The Fast Multipole Method

C++ / Mathematica implementation of the The Fast Multipole Method (FMM) for the evaluation of potentials and force fields in gravitation and electrostatics problems, parallelized via OpenMP. Implementation details are documented in the file FMM_implementation.pdf contained in this repository. A more thorough presentation of the mathematical and algorithmtic aspects of the method, as well as an experimental evaluation of this implementation can be found at the Mathnotes repository

Sample (integrated via Mathematica's symplectic partitioned Runge Kutta integrator):

A plot of error distributions included for its aesthetic value

Overview of the content of various source files:

Tree Classes

file	description
abstract_orthtree.hpp	Abstract base class for quad/octrees
adaptive_orthtree.hpp	Abstract base class for adaptive quad/octrees
balanced_orthtree.hpp	Abstract base class for balanced quad/octrees
abstract_fmm_tree.hpp	Abstract base class for the FMM tree data structure
adaptive_fmm_tree.hpp	Implementation of the adaptive FMM
balanced_fmm_tree.hpp	Implementation of the balanced FMM

Local and Multipole Expansions

file	description
series_expansion.hpp	Abstract base class for series expansions
multipole_expansion.hpp	Implementation of the multipole expansion
local_expansion.hpp	Implementation of the local expansion
vector.hpp	Vector and pointsource classes used in the FMM
fields.hpp	Potential and force field functions, direct algorithm
fmm_tables.hpp	Classes that function as lookup tables
fmm_general.hpp	Frequently used utility functions
debugging.hpp	Code that aided in debugging and IO operations

Mathematica Integration, Examples, Testing & Debugging

folder	description
examples	Folder containing some minimal examples
test	Code used for verification and testing
misc	Miscelleanous items
mathematica	Code for the Mathematica interface
logs	Target directory for logs