A Multiscale Domain Decomposition Algorithm for Boundary Value Problems for Eikonal Equations

Abstract

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.

Erratum: A Multiscale Domain Decomposition Algorithm for Boundary Value Problems for Eikonal Equations

“…In section 4.3 of [1], the complexity and speed-up of the proposed algorithm were incorrectly stated. Section 4.3 should read as follows.…”