A MULTISCALE DOMAIN DECOMPOSITION ALGORITHM FOR BOUNDARY VALUE PROBLEMS FOR EIKONAL EQUATIONS.

In this paper, we present a new multiscale d omain decomposition algorithm for computing solutions of static Eikonal equations. In our new method, the decomposition of the domain does not depend on the slowness function in the Eikonal equati on or the boundary conditions. The novelty of our new method is a coupling of coarse grid and fine grid solvers to propagate information along the characteristics of the equation efficiently. The method involves an iterative parareal-like update scheme in order to stabilize the method and speed up convergence. One can view the new method as a general framework where an effective coarse grid s olver is computed "on the fly" from coarse and fine grid solutions that are computed in previous iterations. We study the optimal weights used to define the effective coarse grid solver and the stable update scheme via a model problem. To demonstrate the framework, we develop a specific scheme using Cartesian grids and the fast sweeping method for solving Eikonal equations. Numerical examples are given to show the method's effectiveness on Eikonal equations involving a variety of multiscale slowness functions. [ABSTRACT FROM AUTHOR]