  We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP)
Algorithm to efficiently solve parabolic equations with heterogeneous
coefficients. This algorithm combines the advantages of multiscale methods that
can deal with heterogeneity in the spacial domain effectively, and the strength
of parareal algorithms for speeding up time evolution problems when sufficient
processors are available. We derive the convergence rate of this algorithm in
terms of the mesh size in the spatial domain, the level parameter used in the
multiscale method, the coarse-scale time step and the fine-scale time step.
Several numerical tests are presented to demonstrate the performance of our
algorithm, which verify our theoretical results perfectly.
