Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

L. Liu, D.E. Keyes
SIAM Journal of Numerical Analysis, 54, 3145-3166, (2016)

Keywords

Nonlinear equations, Nonlinear preconditioning, Multiplicative Schwarz, Local convergence

Abstract

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by eld 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.

Code

DOI: 10.1137/15M1028182

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