LOCA method

LOCA method = {ss | zero | first | alc | tp | pf | hp}

Description/Usage

This optional card is used to specify one of the LOCA continuation algorithms. Valid options are:

ss

Steady state continuation, order to be indicated by the Continuation order card.

zero

Zero-order continuation.

first

First-order continuation.

alc

Arc length continuation.

tp

Turning point (fold) bifurcation tracking.

pf

Pitchfork (symmetry breaking) bifurcation tracking.

hp

Hopf bifurcation tracking.

This card is pertinent only if “loca” is indicated in the Continuation card. If not present, the default is zero.

Examples

To do first-order continuation using the LOCA algorithm, use:

LOCA method = first

To do turning point tracking in LOCA, use:

LOCA method = tp

Technical Discussion

Zero and first order continuation methods in LOCA are similar to those in ac_conti.c.

Arc length continuation is a bordered method to map solution in parameter-solution space; this method has additional optional input cards.

Turning point tracking is a bordered method to map a stability boundary in a two-parameter space; this method has additional required input cards.

Pitchfork tracking also has required cards (as for turning point tracking) to identify the second parameter, and requires an asymmetry eigenvector to be input via a separate EXODUS II file.

Hopf bifurcation tracking also requires cards to identify the second parameter, an initial guess of the bifurcation frequency (Ω), and the names of two EXODUS II input files for the real and imaginary parts of the initial complex null vector such that the corresponding eigenvalue is iΩ with zero real part. These eigenvectors would be generated by an eigensolve at a known Hopf point. To use this algorithm, the Aztec “komplex” library (currently residing in Trilinos) must be compiled in with Goma and the KOMPLEX flag included in the DEFINES list.

Theory

No Theory.

FAQs

No FAQs.

References

No References.