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Efficient computation of Maxwell eigenmodes in axisymmetric cavities using hierarchical vector finite elements
Author(s) -
Venkatarayalu Neelakantam V.
Publication year - 2009
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.741
Subject(s) - eigenvalues and eigenvectors , curl (programming language) , mathematics , basis function , maxwell's equations , mathematical analysis , lanczos resampling , finite element method , physics , computer science , quantum mechanics , thermodynamics , programming language
Computation of Maxwell eigenmodes in an axisymmetric cavity using hierarchical vector finite elements is presented. The use of curl conforming vector basis functions, which span the null space of the curl operator, leads to the appearance of spurious modes with zero eigenvalues. Such spurious modes lead to electric flux solution with non‐zero divergence. Constraining the solution space in the variational statement for the eigenvalue problem by weakly enforcing the flux to be divergence‐free leads to the elimination of such modes. Discrete equivalent of such a constraint equation is developed for axisymmetric problems solved using hierarchical vector and scalar basis functions of orders complete to p =2. The discrete constraint equation, developed individually for Fourier modes m =0 and m ≥1, is efficiently integrated with a subspace iteration‐based eigenvalue solution technique such as the Lanczos/Arnoldi method. The resulting solution technique is free of spurious modes added with an advantage of seeking a solution of a positive definite matrix during each iteration of the eigenvalue solver. Convergence in solution is demonstrated for orders up to p =2, while the proposed technique can be extended to basis functions of arbitrary order. Copyright © 2009 John Wiley & Sons, Ltd.