  The efficient generation of meshes is an important component in the numerical
solution of problems in physics and engineering. Of interest are situations
where global mesh quality and a tight coupling to the solution of the physical
partial differential equation (PDE) is important. We consider parabolic PDE
mesh generation and present a method for the construction of adaptive meshes in
two spatial dimensions using stochastic domain decomposition that is suitable
for an implementation in a multi- or many-core environment. Methods for mesh
generation on periodic domains are also provided. The mesh generator is coupled
to a time dependent physical PDE and the system is evolved using an alternating
solution procedure. The method uses the stochastic representation of the exact
solution of a parabolic linear mesh generator to find the location of an
adaptive mesh along the (artificial) subdomain interfaces. The deterministic
evaluation of the mesh over each subdomain can then be obtained completely
independently using the probabilistically computed solutions as boundary
conditions. The parallel performance of this general stochastic domain
decomposition approach has previously been shown. We demonstrate the approach
numerically for the mesh generation context and compare the mesh obtained with
the corresponding single domain mesh using a representative mesh quality
measure.
