A Mixed Finite Element Method for 3-D Analysis of Cavity Resonators

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This paper presents a finite element method for 3-D analysis of an electro-magnetic eigenvalue problem for cavity resonators. First, we derive some weak formulations for this problem, a typical one of which is a mixed formulation that employs the Lagrange multiplier to deal with the divergence-free condition. Then we give a mixed finite element method based on the mixed formulation. We present concrete finite element models by the use of the Nedelec type finite element spaces for electric or magnetic fields. This approach is mathematically rigorous and is also convenient to deal with the electro-magnetic boundary conditions. We also present some finite element models for the analysis of axisymmetric cavities. Finally, some elementary numerical results are given to demonstrate the validity of our approach.
The University of Tokyo,Department of Mathematics, College of Arts and Sciences, University of Tokyo|Institute of Physical and Chemical Researchの論文