On the stability and performance of the solution of sparse linear systems by partitioned procedures

TL;DR

This paper evaluates parallel Jacobi algorithms with various partitioning strategies for solving large sparse linear systems, demonstrating that substructuring methods outperform band-row splitting in terms of stability and performance.

Contribution

It introduces and compares different partitioned procedures for parallel Jacobi algorithms, highlighting the advantages of substructuring methods for large sparse systems.

Findings

Substructuring methods outperform band-row splitting strategies.

Partitioning impacts the stability and efficiency of parallel Jacobi iterations.

Numerical experiments confirm the effectiveness of substructuring in practical problems.

Abstract

In this paper, we present, evaluate and analyse the performance of parallel synchronous Jacobi algorithms by different partitioned procedures including band-row splitting, band-row sparsity pattern splitting and substructuring splitting, when solving sparse large linear systems. Numerical experiments performed on a set of academic 3D Laplace equation and on a real gravity matrices arising from the Chicxulub crater are exhibited, and show the impact of splitting on parallel synchronous iterations when solving sparse large linear systems. The numerical results clearly show the interest of substructuring methods compared to band-row splitting strategies.