---
title: "A Short Course on Fast Multipole Methods"
authors:
  - "Rick Beatson"
  - "Leslie Greengard"
year: 1997
venue: "Wavelets, Multilevel Methods and Elliptic PDEs (Oxford)"
arxiv: null
doi: null
source: "https://math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf"
topics:
  - "fmm"
  - "short-course"
  - "beatson-greengard"
  - "review"
seed_rank: 1181
seed_batch: "fmm-2026-08-24"
reviewed: "2026-08-24"
pool: "engines"
relevance_score: 10
lineage: fast-multipole
cites:
  - title: "A Fast Algorithm for Particle Simulations"
    url: "https://doi.org/10.1016/0021-9991(87)90140-9"
    year: 1987
    arxiv: null
    doi: "10.1016/0021-9991(87)90140-9"
  - title: "A Hierarchical O(N log N) Force-Calculation Algorithm"
    url: "https://doi.org/10.1038/324446a0"
    year: 1986
    arxiv: null
    doi: "10.1038/324446a0"
  - title: "The Fast Gauss Transform"
    url: "https://doi.org/10.1137/0912004"
    year: 1991
    arxiv: null
    doi: "10.1137/0912004"
  - title: "Computer Simulation Using Particles"
    url: "https://doi.org/10.1201/9781439822050"
    year: 1988
    arxiv: null
    doi: "10.1201/9781439822050"
see:
  - "1166-a-fast-algorithm-for-particle-simulations"
  - "1165-a-hierarchical-o-n-log-n-force-calculation-algorithm"
  - "1164-an-efficient-program-for-many-body-simulation"
  - "1179-the-fast-gauss-transform"
---

# A Short Course on Fast Multipole Methods

## One-sentence takeaway

The canonical FMM short course: analytic foundations, particle and integral-equation views, and a reading list that already names Appel, Barnes–Hut, Hockney–Eastwood, and Fast Gauss.

## Problem

By 1997 the primary papers were spread across JCP / SIAM / Acta Numerica. A lecture-notes chapter was the document people actually learned from.

## Design

Lecture notes (37 pp.) in Ainsworth et al., Wavelets, Multilevel Methods and Elliptic PDEs, Oxford 1997. Degenerate-kernel viewpoint, 2D expansions, translations, complexity, and pointers to Greengard–Rokhlin, Greengard 1988, Greengard–Strain, Appel, Barnes–Hut, Hockney–Eastwood. No new algorithm.

## Evidence

Author PDF at Courant: https://math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf (also cims.nyu.edu/~greengar/shortcourse_fmm.pdf). This is the course the user listed as must-mint.

## Limitations

Pre-kiFMM, pre-bbFMM, pre-MLFMA-as-product. Laplace-first. Not a software paper.

## Implications for Broadside

The onboarding document. Pair with Keyframe Codes for intuition and this for the theorems. Hockney–Eastwood is cited here — that is enough; do not mint the book.

## Bottom line

Mint Beatson–Greengard 1997 as the canonical short course.

## Links

- Author PDF: https://math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf