Concise, efficient three-dimensional fast multipole method for micromagnetics

This paper presents derivation of the three-dimensional (3-D) fast multipole method for use in calculating magnetostatic fields. Many other derivations use complex, inefficient, and awkward function normalizations. In this derivation, tensor functions and an operator are defined that greatly simplify the theory and implementation of the algorithm. This paper provides proof of O(N) scaling, implementation, and parallelization tips, performance results, and an error analysis.