Loading...
Composing Scalable Nonlinear Algebraic Solvers
Brune, Peter R. Knepley, Matthew G. Smith, Barry F. Tu, Xuemin
Brune, Peter R.
Knepley, Matthew G.
Smith, Barry F.
Tu, Xuemin
Citations
Altmetric:
Abstract
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.
Description
Date
2015-11-05
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Iterative Solvers, Nonlinear Problems, Parallel Computing, Preconditioning, Software
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