A reliable and efficient numerical method for indirect eigenvalue problems arising in waveguide and resonator analysis
✍ Scribed by Werner Schroeder; Ingo Wolff
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 154 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0894-3370
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✦ Synopsis
The solution of an indirect (also referred to as non-algebraic or nonlinear) eigenvalue problem is the "nal 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 ine$cient. 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 e!ect it thereby leads to a substantial reduction of numerical e!ort.