School of Mathematical & Statistical Sciences Faculty Publications

Deflation-Based Preconditioning for Parallel Time Stepping Algorithms

Document Type

Article

Publication Date

10-2026

Abstract

Often, in solving large systems of differential equations using a time-stepping algorithm, one must solve multiple linear systems where the coefficient matrix is unchanged or shifted by a constant multiple of the identity. This can be computationally expensive when the coefficient matrix involved is very large. Where direct methods like Gaussian elimination are infeasible, iterative methods like GMRES are often used. It is especially useful when the matrices involved are sparse or allow for fast matrix multiplication algorithms. In this paper, we propose preconditioning strategies that glean information from previous runs of GMRES to build an effective preconditioner for subsequent solves in order to lessen the number of iterations required per step. We explore implementations of this preconditioning method both in serial and in parallel.

Comments

Undergraduate Student publication. 

Copyright © SIAM

Publication Title

SIAM Undergraduate Research Online

DOI

10.1137/25S179350X

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