The PredCorrBdStep classes used by both the pscf_pc and pscf_pg programs implements a predictor corrector Brownian dynamics step algorithm.

Two closely analogous classes named Pscf::Rpc::PredCorrBdStep and Pscf::Rpg::PredCorrBdStep are used to implement this algorithm for the pscf_pc program (using a standard CPU) and for the pscf_pg program (using GPU acceleration), respectively These classes implement the same algorithm and use the same parameter file format, as documented below for both.

Step Algorithm

A general discussion of conventions used in PSCF for BD step algorithms is given here. In what follows, we refer to the fields or fields that are stochastically sampled as \( W_{-} \), or as exchange fields, and the field or fields that are chosen to satisfy a partial saddle point condition as \( W_{+} \). All exchange fields must be associated with negative eigenvalues of the projecte chi matrix. Each step of the predictor corrector algorithm involves the following stages:

Generate and save random displacements of \( W_{-} \) at each grid point. These random displacements will be used for both the predictor and corrector steps.
Use an explicit Euler step algorithm to generate small changes in \( W_{-} \), using forces (i.e., functional derivatives of the Hamiltonian) that were computed in the initial state. This is the "predictor" step.
Use the compressor algorithm chosen by the user to adjust \( W_{+} \) so as to satisfy the partial saddle-point condition at the predicted state.
Compute forces in the predicted state (i.e., i,e., compute functional derivatives of the Hamiltonian with respect to components of \( W_{-} \)).
Apply an explict BD step to the initial configuration with forces that are the average of those computed at the initial state and thosed computed in the predicted state, using the same random field displacements as those used in the predictor step. This is the "corrector" step.
Use the compressor to adjust \( W_{+} \) so as to again satisfy the partial saddle-point condition in the final state.

Parameter File

The only parameter need by this algorithm is a required parameter named "mobility", which gives the value of parameter denoted by \( \gamma \) in the our description of an explicit Euler algorithm.
A typical example of the contents of the block is shown below:

PredCorrBdStep{
  mobility     1e-3
}

The format of this block is simply

PredCorrBdStep{
   mobility      float
}

The mobility parameter is requred.