Finite volume method for self-consistent field theory of polymers: Material conservation and application

Area of Science:

• Polymer physics
• Computational materials science
• Numerical analysis

Background:

• Self-consistent-field theory (SCFT) is crucial for simulating polymeric systems.
• Accurate numerical algorithms are essential for reliable SCFT calculations.
• Material conservation is a key metric for evaluating numerical method performance.

Purpose of the Study:

• To develop and apply an algebraic method for assessing material conservation in SCFT algorithms.
• To compare the material conservation properties of different numerical methods.
• To identify optimal numerical approaches for real-space SCFT simulations.

Main Methods:

• Development of an algebraic method using matrix and bra-ket notation.
• Tracing the Hermiticity of volume and evolution matrices for material conservation tests.
• Application of the finite-volume method (FVM) with Crank-Nicolson in orthogonal coordinates.
• Incorporation of fractional cells within the FVM for irregular geometries.

Main Results:

• The pseudospectral method on a Cartesian grid demonstrates perfect material conservation.
• The FVM combined with the Crank-Nicolson method is suitable for orthogonal coordinate systems.
• Alternating direction implicit methods with FVM show minimal mass errors in SCFT.
• FVM with fractional cells enables accurate SCFT for complex geometries.

Conclusions:

• The developed algebraic method provides a robust way to evaluate material conservation in SCFT.
• The FVM is a highly accurate and versatile method for real-space SCFT, particularly for systems with complex geometries.
• Numerical choices significantly impact the accuracy and reliability of polymer simulations.