Nonlinear optimization of the shape functions in the finite element method when determining cutoff frequencies of waveguides of arbitrary cross section

The present paper deals with a review of the recently developed k optimization process of the finite element method when solving eigenvalue problems. The methodology is then applied to the determination of the fundamental cutoff frequency of a hollow-piped waveguide of cardioidal cross section. It is shown that a considerable reduction in computer memory and/or CPU time is achieved.