A Multiscale Domain Decomposition Algorithm For Boundary Value Problems For Eikonal Equations
For researchers solving boundary value problems for Eikonal equations, this algorithm offers a new iterative two-scale approach that improves convergence speed.
The paper presents a multiscale domain decomposition algorithm for static Eikonal equations, using a parareal-like update scheme to accelerate convergence while maintaining accuracy. Numerical examples demonstrate the method's effectiveness.
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.