Eigenvalues for ridged and other waveguides containing corners of angle 3 pi /2 or 2 pi by the finite element method

Abstract

Superelements developed to enable the finite-element method to be used for computing eigenvalues of the Laplacian over domains containing reentrant corners of angle 3 pi /2 or 2 pi are discussed. The superelements embody mesh refinement and include basis functions which emulate the singular behavior of the solution at the corner. Being compatible with linear or bilinear elements, the superelements are easily incorporated into standard finite element programs. The method which has been used to compute transverse electric (TE) and transverse magnetic (TM) mode eigenvalues for ridges and other waveguides is described. The results agree well with those obtained using various other methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>