3.2.5.6. Secant Newton Algorithm

This command is used to construct a SecantNewton algorithm object which uses the two-term update to accelerate the convergence of the modified newton method.

algorithm SecantNewton <-iterate $tangIter> <-increment $tangIncr> <-maxDim $maxDim> <-numTerms $numTerms> <-cutOut $R1 $R2> <-factorOnce>

Argument	Type	Description
-iterate	string	tangent to iterate on, options are current, initial, noTangent. default is current.
-increment	string	tangent to increment on, options are current, initial, noTangent. default is current.
-maxDim	integer	max number of iterations until the tangent is reformed and acceleration restarts (default = 3).
-numTerms	integer	number of terms in the secant accelerator update (default = 2).
-cutOut	list float	optional flag followed by cut-out factors $R1 and $R2 to suppress overly aggressive secant updates. Crisfield’s recommended values are 3.5 and 0.3.
-factorOnce	string	optional flag to assemble and factor the increment tangent in the first analysis step, keep it fixed in all later steps, and update it only after a domain change (for example, nodes or elements added or removed). Also accepted as -factorIncrementOnce.

Note

Secant-Newton already uses one increment tangent per equilibrium solve within each analysis step. -factorOnce carries that same tangent forward to later steps instead of reforming it each time. Using -increment initial with -iterate noTangent or -iterate initial also enables -factorOnce automatically. If -factorOnce is given without -iterate, OpenSees warns and defaults to -iterate noTangent. If -factorOnce conflicts with the chosen -iterate tangent (for example, -iterate current), OpenSees warns and disables -factorOnce.

Note

References:

• Crisfield, M.A. “Non-linear Finite Element Analysis of Solids and Structures”, Vol. 1, Wiley, 1991.