Technical report | Magnetic signatures of spherical bodies in Earth’s magnetic field — a comparison of analytical and finite element analysis solutions

Abstract

Calculating magnetic signatures using analytical techniques becomes infeasible for complex geometries such as submarines, hence numerical techniques, such as finite element analysis, must be used instead. In this report we compare analytical and finite element solutions utilising COMSOL for calculating the magnetic induction of a permeable spherical shell with an internal current band in uniform magnetic induction. The analytical and finite element analysis solutions were found to be approximately equal, this verifies that modelling of magnetic signatures of submarines using COMSOL will generate correct data.

Executive Summary

In this report we compare analytical and finite element solutions to validate the use of COMSOL software for calculating the magnetic signature of permeable materials with current bands in background magnetic fields.

The analytical techniques used for determining the magnetic signature of a simple shape, such as a spherical shell, cannot be used to calculate the magnetic signature of a submarine due to its complex structure. Instead, the magnetic signature of a submarine must be numerically calculated using finite element analysis. However, finite element analysis introduces both discretisation and numerical errors. This report quantifies these errors. The magnetic signature is calculated for the following domains:

• a permeable spherical shell in uniform magnetic induction B₀
• a permeable spherical shell with an internal current band
• a permeable spherical shell with an internal current band in uniform magnetic induction B₀.

The finite element solutions were found to closely approximate the analytical solutions. These solutions may be used to study the induced magnetic signatures of ferromagnetic bodies and coils found on modern submarines. COMSOL may be used to calculate the magnetic induction of permeable materials with internal current bands in background magnetic fields.