Efficient analysis of eigenvalue problems using higher order tetrahedral vector elements

3D electromagnetic eigenvalue problems are analyzed by using H₁(curl) tetrahedral vector elements. For a dense matrix algorithm, the number of zero eigenvalues is predicted exactly and the degree of suppression of spurious modes is discussed. For a sparse matrix solver, sparsity of global matrix is analyzed, only nonzero terms are stored, and the bandwidth of the matrix is reduced by RCM reordering technology. ARPACK eigensolvers based on sparse solving techniques are also applied to large-scale eigen-solution of complex cavities.