The PSCF paramater file format allows the user to choose from among several "compressor" algorithms.

Overview

A PSCF "compressor" is an iterative algorithm that adjusts the pressure-like field \( W_{+} \) field so as to satisfy a partial saddle-point condition. A compressor algorithm must applied at least once per BD or MC step, after each change in the field or fields that couple to composition fluctuations. The parameter file for a BD or MC simulation must contain a block that specifies a choice of compressor algorithm. PSCF users may choose a compressor algorithm independently of their choice for a BD step or MC move algorithms: Any compressor algorithm may be used in the context of any BD or MC step algorithm.

Solution of the saddle-point condition normally requires multiple iterations of \( W_{+} \). Each iteration normally involves a proposed adjustment of \( W_{+} \) followed by solution of the modified diffusion equation (MDE) in the resulting state and evaluation of the remaining error in the partial saddle-point (incompressiblity) condition. Because repeated solution of the MDE is the most expensive operation in a FTS, and the compressor algorithm requires multiple solutions of the MDE for each BD or MC step, almost all of the computational time of a PS-FTS calculation is actually spent within the iterative loop of a compressor algorithm. The design of a BD step or MC move algorithm determines the number of stochastic steps (BD steps or attempted MC moves) required to obtain specified levels of systematic and statistical error, but the computational cost per step is primarily determined by the average number iterations required by the compressor algorithm.

Algorithms

The available compressor algorithms are listed below. Users may click on the link associated with each algorithm label to access more a detailed description of each algorithm, and of the format of the associated parameter file block.

LrAmCompressor: A linear-response Anderson mixing algorithm
LrCompressor: A simple linear-response algorithm
AmCompressor: An Anderson-mixing algorithm

The LrAmCompressor is the default choice, and is recommended for general use.

All three of the compressor algorithms listed above are described and compared in the following reference:

"Improved algorithm for identifying partial saddle-points in polymer field theoretic simulations", K. Chen and D.C. Morse, J. Chem. Phys. 162 , 243901 (2025). ,

The AmCompressor algorithm is similar to the Anderson mixing algorithm used in most previously published PS-FTS calculations. This algorithm uses information from previous iterations to guide the choice of a new field configuration during each iteration after the first.

The LrAmCompressor and LrCompressor algorithms both use a quasi-Newton approximation that uses the analytically calculated linear response of a hypothetical homogeneous state as an approximation to the actual linear response of the monomer concentration in an inhomgeneous state to small changes in the pressure-like field. The Lr algorithm is a straightforward quasi-Newton algorithm based on this approximation. The LrAm uses this quasi-Newton step as one stage of a modified Anderson mixing algorithm that also uses information from previous steps.

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