Composing Scalable Nonlinear Algebraic Solvers
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Issue Date
2015-11-05Author
Brune, Peter R.
Knepley, Matthew G.
Smith, Barry F.
Tu, Xuemin
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Type
Article
Article Version
Scholarly/refereed, publisher version
Rights
Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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Show full item recordAbstract
Most efficient linear solvers use composable algorithmic components, with the most common
model being the combination of a Krylov accelerator and one or more preconditioners.
A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition
of different nonlinear solvers may significantly improve the time to solution. We
describe the basic concepts of nonlinear composition and preconditioning and present a
number of solvers applicable to nonlinear partial differential equations. We have developed
a software framework in order to easily explore the possible combinations of solvers. We
show that the performance gains from using composed solvers can be substantial compared
with gains from standard Newton–Krylov methods.
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Citation
Brune, P. R., Knepley, M. G., Smith, B. F., & Tu, X. (2015). Composing Scalable Nonlinear Algebraic Solvers. SIAM Review, 57(4), 535-565. doi:10.1137/130936725
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