Efficient generation of divergence-free fields for the finite element analysis of 3D cavity resonances

Spurious modes can be eliminated from the finite element solutions of three-dimensional resonant cavities by imposing solenoidality. The addition of a penalty term to the functional has the effect of pushing the spurious modes out of the range of interest. This approach is preferred because it does not destroy matrix sparsity; however, the selection of a suitable penalty parameter is difficult. A method is presented that allows for one penalty parameter per mode instead of one overall and adjusts the parameters automatically as the modes are computed. Results of using the method to analyze empty and dielectric-loaded cavities are presented