ARBTools: A Tricubic Spline Interpolator for Three-Dimensional Scalar or Vector Fields

Paul Walker,Ulrich Krohn,David Carty

doi:10.5334/jors.258

Abstract

ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid. ARBTools was developed for simulations of magnetic molecular traps, in which the magnitude, gradient and vector components of a magnetic field are required. Numerical integrators for solving particle trajectories are included, but the core interpolator can be used for any scalar or vector field. The only additional system requirements are NumPy.

Highlights

ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid
The main difference in ARBTools, is the direct availability of the derivatives of an interpolated scalar field, knowledge of these derivatives being a prerequisite for calculating the force arising due to a potential gradient. (Unlike other interpolation methods in which the gradients are recovered via finite-differences, in the tricubic scheme the approximating polynomial function can be analytically differentiated)
The software can directly work with a vector field; for example, in the context of molecular and atomic traps this is needed when calculating the probabilities of non-adiabatic spin transitions [6], or simulating laser-cooling interactions [7]

Summary

Introduction

ARBTools: A Tricubic Spline Interpolator for Three-Dimensional Scalar or Vector Fields ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid. ARBTools was developed for simulations of magnetic molecular traps, in which the magnitude, gradient and vector components of a magnetic field are required.

Results

Conclusion