TY - JOUR
T1 - An Adaptive Inverse Iteration FEM for the Inhomogeneous Dielectric Waveguides
AU - Jianhua Yuan
JO - Journal of Computational Mathematics
VL - 2
SP - 169
EP - 184
PY - 2007
DA - 2007/04
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8683.html
KW - Waveguides, Eigenvalue Problem, Inverse Iteration Algorithm, Adaptive Finite
Element Method.
AB - <p style="text-align: justify;">We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iteration finite element algorithm. Adaptive finite element methods based on a posteriori error estimate are known to be successful in resolving singularities of eigenfunctions which deteriorate the finite element convergence. We construct a posteriori error estimator for the electromagnetic guided waves problem. Numerical results are reported to illustrate the quasi-optimal performance of our adaptive inverse iteration finite element method.</p>