Recursive Schur Decomposition

TL;DR

This paper introduces a parallel recursive algorithm based on multi-level domain decomposition as a preconditioner for Krylov methods, demonstrating excellent scalability for solving large sparse linear systems from PDE discretizations.

Contribution

The paper presents a novel parallel recursive algorithm using multi-level domain decomposition as a preconditioner for Krylov methods, effective for very large PDE-based linear systems.

Findings

Algorithm scales well with increasing sub-domains

Effective for systems with over a billion degrees of freedom

Performs efficiently across various PDEs and problem sizes

Abstract

In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization of partial differential equations (PDEs). We tested the effectiveness of the algorithm on several PDEs using different number of sub-domains (ranging from 8 to 32768) and various problem sizes (ranging from about 2000 to over a billion degrees of freedom). We report the results from these tests; the results show that the algorithm scales very well with the number of sub-domains.