3.2.5.5. Krylov-Newton Algorithm

algorithm KrylovNewton <-iterate $tangIter> <-increment $tangIncr> <-maxDim $maxDim> <-factorOnce>

Argument	Type	Description
$tangIter	string	tangent to iterate on, options are current, initial, noTangent. default is current.
$tangIncr	string	tangent to increment on, options are current, initial, noTangent. default is current
$maxDim	float	max number of iterations until the tangent is reformed and acceleration restarts (default = 3) of iterations within a time step until a new tangent is formed
-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

Krylov-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.

This command is used to construct a KrylovNewton algorithm object which uses a modified Newton method with Krylov subspace acceleration to advance to the next time step.

Note

References: * Scott, M.H. and G.L. Fenves. “A Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames.” Journal of Structural Engineering, 136(5), May 2010. DOI