Use of the Simultaneous Diagonalization Technique in the Alpha chi = lambda Beta chi Eigenproblem Applied to the Computation of the Characteristic Modes

Abstract

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 chi=lambda 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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2002
Accession Number
ADP013475

Entities

People

  • F. Venneri
  • G. Angiulli

Organizations

  • Mediterranea University of Reggio Calabria

Tags

DTIC Thesaurus Topics

  • Computations
  • Continuous Spectra
  • Current Density
  • Delta Functions
  • Eigenvalues
  • Eigenvectors
  • Electromagnetic Fields
  • Equations
  • Galerkin Method
  • Inversion
  • Matrix Theory
  • Method Of Moments
  • Plane Waves
  • Radiation
  • Scattering
  • Technical Information Centers
  • Theorems

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Statistical inference.