FastMultipole

A fast, multi-system, multi-kernel, differentiable implementation of the fast multipole method for use with scalar-plus-vector potential N-body problems in pure Julia.

Author: Ryan Anderson

Features:

• solves $N$-body problems governed by the Laplace ($1/r$) kernel, with work planned to support the Helmholtz kernel in the future
• incorporates seamlessly into existing Julia code without modifications (just the addition of a few interface functions)
• offers convenience functions for determining the expansion coefficients for source, dipole, and vortex points, filaments, and panels (this list is growing!)
• provides velocity and velocity gradient (or their equivalent for non-fluids problems) obtained using analytic expressions (no finite difference)
• uses $O(p^3)$ translation operators (where $p$ is the expansion order)
• automated CPU-parallelization of expansions and direct interactions
• supports GPU-parallelization of direct interactions with user-defined kernels
• ForwardDiff and ReverseDiff compatible

Installation:

pkg> add https://github.com/byuflowlab/FastMultipole.git

Documentation:

• learn basic useage in the Quick Start tutorial
• see how to implement FastMultipole in your code in the Gravitational Example
• explore more details in the Vortex Filament Example
• learn about the Tuning Parameters
• run FMM simultaneously on multiple systems in Multiple Systems section
• fine-tune performance in the Automated Tuning
• see the full API