Inexact subdomain solves using deflated GMRES for Helmholtz problems

TL;DR

This paper demonstrates that using a two-level deflation preconditioner with GMRES allows for efficient inexact subdomain solves in Helmholtz problems, reducing computational cost for large-scale 3D high-frequency applications.

Contribution

It introduces an iterative approach with inexact subdomain solves combined with a two-level deflation preconditioner for Helmholtz problems, enhancing efficiency.

Findings

Inexact subdomain solves do not significantly increase outer iterations.

The method is promising for large 3D high-frequency Helmholtz problems.

Iterative subdomain solutions can replace direct methods effectively.

Abstract

We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method can be replaced with an iterative approach. This will be particularly important when solving large 3D high-frequency problems as subdomain problems can be too large for direct inversion or otherwise become inefficient. We additionally show that, even with a relatively low tolerance, inexact solution of the subdomain systems does not lead to a drastic increase in the number of outer iterations. As a result, it is promising that a combination of a two-level domain decomposition preconditioner with inexact subdomain solves could provide more economical and memory efficient numerical solutions to large-scale Helmholtz problems.