Use of the Simultaneous Diagonalization Technique in the Alpha chi = lambda Beta chi Eigenproblem Applied to the Computation of the Characteristic Modes
MEDITERRANEA UNIV CALABRIA (ITALY) DIPDI INFORMATICA MATEMATICA ELETTRONICAE TRASPORTI
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Characteristic modes developed by Carbacz, Harrington and Mautz have long been used in the analysis of radiation and scattering from conducting bodies and apertures. For their computation, it is necessary to solve an eigensystem of the form Alpha chilambda Beta chi. If the matrices Alpha, Beta are Hermitian and Beta is positive definite, the generalized eigenvalue problem can be accurately solved using the simultaneous diagonalization technique SDT. Because of numerical approximations and rounding sometimes it may happen that the matrices properties deteriorate and the SDT procedure becomes inapplicable. In this work a new technique, developed recently by Higham and Cheng is proposed as a method to solve these deteriorate cases. It is applied to the computation of the characteristic modes for some scattering problems. Results are analyzed and discussed.
- Theoretical Mathematics
- Radiofrequency Wave Propagation
- Electricity and Magnetism