PVFMM

PVFMM (Parallel Volume Fast Multipole Method) is a library for solving certain types of elliptic partial differential equations: it supports Stokes, Poisson, Biot–Savart, and Helmholtz problems on the unit cube, with free-space or periodic boundary conditions. The method is based on a volume-potential integral-equation formulation accelerated by the kernel-independent fast multipole method (KIFMM), and the same machinery provides fast \(O(N)\) particle N-body sums.

PVFMM is written in C++17 (MPI + OpenMP, optional CUDA) with interfaces for C, Fortran, Python, and Julia. It scales from laptops to distributed-memory supercomputers.

• Source code: github.com/dmalhotra/pvfmm

• Doxygen class reference: pvfmm.org

• License: LGPLv3 (see COPYING in the source distribution)

Getting started

• Introduction
• Installation
• Getting started

Tutorials

• Particle FMM in C++
• Volume FMM in C++
• Using the C and Fortran interfaces
• Using the Python and Julia bindings
• Test drivers and advanced usage

Concepts

• Kernel functions
• Boundary conditions
• Precomputed operator files
• Performance and tuning

API reference

• API reference
  • C++ interface
  • C interface
  • Fortran interface
  • Python interface
  • Julia interface

Citing PVFMM

• D. Malhotra and G. Biros, PVFMM: A parallel kernel independent FMM for particle and volume potentials, Communications in Computational Physics, 18 (2015), pp. 808–830.

• D. Malhotra and G. Biros, Algorithm 967: A distributed-memory fast multipole method for volume potentials, ACM Transactions on Mathematical Software, 43 (2016).

Acknowledgments

This software has been developed as part of work supported by the US National Institutes of Health (10042242), the US Department of Energy (DE-SC0010518, DE-SC0009286), the US National Science Foundation (CCF-1337393), and the US Air Force Office of Scientific Research (FA9550-12-10484). The authors also thank ORNL/OLCF and TACC for providing access to computing resources used in the development, testing, and benchmarking of this software.