'FINITE ELEMENT MODELLING OF ELECTROMAGNETIC WAVES IN DOUBLY AND TRIPLY PERIODIC STRUCTURES'

摘要

It has come to our attention that within the range of k_(0) values of the two dispersion curves shown in Fig. 12 of the above paper [1], other eigenvalues exist. In particular, there is a multiplicity of eigenvalues and in the B -> F region there is a distinct dispersion curve between the two shown. The aim in [1] was to apply the finite element method (FEM) to a 3-D triply periodic problem and demonstrate the FEM code/formulation accuracy. Owing to computational constraints, the structure in Fig. 11 of [1] was chosen because of its computational convenience, not its properties. Thus, it was not our intention to analyse exhaustively the dispersion characteristics of the structure which may have a poor electromagnetic bandgap behaviour. Consequently, only two distinct eigenvalues were computed, one at a time. These eigenvalues were identified at the start of the A->B region and their corresponding dispersion curves were plotted over all regions shown by using, for each set of ((beta)_(x), (beta)_(y), (beta)_(z)) values, the previously calculated eigenvalue and eigenvector as the initial guesses for the subspace iteration program. There were the following exceptions to this approach: (i) for the 1st eigenvalue, the first three values were computed by specifying a user defined initial guess; (ii) for the 2nd distinct eigenvalue, the first two values were computed by specifying a user defined initial guess.