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A reliable and efficient numerical method for indirect eigenvalue problems arising in waveguide and resonator analysis
Author(s) -
Schroeder Werner,
Wolff Ingo
Publication year - 1999
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/(sici)1099-1204(199905/06)12:3<197::aid-jnm335>3.0.co;2-5
Subject(s) - eigenvalues and eigenvectors , scalar (mathematics) , mathematics , matrix (chemical analysis) , divide and conquer eigenvalue algorithm , numerical analysis , function (biology) , nonlinear system , algebraic number , resonator , gravitational singularity , mathematical analysis , algorithm , physics , optics , geometry , quantum mechanics , materials science , evolutionary biology , composite material , biology
The solution of an indirect (also referred to as non‐algebraic or nonlinear) eigenvalue problem is the final step of a variety of well established numerical methods for guided wave and resonator analysis. It amounts to a numerical search for the singularities of a matrix valued function of wave number or frequency. If a larger number of eigenvalues is required, such a procedure is often unreliable and inefficient. The present paper derives a novel approach, which by investigation of the full matrix function, instead of a scalar characteristic equation, assures reliable detection of large numbers of arbitrarily distributed simple or degenerated eigenvalues. The new Multiple Eigenvalue Search Algorithm allows for a sampling step width larger than the eigenvalue separation. As a side effect it thereby leads to a substantial reduction of numerical effort. Copyright © 1999 John Wiley & Sons, Ltd.