Communications in Mathematical Sciences

Volume 11 (2013)

Number 2

A fast algorithm for reiterated homogenization

Pages: 635 – 649

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2013.v11.n2.a16

Authors

Björn Engquist (Department of Mathematics and ICES, The University of Texas at Austin, U.S.A.)

Lexing Ying (Department of Mathematics and ICES, The University of Texas at Austin, U.S.A.)

Abstract

This paper considers the numerical evaluation of effective coefficients for multiscale homogenization problems and proposes a highly efficient algorithm for a certain class of reiterated homogenization problems of practical importance. The main idea of the proposed approach is to introduce a novel object called the homogenization map, approximate it through adaptive interpolation, and replace solutions of the cell problems with fast evaluations of the interpolant. Numerical results are provided for both 2D and 3D problems to demonstrate the efficiency and accuracy of the proposed algorithm.

Keywords

reiterated homogenization, upscaling, effective coefficients, homogenization map, fast algorithms, adaptive sampling

2010 Mathematics Subject Classification

35B27, 65K10, 65Y20

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