Accelerating the calculation of dipolar interactions in particle based simulations with open boundary conditions by means of the P2NFFT method

TL;DR

This paper introduces a fast P2NFFT-based method for calculating dipolar interactions in particle simulations with open boundary conditions, enabling shape-dependent magnetic gel studies without the limitations of periodic boundaries.

Contribution

The paper develops and implements a dipolar P2NFFT method for open boundary conditions, improving computational efficiency and flexibility in simulating magnetic soft matter.

Findings

Achieves N log N scaling for dipolar interactions

Successfully integrated into ESPResSo simulation software

Demonstrates applicability to magnetic gel models

Abstract

Magnetic gels are soft elastic materials consisting of magnetic particles embedded in a polymer network. Their shape and elasticity can be controlled by an external magnetic field, which gives rise to both, engineering and biomedical applications. Computer simulations are a commonly used tool to study these materials. A well-known bottleneck of these simulations is the demanding calculation of dipolar interactions. Under periodic boundary conditions established algorithms are available for doing this, however, at the expense of restricting the way in which the gels can deform in an external magnetic field. Moreover, the magnetic properties depend on the sample shape, ruling out periodic boundary conditions entirely for some research questions. In this article we will employ the recently developed dipolar variant of the P$^2$NFFT method that is able to calculate dipolar interactions under open boundary conditions with an $N \log N$ scaling in the number of particles, rather than the expensive $N^2$ scaling of a direct summation of pair forces. The dipolar P$^2$NFFT method has been implemented within the ScaFaCoS library. The molecular dynamics software ESPResSo has been extended to make use of the library. After a short summary of the method, we will discuss its value for studying magnetic soft matter systems. A particular focus is put on developing a tuning strategy to reach the best performance of the method at a predefined accuracy, and lastly applying the method to a magnetic gel model. Here, adapting to the gel's change in shape during the course of a simulation is of particular interest.