Nonlinear Krylov-Secant Solvers

Klíe, Héctor; Wheeler, Mary F.

doi:10.21236/ada446287

Search citation statements

Order By: Relevance

Paper Sections

Select...

Newton1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 33 publications

(48 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Quasi-Newton (QN). The class of methods for nonlinear systems of equations known as quasi-Newton methods [24] uses previous changes in residual and solution or other low-rank expansions [40] to form an approximation of the inverse Jacobian by a series of low rank updates. The approximate Jacobian inverse is then used to compute the search direction.…”

Section: Newtonmentioning

confidence: 99%

Composing Scalable Nonlinear Algebraic Solvers

Brune¹,

Knepley²,

Barry³

et al. 2015

SIAM Rev.

136

117

View full text Add to dashboard Cite

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.

show abstract

Section: Newtonmentioning

confidence: 99%