Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

Lulu Liu; David E. Keyes

doi:10.1137/15M1028182

Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

Lulu Liu, David E. Keyes

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

Original language	English (US)
Pages (from-to)	3145-3166
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	54
Issue number	5
DOIs	https://doi.org/10.1137/15M1028182
State	Published - Oct 26 2016

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https://repository.kaust.edu.sa/bitstream/10754/621850/1/15m1028182.pdf

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abstract = "The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.",

author = "Lulu Liu and Keyes, {David E.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported by the Extreme Computing Research Center at KAUST and by the Aramco KAUST Master Research Agreement ORS 1438",

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N2 - The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

AB - The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

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Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

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