LOCA Parameter Reference Page

As in NOX, all parameters are passed to LOCA through parameter lists defined by the NOX::Parameter::List class. Nearly all parameters are passed to the LOCA::Stepper class during construction, although a few can be passed to the LOCA::Abstract::Group. Below is a listing of all of the parameters that can be passed to the stepper with links to relevant classes that use those parameters, followed by parameters that can be passed to the LOCA::Abstract::Group constructor.

Stepper Parameters

The parameter list passed to the Stepper has two sublists, "LOCA" and "NOX". The "LOCA" sublist contains parameters and sublists for the Stepper and various LOCA support classes, while the "NOX" sublist contains parameters and sublists specific to NOX solvers. The NOX sublist is passed directly to an instance of the NOX::Solver::Manager class in the Stepper and therefore has the same structure as any NOX solver parameter list hierarchy. Please see the NOX Parameter Reference page for more details on the structure of this list.

• "NOX" sublist -- See NOX Parameter Reference for more details
• "LOCA: sublist
  • "Stepper" sublist -- used by LOCA::Stepper to set parameters relevant for continuation run
    • "Continuation Method" -- [string] (default: "Natural") Type of continuation to use. Choices are:
      • "Natural" -- Natural continuation (LOCA::Continuation::NaturalGroup)
      • "Arc Length" -- Pseudo arc-length continuation using bordering (LOCA::Continuation::ArcLengthGroup)
      • "Householder Arc Length" -- Pseudo arc-length continuation using Householder transformations (LOCA::Continuation::HouseholderGroup)
    • "Continuation Parameter" -- [string] (Must be supplied) Name of continuation parameter
    • "Initial Value" -- [double] (Must be supplied) Initial value of continuation parameter
    • "Max Value" -- [double] (Must be supplied) Maximum value of continuation parameter
    • "Min Value" -- [double] (Must be supplied) Minimum value of continuation parameter
    • "Max Steps" -- [int] (default: 100) Maximum number of continuation steps (including failed steps)
    • "Max Nonlinear Iterations" -- [int] (default: 15) Maximum number of nonlinear iterations per continuation step
    • "Enable Arc Length Scaling" -- [bool] (default: true) Enable arc-length scaling to equilibrate solution and parameter components to arc-length equations (see LOCA::Continuation::ArcLengthGroup)
    • "Goal Arc Length Parameter Contribution" -- [double] (default: 0.5) Goal for parameter contribution to arc-length equation
    • "Max Arc Length Parameter Contribution" -- [double] (default: 0.0) Max for parameter contribution to arc-length equation, triggering rescaling
    • "Initial Scale Factor" -- [double] (default: 1.0) Initial scale factor for parameter term of arc-length equation
    • "Min Scale Factor" -- [double] (default: 1.0e-3) Minimum scale factor for scaling parameter term of arc-length equation
    • "Enable Tangent Factor Step Size Scaling" -- [bool] (default: false) Enable step size scaling by cosine between two consective tangent vectors and to continuation curve: where is the tangent factor exponent.
    • "Min Tangent Factor" -- [double] (default: 0.1) Minumum cosine between two consecutive tangent vectors, below which the continuation step is failed
    • "Tangent Factor Exponent" -- [double] (default: 1.0) Exponent on the cosine between two consecutive tangent vectors, which then modifies the step size
    • "Compute Eigenvalues" -- [bool] (default: false) Flag for requesting eigenvalue calculation after each continuation step
  • "Bifurcation" sublist -- used by LOCA::Bifurcation::Manager to determine what type of bifurcation calculation, if any, to use
    • "Method" -- [string] (default: "None") Bifurcation method to use. Choices are
      • "None" -- No bifurcation and do equilibrium continuation instead
      • "Turning Point" -- Turning point tracking using bordering (LOCA::Bifurcation::TPBord::ExtendedGroup)
      • "Modified Turning Point" -- Turning point tracking using modified bordering to avoid singular Jacobian solves (LOCA::Bifurcation::TPBord::ModifiedBorderingGroup)
      • "Nic-Day Modified Turning Point" -- Turning point tracking using a combination of Nic-Day deflation ideas with the modified turning point approach (LOCA::Bifurcation::TPBord::NicDayModifiedBorderingGroup)
      • "Pitchfork" -- Pitchfork tracking using bordering (LOCA::Bifurcation::PitchforkBord::ExtendedGroup)
      • "Hopf" -- Hopf point tracking using bordering (LOCA::Bifurcation::HopfBord::ExtendedGroup)
    • "Bifurcation Parameter" -- [string] (Must be supplied if "Method" is not "None") Name of bifurcation parameter
    • "Length Normalization Vector" -- [NOX::Abstract::Vector*] (Must be supplied if "Method" is not "None) Pointer to NOX::Abstract::Vector holding length normilization vector used in turning point, pitchfork, and Hopf bifurcation algorithms
    • "Initial Null Vector" -- [NOX::Abstract::Vector*] (Must be supplied for tuning point and pitchfork problems) Initial guess for null vector in turning point and pitchfork algorithms
    • "Asymmetric Vector" -- [NOX::Abstract::Vector*] (Must be supplied for pitchfork problems) Pointer to NOX::Abstract::Vector holding asymmetric vector used in pitchfork algorithm
    • "Initial Real Eigenvector" -- [NOX::Abstract::Vector*] (Must be supplied for Hopf problems) Initial guess for real component of generalized eigenvector in Hopf algorithm
    • "Initial Imaginary Eigenvector" -- [NOX::Abstract::Vector*] (Must be supplied for Hopf problems) Initial guess for imaginary component of generalized eigenvector in Hopf algorithm
    • "Initial Frequency" -- [double] (Must be supplied for Hopf problems) Initial guess for Hopf frequency in Hopf algorithm
    • "Perturb Initial Solution" -- [bool] (default: false) Flag indicating whether to apply an initial perturbation to the initial guess for the solution vector before starting bifurcation algorithm
    • "Relative Perturbation Size" -- [double] (default: 1.0e-3) Size of relative perturbation of initial guess for solution vector
  • "Predictor" sublist -- used by LOCA::Predictor::Manager to determine what type of predictor to use for each continuation step
    • "Method" -- [string] (default: "Constant") Predictor method to use for computing the initial guess for each continuation step. Choices are
      • "Constant" -- Use previous solution as initial guess for next step (LOCA::Predictor::Constant)
      • "Secant" -- Use secant vector to continuation curve to compute initial guess (LOCA::Predictor::Secant)
      • "Tangent" -- Use tangent vector to continuation curve to compute initial guess (LOCA::Predictor::Tangent)
      • "Random" -- Use a random perturbation of previous solution to compute initial guess (LOCA::Predictor::Random)
    • "Epsilon" -- [double] (default: 1.0e-3) Relative size of perturbation for random predictor
    • "First Step Predictor" sublist -- used by the secant predictor to determine which predictor to use for the first continuation step -- Replicates "Predictor" sublist structure
    • "Last Step Predictor" sublist -- Predictor to use for last step of arc-length continuation to hit target (max or min) value exactly (usually "Constant" or "Random") -- Replicates "Predictor" sublist structure
  • "Step Size" sublist -- used by LOCA::StepSize::Manager to determine step size constrol strategies
    • "Method" -- [string] (default: "Constant") Step size control strategy to use. Choices are
      • "Constant" -- Use a constant step size in general, reducing the step size after a failure and increasing step size back up to original value after subsequent successes (see LOCA::StepSize::Constant)
      • "Adaptive" -- Use an adaptive step size control strategy that adjusts step size according to the number of Newton iterations per step (see LOCA::StepSize::Adaptive)
      • "Initial Step Size" -- [double] (default: 1.0) Initial parameter step size
      • "Min Step Size" -- [double] (default: 1.0e-12) Minimum parameter step size
      • "Max Step Size" -- [double] (default: 1.0e+12) Maximum parameter step size
      • "Failed Step Reduction Factor" -- [double] (default: 0.5) Factor by which step size is reduced after a failed step
      • "Successful Step Increase Factor" - [double] (default: 1.26) Factor by which step size is increased after a successful step when the step size is smaller than the initial step size (Constant step size method only).
      • "Aggressiveness" -- [double] (default: 0.0) Aggressiveness factor in adaptive step size adjustment
    • "Utilities" sublist -- used by LOCA::Utils to control screen output
      • "Output Information" -- [int] (default: 0xf) Sum of message types (see LOCA::Utils)
      • "Output Processor" -- [int] (default: 0) ID of printing processor
      • "MyPID" -- [int] (default: 0) Processor ID
      • "Output Precision" -- [int] (default: 3) Precision of output
    • "Anasazi" sublist -- used by LOCA::Continuation::AnasaziGroup to compute eigenvalues using the Anasazi package
      • "Block Size" -- [int] (default: 1) block size
      • "Arnoldi Size" -- [int] (default: 30) maximum length of the Arnoldi factorization
      • "NEV" -- [int] (default: 4) number of requested eigenvalues
      • "Tol" -- [double] (default: 1.0e-7) tolerance for the converged eigenvalues
      • "Convergence Check" -- [int] (default: 1) checks convergence every so many steps
      • "Restarts" -- [int] (default: 1) number of restarts allowed
      • "Frequency" -- [int] (default: 1) how often to recalculate eigenvalues
      • "Debug Level" -- [int] (default: 1) Anasazi Debug level
      • "Sorting Order" -- [string" (default: "LM") Sorting order of printed eigenvalues

LOCA::Abstract::Group parameters

Parameters can also be passed to the LOCA::Abstract::Group constructor. Currently, the only parameters used by the group are passed to the LOCA::Bifurcation::TPBord::SingularSolveGroup parent class, which provides techniques for approximating the solution to a (nearly) singular set of linear equations.

• "Singular Solve" sublist -- Used by LOCA::Bifurcation::TPBord::SingularSolveGroup to determine which method to use for computing solutions to nearly singular systems
  • "Method" -- [string] (default: "Default") Method to use. Choices are
    • "Default" -- Use default solution method
    • "Nic" -- Use "Nic" approach (LOCA::SingularJacobianSolve::Nic)
    • "Nic-Day" -- Use "Nic-Day" approach (LOCA::SingularJacobianSolve::NicDay)
    • "Iterative Refinement" -- Use iterative refinement (LOCA::SingularJacobianSolve::ItRef)

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