Mode Tracking for Parametrized Eigenvalue Problems in Computational Electromagnetics
Keywords:
Eigenvalue Derivatives, Finite Element Method, Finite Integration Technique, Mode Tracking, Parametrized Eigenvalue ProblemsAbstract
An algorithm to perform a mode tracking for parameter dependent eigenvalue problems in computational electromagnetics is presented. It is based on a Taylor expansion using the derivatives of the eigenvalue and the eigenvector and allows distinguishing between intersection and touching points in the eigenvalue curves. The method is applied to discretizations with both the finite integration technique (FIT) and the finite element method (FEM), leading to simple and generalized eigenvalue problems, respectively. The applications include the calculation of the Brillouin diagram for a periodic structure and the variation of a material parameter in a filter structure.
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