Lindsay Martin: A Parareal-like Domain Decomposition Algorithm for Boundary Value Problems for Eikonal Equations

Abstract: 

The Eikonal equation has many applications in optimal control, path planning, seismology, geometrical optics, etc. The equation is fully nonlinear and classified as a Hamilton-Jacobi equation. Many serial algorithms exist for computing numerical solutions to Eikonal equations. However, these algorithms have limitations when applied to large scale discretized systems. I will present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The 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. An adapted weighted version of the parareal method is used for stability, and the optimal weights are studied via a model problem. I will present numerical results to demonstrate the method.