Sandia National Laboratories Tramonto

LOCA Continuation Parameters

These parameters define how LOCA continuation capabiliites will be used in a Tramonto calcualtion. Note that the LOCA documentation provides more details on the library, and its integration with the NOX nolinear solvers. While NOX is not the default nonlinear solver for Tramonto as of the v2.1 release, it may be accessed if Tramonto is configured using the option --with-nox-loca.

  • Continuation Method(int): Several types of continuation may be performed using LOCA. The options available to Tramonto are:
    • -1: None.
    • 0: 0th order continuation using a constant step (non-adaptive).
    • 1: 1st order continuation.
    • 2: 2nd order, i.e. arc-length, continuation.
    • 3: Track spinodal (turning) points. If restarting, this requires two density files as input (dft_dens.dat and dft_dens2.dat).
    • 4: Track binodal points, where two different density solutions have the same free energy at the same state point. Use this to following phase transitions. If restarting, this option requires two density files (dft_dens.dat and dft_dens2.dat) as input. These files should contain different density profiles of the two different morphologies at or near a state point where the free energies of the two branches cross.
  • Continuation parameter(int): One of the continuous parameters of the system that will be used for continuation calculations. Various options are provided in dft_input.dat, and more can be added by augmenting the case list in dft_continuation.c.
  • Scale_fac(real): Some of the continuation variables can be changed by a multiplicative scaling factor given by this value, as opposed to increasing or decreasing the parameter in an additive manner. In these cases, Scale_fac itself is the continuation parameter. These cases are identified by the word SCALE in the name.
  • Step_size(real): Initial value for the change in the parameter with continuation. This step size will be adjusted by the algorithm as continuation proceeds unless 0th order continuation is used. Large values will sometimes fail to converge, while small values can lead to very small step sizes along a continuation curve.
  • N_steps(int): The number of continuation steps to perform.
  • Agressiveness(real): A measure of how fast the algorithm will step along the continuation curve.
  • Second Continuation Parameter(int): For binodal calculations (method 4), this is the second parameter that is varied in order to keep the two systems at the same free energy. It can be any of the implemented continuation parameters in the code. For example, one might have a phase transition at a given chemical potential (Rho_b) and temperature, and the goal is to track the transition as a function of temperature. Then the temperature should be the first continuation variable, that will be increased or decreased as specified by the Step_size parameter. The chemical potential variable will be the second parameter, and it will be adjusted by the code as necessary in order to maintain the system at the phase transition.