A trilinear method for finding null points in a 3D vector space

TL;DR

The paper introduces a trilinear method for efficiently locating null points in 3D vector fields, ensuring accuracy and consistency with fieldline tracing, and compares it with existing Poincare index-based methods.

Contribution

A novel trilinear technique for finding null points in 3D vector fields that improves accuracy and efficiency over previous methods.

Findings

The trilinear method accurately finds null points consistent with fieldline tracing.

It offers improved efficiency over traditional null point detection techniques.

Comparison shows the method's accuracy and limitations relative to Poincare index-based approaches.

Abstract

Null points are important locations in vector fields, such as a magnetic field. A new technique (a trilinear method for finding null points) is presented for finding null points over a large grid of points, such as those derived from a numerical experiment. The method was designed so that the null points found would agree with any fieldlines traced using the commonly used trilinear interpolation. It is split into three parts: reduction, analysis and positioning, which, when combined, provide an efficient means of locating null points to a user-defined sub-grid accuracy. We compare the results of the trilinear method with that of a method based on the Poincare index, and discuss the accuracy and limitations of both methods.