symplectic conservation conditions of FEM formulation,the integrand in the variational principle is rewritten in symmetrical form for duality variables.The boundary integral terms of the variational principle are cancelled mutually for the adjacent elements.Because the dual variables are interpolated independently at C0 level,the difficulty of C1 continuity requirement is avoided.Zero eigenvalues can be eliminated using singular value decomposition(SVD) method.Numerical results for rectangular and cylinder cavity resonance demonstrate the efficiency of the symplectic finite element method. |
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