Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm
نویسندگان
چکیده
منابع مشابه
On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
The additive Schwarz preconditioned inexact Newton (ASPIN) method was recently introduced [X.-C. Cai and D. E. Keyes, SIAM J. Sci. Comput., 24 (2002), pp. 183–200] to solve the systems of nonlinear equations with nonbalanced nonlinearities. Although the ASPIN method has successfully been used to solve some difficult nonlinear equations, its convergence property has not been studied since it was...
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A nonlinear additive Schwarz preconditioned inexact Newton method (ASPIN) was introduced recently for solving large sparse highly nonlinear system of equations obtained from the discretization of nonlinear partial differential equations. In this paper, we discuss some extensions of ASPIN for solving the steady-state incompressible Navier-Stokes equations with high Reynolds numbers in the veloci...
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Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations F (u∗) = 0 arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust region, the methods often stagnate at local minima of ‖F‖, especially for problems with unbalanced nonlinearities, because the methods do not have bui...
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The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partiti...
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We propose and test a new class of two-level nonlinear additive Schwarz preconditioned inexact Newton algorithms (ASPIN). The two-level ASPIN combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. This approach is more attractive than the two-level method introduced in [Cai, Keyes, and Marcinkowski, Nonlinear additive Schwarz preconditioners and ap...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2016
ISSN: 0036-1429,1095-7170
DOI: 10.1137/15m1028182