Eigenvalue and eigenvector perturbation and adaptive mesh generation in the analysis of waveguides

The use of adaptive mesh generation in the analysis of waveguide modes is described. Two types of adaptive schemes are described, both of which are extensions of the nodal perturbation scheme for the Poisson equation. Under the first scheme, one examines the change in the eigenvalue of the mode of interest and repeatedly refines the mesh until the change is acceptable. The scheme gives reliable results but is not as economic as the second. The second scheme examines the change in the normalized eigenvector from mesh cycle to mesh cycle and accordingly refines the mesh at selective locations where the change is unacceptably high. The procedure accurately extracts a particular mode of the guide with great economy