Multiscale asymptotic method for Maxwell's equations in composite materials

Liqun Cao, Ya Zhang, Walter Allegretto, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

29 Citations (Scopus)

Abstract

In this paper we discuss the multiscale analysis of Maxwell's equations in composite materials with a periodic microstructure. The new contributions in this paper are the determination of higher-order correctors and the explicit convergence rate for the approximate solutions (see Theorem 2.3). Consequently, we present the multiscale finite element method and derive the convergence result (see Theorem 4.1). The numerical results demonstrate that higher-order correctors are essential for solving Maxwell's equations in composite materials.
Original languageEnglish
Pages (from-to)4257-4289
Number of pages33
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number6
DOIs
Publication statusPublished - 5 Mar 2010

Keywords

  • Composite materials
  • Edge element
  • Homogenization
  • Maxwell's equations
  • Multiscale asymptotic expansion

ASJC Scopus subject areas

  • Numerical Analysis

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