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 language | English |
---|---|
Pages (from-to) | 4257-4289 |
Number of pages | 33 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 47 |
Issue number | 6 |
DOIs | |
Publication status | Published - 5 Mar 2010 |
Keywords
- Composite materials
- Edge element
- Homogenization
- Maxwell's equations
- Multiscale asymptotic expansion
ASJC Scopus subject areas
- Numerical Analysis