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

TL;DR

This paper introduces a multiscale domain decomposition algorithm that accelerates the solution of static Eikonal equations using an iterative two-scale approach combined with a parareal-like update scheme, enhancing convergence and accuracy.

Contribution

It proposes a novel multiscale domain decomposition method with a parareal-like scheme tailored for Eikonal equations, improving computational efficiency and stability.

Findings

The method accelerates convergence compared to standard solvers.

Optimal weights for stability are identified through a model problem.

Numerical examples validate the effectiveness of the proposed algorithm.

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.