Note on transformation to general curvilinear coordinates for Maxwell's curl equations (Is the magnetic field vector axial?)

TL;DR

This paper revisits the axial nature of magnetic field vectors in Maxwell's equations, analyzing the compatibility of complex-coordinate methods with their pseudo-vector properties in computational electrodynamics.

Contribution

It critically examines the assumption that H and B are axial vectors, highlighting conflicts with numerical methods used in computational electromagnetics.

Findings

Complex-coordinate methods challenge the axial vector assumption for H and B.

The paper questions the conventional classification of magnetic field vectors in numerical contexts.

Results suggest a need to reconsider vector properties in computational electromagnetic models.

Abstract

Arguments for H and B to be considered `axial', or pseudo vectors, are revisited. As a point against, we examine the complex-coordinate method for numerical grid truncation and mode loss analysis proved very successful in computational electrodynamics. This method is not compatible with convention that H and B are axial.