A STUDY ON THE 3-DIM. EIGENMODE OF THE RECTANGULAR RESONANT CAVITY BY FEM

FEM has been applied to obtain the 3-dim. eigenmode of the rectangular resonant cavity. The vector Helmholtz equation has been analysed for the resonant field strength in homogeneous media. An eigen-equation has been constructed from element equations basing on tangential edges of the tetrahedra element. This equation made up of two square matrices associated with the curl-curl form of the Helmholtz equation. To obtaine the more stable result, the equation was treated with the shift-invert strategy. By performing Krylov-Schur iteration loop on the eigen-equation, the matrix has been transformed into the Schur form. Eigen-values have been determined from diagonal elements of the Schur matrix. Eigen-modes were determined from the unitary similar transforming matrix of Krylov-Schur iteration loop. Eigen-pairs as a result have been revealed visually in the schematic representations