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

الملخص EN

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.