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Mathematical Problems in Engineering
Volume 2014, Article ID 217869, 12 pages
Research Article

Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 19 September 2013; Accepted 3 March 2014; Published 8 April 2014

Academic Editor: Igor Andrianov

Copyright © 2014 Xin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.