Overlapping Optimized Schwarz Methods for Parabolic Equations in n-Dimensions

TL;DR

This paper presents a new convergence proof technique for Overlapping Optimized Schwarz Methods applied to n-dimensional linear parabolic equations, focusing on boundary error estimates in overlapping regions.

Contribution

The paper introduces a novel analytical tool for proving convergence of Schwarz methods with multiple subdomains in high-dimensional parabolic problems.

Findings

Convergence of Schwarz methods established for n-dimensional parabolic equations.

Error estimates on boundary overlaps are key to the proof.

Method applicable to multisubdomain configurations.

Abstract

We introduce in this paper a new tool to prove the convergence of the Overlapping Optimized Schwarz Methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our guiding example is an n-Dimensional Linear Parabolic Equation.