  We propose a new computational framework that combines the recently developed
time-parallel (TP) and the compound wavelet matrix (CWM) methods. The
framework, termed tpCWM, offers significant computational acceleration by
making multiscale/multiphysics simulations computationally scalable in time and
space domains. We demonstrate the accuracy and the scalability of the method on
a prototype problem with oscillatory trajectory. The method corrects the coarse
solution by iterative use of the CWM, which compounds the fine and the coarse
solutions for the processes. Computational savings, over the fine solution as
well as the TP method, in terms of the real time required to perform the
simulations, can reach several orders of magnitude. We believe that this method
is general enough to be applicable to a wide-class of computational physics
problems. Tendency towards large number of cores and processors in parallel
computers is compatible with the computational scalability of the algorithm.
