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Main Title: On adaptive finite element methods for the simulation of two-dimensional photonic crystals
Author(s): Froidevaux, Marine
Type: Research Paper
Abstract: The first part of this paper is devoted to the modeling of wave propagation inside a perfect two-dimensional photonic crystal and the spectral analysis of the resulting eigenvalue problem. In the second part of the paper, we focus on a special case, where the eigenvalue problem is linear and Hermitian. We introduce a residual-based estimator approximating the algebraic error, i.e., the error in the computed eigenvector induced by iterative methods. The estimator for the algebraic error approximates the error in the same norm as the one used in already existing estimators for the discretization error, therefore enabling error balancing between both types of errors, and thus improving the efficiency of the adaptive finite element procedure.
Subject(s): photonic crystals
error estimators
adaptive finite element methods
Issue Date: 31-Jul-2018
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 78M10 Finite element methods
65F15 Eigenvalues, eigenvectors
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2018, 06
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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