L. Liu and D. E. Keyes
SIAM Journal on Scientific Computing, 37, pp. A1388-A1409, (2015)
Nonlinear equations, Nonlinear preconditioning, Field splitting, Newton method, NavierStokes equations
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 partitioning
of degrees of freedom in a nonlinear PDE system by field type rather
than by subdomain, where a modest factor of concurrency can be
sacrificed for physically motivated convergence robustness. ASPIN,
originally introduced for decompositions into subdomains, is natural for
high concurrency and reduction of global synchronization. We consider
both types of inexact Newton algorithms in the field-split context, and
we augment the classical convergence theory of ASPIN for the
multiplicative case. Numerical experiments show that MSPIN can be
significantly more robust than Newton methods based on global
linearizations, and that MSPIN can be more robust than ASPIN and
maintain fast convergence even for challenging problems, such as high
Reynolds number Navier--Stokes equations.