  In this paper, we present a new multiscale domain decomposition algorithm for
computing solutions of static Eikonal equations. The new method is an iterative
two-scale method that uses a parareal-like update scheme in combination with
standard Eikonal solvers. The purpose of the two scales is to accelerate
convergence and maintain accuracy. We adapt a weighted version of the parareal
method for stability, and the optimal weights are studied via a model problem.
Numerical examples are given to demonstrate the method.
