---
title: "The Rapid Evaluation of Potential Fields in Particle Systems"
authors:
  - "Leslie F. Greengard"
year: 1988
venue: "MIT Press (ACM Distinguished Dissertation)"
arxiv: null
doi: "10.7551/mitpress/5750.001.0001"
source: "https://doi.org/10.7551/mitpress/5750.001.0001"
topics:
  - "fmm"
  - "greengard"
  - "potential-fields"
  - "dissertation"
seed_rank: 1167
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: "Rapid Solution of Integral Equations of Classical Potential Theory"
    url: "https://doi.org/10.1016/0021-9991(85)90002-6"
    year: 1985
    arxiv: null
    doi: "10.1016/0021-9991(85)90002-6"
see:
  - "1166-a-fast-algorithm-for-particle-simulations"
  - "1163-rapid-solution-of-integral-equations-of-classical-potential-the"
  - "1169-a-new-version-of-the-fast-multipole-method-for-the-laplace-equa"
---

# The Rapid Evaluation of Potential Fields in Particle Systems

## One-sentence takeaway

Greengard's Yale thesis, published as the 1988 MIT Press ACM Distinguished Dissertation book: the complete 2D and 3D potential-field FMM with proofs, not just the 1987 JCP letter.

## Problem

The 1987 JCP paper is 24 pages and 2D-first. The dissertation is the place the 3D Laplace expansions, error bounds, and the rapid evaluation of potential fields slogan actually live.

## Design

Chapters develop 2D complex-log FMM, then 3D spherical-harmonic multipoles, translation operators, and complexity. Same P2M/M2M/M2L/L2L/L2P skeleton. The book is the thesis; do not mint a second 1987 Yale dissertation card.

## Evidence

MIT Press 1988, DOI 10.7551/mitpress/5750.001.0001. ACM Distinguished Dissertation Award. Every later FMM paper that says Greengard 1988 means this book.

## Limitations

Still mostly uniform trees and Laplace. Adaptive 2D is Carrier et al. 1988; practical 3D adaptive is Cheng–Greengard–Rokhlin 1999. Not a software artifact.

## Implications for Broadside

Cite this when you need the 3D Laplace expansions before 1997/1999. For an engine, the 1987 paper + Cheng 1999 are the implementable pair; the book is the proof spine.

## Bottom line

Mint the 1988 book as the thesis/book, one card. Do not remint the unpublished dissertation separately.

## Links

- DOI: [10.7551/mitpress/5750.001.0001](https://doi.org/10.7551/mitpress/5750.001.0001)
- MIT Press: https://mitpress.mit.edu/9780262570749/