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Main Title: PDE Eigenvalue Iterations with Applications in Two-dimensional Photonic Crystals
Author(s): Altmann, Robert
Froidevaux, Marine
Type: Research Paper
Abstract: The first part of this paper is devoted to the approximative solution of linear and Hermitian eigenvalue problems where the differential operator satisfies a Garding inequality. For this, known iterative schemes for the matrix case such as the inverse power or Arnoldi method are extended to the infinite-dimensional case. This formally allows one to apply different spatial discretizations in each iteration step and thus, justifies the use of adaptive methods. The second part considers eigenvalue problems as they appear in two-dimensional models of photonic crystals for the computation of band-gaps. If the permittivity of the material is frequency-dependent, then this leads to a nonlinear eigenvalue problem. For this, we consider two strategies. First, a linearization combined with the application of the inverse power method and second, a direct application of Newton's iteration.
Subject(s): nonlinear eigenvalue problem
photonic crystals
inverse power
Newton iteration
Issue Date: 30-Jul-2018
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65N25 Eigenvalue problems
65J10 Equations with linear operators
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2018, 05
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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