Finite macro-element method for two-dimensional eigen-value problems

This paper presents a finite macro-element method based on a new macro basis function constructed from the modal solutions of Helmholtz equation. Different from existing basis functions, the proposed macro basis function satisfies Helmholtz equation automatically, and it allows the use of coarse elements. As an example, the proposed method is applied to calculate the cutoff wavenumbers of waveguides, and its advantages are demonstrated.