  We use a time-relaxed linear grid generator of Winslow type to propose a new
deterministic-stochastic domain decomposition approach to the generation of
adaptive moving meshes. The method uses the probabilistic form of the exact
solution of the linear mesh generator to provide the sub-domain interface
values that serve as boundary conditions for the domain decomposition. The
meshes over the single sub-domains can then be obtained independently of each
other in an entirely parallel fashion. We demonstrate numerically the
capability of the method to yield smooth, time-evolving meshes.
