Arbitrarily shaped hollow waveguide analysis by the alpha-interpolation method

The alpha-interpolation method (AIM) is presented as an efficient numerical method for the solution of hollow waveguide problems. The element matrix eigensystem for the AIM is presented, and the alpha-mass matrix is formulated as the weighted average, or interpolation, of the consistent mass matrix and the lumped mass matrix for the linear triangular elements. Numerical results are presented for the cases of rectangular waveguides and bent waveguides with nonconvex cross section, and it is shown that the convergence and accuracy of the AIM cutoff wavenumbers and exact eigenvalues are comparable to or better than those of the finite element method or the method of least squares boundary residuals.