Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy

TL;DR

This paper introduces an extrapolation method to enhance the accuracy of discrete dipole approximation calculations, demonstrating significant error reduction and reliable error estimates through extensive simulations.

Contribution

It presents a novel extrapolation technique for DDA accuracy improvement, validated by empirical simulations and error estimation methods.

Findings

Error decreased by two orders of magnitude.

Extrapolation quality improves with finer discretization.

Reliable estimates of extrapolation error were developed.

Abstract

We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.