Highly Parallel Demagnetization Field Calculation Using the Fast Multipole Method on Tetrahedral Meshes with Continuous Sources

TL;DR

This paper introduces an efficient implementation of the Fast Multipole Method for calculating the long-range magnetic field in micromagnetic simulations, significantly reducing computational time and memory usage for tetrahedral meshes with continuous sources.

Contribution

It presents a novel FMM-based approach tailored for linearly magnetized tetrahedral sources, addressing vectorial and continuous field aspects in micromagnetics.

Findings

Calculations scale linearly in time and memory.

The method effectively handles the vectorial and continuous nature of magnetic fields.

Significant reduction in computational bottleneck for micromagnetic simulations.

Abstract

The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. We assume linearly magnetized tetrahedral sources, treat the near field directly and use analytical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.